The pulsar map used by Pioneer and Voyager is a diagram of the position of the Sun relative to 14 galactic pulsars. It encodes their positions, distances, and pulse periods, which in theory makes it a decent tool for identifying where the Solar System is (although there are some issues with it). To make a similar map for an arbitrary point in the galaxy, you'd need to find a selection of pulsars near that location, and encode the same amount of information. To do that, you need a database of pulsars.

The Australian Telescope National Facility (ATNF) has a really excellent pulsar catalogue that I like to use, with over 2600 entries. You can query it fairly easily using a number of parameters, including distance, dispersion measure, coordinates, pulse period, etc. This makes it a handy tool to match observations with already known pulsars, but it should also be well-suited to your needs. You can get a list of pulsar names, coordinates, periods and distances by checking the JName, RaJ, DecJ, P0 and Dist parameters in the search interface, then click the button to get a table of the results. You should then be able to compute the positions of all of the pulsars in the catalogue in your coordinate system of choice, then re-compute their positions with respect to a chosen location in space.

The output of the first hundred rows looks like this:

---------------------------------------------------------------------------------------------------------------------------------------------------
#     NAME                     RAJ                                DECJ                               P0                                     DIST
                               (hms)                              (dms)                              (s)                                    (kpc)
---------------------------------------------------------------------------------------------------------------------------------------------------
1     J0002+6216    cwp+17     00:02:58.17          2  cwp+17     +62:16:09.4          1  cwp+17     0.1153635682680         14  cwp+17     *
2     J0006+1834    cnt96      00:06:04.8           2  cn95       +18:34:59            4  cn95       0.69374767047           14  cn95       0.86
3     J0007+7303    aaa+09c    00:07:01.7           2  awd+12     +73:03:07.4          8  awd+12     0.3158731909             3  awd+12     1.40
4     J0011+08      dsm+16     00:11:34           114  dsm+16     +08:10               8  dsm+16     2.55287                  0  dsm+16     5.40
5     B0011+47      dth78      00:14:17.75          4  hlk+04     +47:46:33.4          3  hlk+04     1.240699038946          11  hlk+04     1.78

6     J0023+0923    hrm+11     00:23:16.878141      9  abb+18     +09:23:23.8652       3  abb+18     0.003050203104480002     7  abb+18     1.11
7     J0024-7201Z              00:24:06.041         2  frk+17     -72:05:01.480        6  frk+17     0.004554447383906        3  frk+17     2.56
8     J0024-7204aa  phl+16     00:24:05.67          0  mam+06     -72:04:52.62         0  mam+06     0.00184                  0  phl+16     2.69
9     J0024-7204ab  phl+16     00:24:08.1615        5  frk+17     -72:04:47.602        2  frk+17     0.0037046394947985       6  frk+17     2.54
10    B0021-72C     mld+90     00:23:50.3546        1  frk+17     -72:04:31.5048       4  frk+17     0.00575677999551635     14  frk+17     4.69

11    B0021-72D     mlr+91     00:24:13.88092       6  frk+17     -72:04:43.8524       2  frk+17     0.00535757328486573      9  frk+17     4.69
12    B0021-72E     mlr+91     00:24:11.10528       5  frk+17     -72:05:20.1492       2  frk+17     0.00353632915276244      4  frk+17     4.69
13    B0021-72F     mlr+91     00:24:03.85547      10  frk+17     -72:04:42.8183       2  frk+17     0.00262357935251262      4  frk+17     4.69
14    B0021-72G     rlm+95     00:24:07.9603        1  frk+17     -72:04:39.7030       5  frk+17     0.00404037914356515     14  frk+17     4.69
15    B0021-72H     mlr+91     00:24:06.7032        2  frk+17     -72:04:06.8067       6  frk+17     0.00321034070935032     11  frk+17     4.69

16    B0021-72I     mlr+91     00:24:07.9347        2  frk+17     -72:04:39.6815       7  frk+17     0.00348499206166289     13  frk+17     4.69
17    B0021-72J     mlr+91     00:23:59.4077        1  frk+17     -72:03:58.7908       5  frk+17     0.00210063354535246      5  frk+17     4.69
18    B0021-72L     rlm+95     00:24:03.7721        3  frk+17     -72:04:56.923        2  frk+17     0.0043461679994616       4  frk+17     4.69
19    B0021-72M     mlr+91     00:23:54.4899        3  frk+17     -72:05:30.756        2  frk+17     0.0036766432176002       3  frk+17     4.69
20    B0021-72N     rlm+95     00:24:09.1880        2  frk+17     -72:04:28.8907       7  frk+17     0.00305395434626085     10  frk+17     4.69

21    J0024-7204O   clf+00     00:24:04.65254       6  frk+17     -72:04:53.7670       2  frk+17     0.00264334329724357      5  frk+17     4.69
22    J0024-7204P   clf+00     00:24:20            29  rft+16     -72:04:10           62  rft+16     0.0036430207             3  rft+16     4.69
23    J0024-7204Q   clf+00     00:24:16.4909        1  frk+17     -72:04:25.1644       6  frk+17     0.00403318118457258     15  frk+17     4.69
24    J0024-7204R   clf+00     00:24:07.5851        2  frk+17     -72:04:50.3954       5  frk+17     0.00348046270749329     13  frk+17     4.69
25    J0024-7204S   clf+00     00:24:03.9794        1  frk+17     -72:04:42.3530       4  frk+17     0.00283040595787912      8  frk+17     4.69

26    J0024-7204T   clf+00     00:24:08.5491        5  frk+17     -72:04:38.932        3  frk+17     0.0075884798073671      12  frk+17     4.69
27    J0024-7204U   clf+00     00:24:09.8366        1  frk+17     -72:03:59.6882       4  frk+17     0.00434282669639233     12  frk+17     4.69
28    J0024-7204V   clf+00     00:24:05.67          0  mam+06     -72:04:52.62         0  mam+06     0.00481016762            7  rft+16     4.69
29    J0024-7204W   clf+00     00:24:06.058         1  rft+16     -72:04:49.088        2  rft+16     0.0023523445319370       3  rft+16     4.69
30    J0024-7204X   fre08      00:24:22.38565       9  rft+16     -72:01:17.4414       7  rft+16     0.00477152291069356      5  rft+16     4.69

31    J0024-7204Y   frk+17     00:24:01.4026        1  frk+17     -72:04:41.8363       4  frk+17     0.00219665714352123      5  frk+17     4.69
32    J0024-7204Z   fre08      00:24:05.67          0  mam+06     -72:04:52.62         0  mam+06     0.004554                 0  fre08      4.69
33    J0026+6320    jml+09     00:26:50.561         8  jml+09     +63:20:00.87         5  jml+09     0.318357731235           1  jml+09     6.42
34    J0030+0451    lzb+00     00:30:27.42781       4  abb+18     +04:51:39.7113      14  abb+18     0.0048654532112551       3  abb+18     0.32
35    J0033+57      hrk+08     00:33                0  hrk+08     +57                  0  hrk+08     0.315                    0  hrk+08     2.25

36    J0033+61      hrk+08     00:33                0  hrk+08     +61                  0  hrk+08     0.912                    0  hrk+08     1.64
37    J0034-0534    bhl+94     00:34:21.83422       8  dcl+16     -05:34:36.722        3  dcl+16     0.0018771818845850       2  aaa+10b    1.35
38    B0031-07      lvw69a     00:34:08.8703        1  cbv+09     -07:21:53.409        2  cbv+09     0.9429509945598         17  hlk+04     1.03
39    J0034+69      slr+14     00:34                3  slr+14     +69:43              18  slr+14     0.03680412              16  slr+14     2.28
40    B0037+56      dtws85     00:40:32.362         6  hlk+04     +57:16:24.91         6  hlk+04     1.1182253452412         13  hlk+04     2.42

41    J0045-7042    mfl+06     00:45:25.69         17  mfl+06     -70:42:07.1         13  mfl+06     0.63233580002            6  mfl+06     59.70
42    J0045-7319    mmh+91     00:45:35.16          7  kbm+96     -73:19:03.0          2  kbm+96     0.92627590497            3  kbm+96     59.70
43    B0045+33      dtws85     00:48:33.98          3  hlk+04     +34:12:08.0          4  hlk+04     1.217094296058           8  hlk+04     4.50
44    J0050+03      dsm+16     00:50:31           113  dsm+16     +03:48               8  dsm+16     1.36656                  0  dsm+16     25.00
45    J0051+0423    snt97      00:51:30.1           2  snt97      +04:22:49            6  snt97      0.35473179890            1  snt97      1.25

46    J0053+69      slr+14     00:53                3  slr+14     +69:39              18  slr+14     0.832938                28  slr+14     2.75
47    J0054+66      hrk+08     00:54                0  hrk+08     +66                  0  hrk+08     1.39                     0  hrk+08     0.90
48    J0054+69      kkl+15     00:54:28            25  kkl+15     +69:26               2  kkl+15     *                        0  *          2.35
49    B0052+51      dtws85     00:55:45.378        10  hlk+04     +51:17:24.97        11  hlk+04     2.115171148865           4  hlk+04     1.94
50    B0053+47      dtws85     00:56:25.51          2  hlk+04     +47:56:10.5          3  hlk+04     0.472036662076           7  hlk+04     1.12

51    J0057-7201    ckm+01     00:57:44.0           4  ckm+01     -72:01:19            2  ckm+01     0.7380624426             2  ckm+01     3.48
52    J0058+6125    hrk+08     00:58                0  hrk+08     +61:25               0  hrk+08     0.637                    0  hrk+08     2.61
53    J0059+50      slr+14     00:59                2  slr+14     +50:02              18  slr+14     0.996009                61  slr+14     2.61
54    J0100-7211    lfmp02     01:00:43.03         11  mgr+05     -72:11:33.6          5  mgr+05     8.020392                 9  mgr+05     59.70
55    J0101-6422    kcj+12     01:01:11.1163        2  kcj+12     -64:22:30.171        2  kcj+12     0.0025731519721683       2  kcj+12     1.00

56    J0102+4839    hrm+11     01:03                0  hrm+11     +48:00               0  *          0.00296                  0  hrm+11     2.38
57    B0059+65      dbtb82     01:02:32.958        16  hlk+04     +65:37:13.40        11  hlk+04     1.679164229064          12  hlk+04     1.98
58    J0103+54      kkl+15     01:03:37            20  kkl+15     +54:02               5  kkl+15     0.354304                 6  kkl+15     2.01
59    J0106+4855    pga+12     01:06:25.06          1  pga+12     +48:55:51.8          2  pga+12     0.0831573050050          6  pga+12     3.06
60    J0108-1431    tnj+94     01:08:08.347016     88  dtbr09     -14:31:50.1871      11  dtbr09     0.807564614019          20  hlk+04     0.21

61    B0105+65      dls72      01:08:22.64          5  hlk+04     +66:08:34.0          3  hlk+04     1.2836598429             5  hlk+04     1.46
62    B0105+68      dtws85     01:08:29.50          2  hlk+04     +69:05:52.63        11  hlk+04     1.071118109859           5  hlk+04     1.98
63    J0111-7131    mfl+06     01:11:28.77          9  mfl+06     -71:31:46.8          6  mfl+06     0.68854151164            5  mfl+06     59.70
64    J0112+66      slr+14     01:12                3  slr+14     +66:22              18  slr+14     4.30124                 70  slr+14     2.42
65    J0113-7220    ckm+01     01:13:11.09          3  ckm+01     -72:20:32.20        15  ckm+01     0.32588301613            1  ckm+01     59.70

66    B0114+58      stwd85     01:17:38.661         3  hlk+04     +59:14:38.39         3  hlk+04     0.1014390664824         20  hlk+04     1.77
67    J0125+62      slr+14     01:26                3  slr+14     +62:35              18  slr+14     1.708233                98  slr+14     2.40
68    J0131-7310    mfl+06     01:31:28.51          3  mfl+06     -73:10:09.34        13  mfl+06     0.348124045581           7  mfl+06     59.70
69    J0133-6957    lml+98     01:33:32.46          1  dsb+98     -69:57:29.68         3  dsb+98     0.463473741703           3  dsb+98     2.44
70    J0134-2937    mld+96     01:34:18.6824        3  lwy+16     -29:37:17.042        7  lwy+16     0.136961610513651       14  lwy+16     25.00

71    J0136+63      slr+14     01:36                3  slr+14     +63:42              18  slr+14     0.717895                27  slr+14     9.12
72    J0137+1654    lxf+05     01:37:23.88          1  lxf+05     +16:54:42.1          4  lxf+05     0.4147630265082          5  lxf+05     3.06
73    J0139+33      ttm+18     01:39:10           120  ttm+18     +33:10              15  ttm+18     *                        0  *          1.47
74    J0139+5621    cvh+14     01:39:38.56          2  cvh+14     +56:21:36.8          4  cvh+14     1.77534382596           10  cvh+14     2.41
75    B0136+57      dth78      01:39:19.7401       12  cbv+09     +58:14:31.819       17  cbv+09     0.272450630950          15  hlk+04     2.60

76    B0138+59      mth72      01:41:39.938         8  hlk+04     +60:09:32.30         7  hlk+04     1.2229485205457         18  hlk+04     2.30
77    J0141+63      slr+14     01:41                2  slr+14     +63:08               8  slr+14     0.04668588              49  slr+14     8.77
78    J0146+31      ttol16     01:46:15            40  ttol16     +31:04              10  ttol16     0.9381                   0  ttol16     1.83
79    J0146+6145    ims94      01:46:22.42         10  pkw+03     +61:45:02.8          7  pkw+03     8.6889941                4  dk14       3.60
80    B0144+59      stwd85     01:47:44.6457       17  ywml10     +59:22:03.293       15  ywml10     0.19632137543003        16  ywml10     1.58

81    B0148-06      mlt+78     01:51:22.701        11  hlk+04     -06:35:02.8          4  hlk+04     1.464664549334           7  hlk+04     25.00
82    J0152+0948    clm+05     01:52:23.73          5  clm+05     +09:48:10            2  clm+05     2.74664729014           10  clm+05     2.48
83    B0149-16      mlt+78     01:52:10.8536       17  hlk+04     -16:37:52.99         4  hlk+04     0.8327416126878         13  hlk+04     0.92
84    J0156+04      dsm+16     01:56:01           114  dsm+16     +04:02               8  dsm+16     *                        0  *          25.00
85    B0153+39      dtws85     01:56:55.2           3  hlk+04     +39:49:29            5  hlk+04     1.81156061131           10  hlk+04     4.91

86    B0154+61      dls72      01:57:49.93          3  hlk+04     +62:12:25.90        17  hlk+04     2.35174493646            7  hlk+04     1.39
87    J0158+21      dsm+13     01:58:29            32  dsm+13     +21:08               8  dsm+13     0.5053                   0  dsm+13     1.57
88    J0201+7005    kkl+15     02:01:41.344         7  kkl+15     +70:05:18.11         6  kkl+15     1.349184471846          10  kkl+15     1.17
89    J0205+6449    mss+02     02:05:37.92247      15  bkr+13     +64:49:41.3343      10  bkr+13     0.06571592849324         9  lrc+09     3.20
90    B0203-40      mlt+78     02:06:01.268         9  smd93      -40:28:04.33        14  smd93      0.630550140847           6  smd93      1.26

91    J0211-8159    lml+98     02:11:59.0           3  dsb+98     -81:59:36.2          3  dsb+98     1.0773327013             8  dsb+98     1.52
92    J0212+5222    bck+13     02:12:52.2           6  bck+13     +52:22:45           13  bck+13     0.376386292              1  bck+13     1.56
93    J0214+5222    slr+14     02:14:55.2713       34  slr+14     +52:22:40.95        19  slr+14     0.02457529479071        22  slr+14     1.16
94    J0215+6218    llc98      02:15:56.626        10  hlk+04     +62:18:33.37        10  hlk+04     0.548879819155           3  hlk+04     2.00
95    J0218+4232    nbf+95     02:18:06.358569      4  dyc+14     +42:32:17.37515      8  dyc+14     0.00232309053151224      8  dcl+16     3.15

96    J0220+36      ttol16     02:20:50            60  ttol16     +36:22              15  ttol16     1.0297                   0  ttol16     2.25
97    J0229+20      dsm+13     02:29:03            32  dsm+13     +20:58               8  dsm+13     0.8069                   0  dsm+13     2.09
98    B0226+70      dtws85     02:31:13.99          3  hlk+04     +70:26:33.88        17  hlk+04     1.466820306152           7  hlk+04     1.76
99    J0241+16      dsm+13     02:41:46            31  dsm+13     +16:04               8  dsm+13     1.5454                   0  dsm+13     0.94
100   J0242+62      hrk+08     02:42:35             3  cvh+14     +62:56:50           36  cvh+14     0.592                    0  hrk+08     0.22

The peculiar numbers are links in the table to the referenced publications that are the sources of the data. Ignoring those, the output is pretty simple to parse (manually or via a script, if you want).

Some things to keep in mind:

Not all of the pulsars have all five parameters, so not all of the entries will be useful for you.
This isn't a complete list of all pulsars in the galaxy; it's just the most comprehensive one I know (and have used). We only know a small fraction of the total galactic pulsar population.
Keep your units in mind. Right ascension is given in hours-minutes-seconds format, declination is give in degrees-minutes-seconds format, and distances are in kiloparsecs.

This information should allow you to create a pulsar map for use within the Milky Way. It might not be terribly helpful, given our small (and incomplete) sample, but it's a start.


Any simple experiment with an H-alpha telescope?

If you have the right filters and equipment you can make doppler measurements of the $H_\alpha$ line from the sun. Since an H-alpha telescope directly detects this you can use this to measure the doppler shift. Using this you can measure the rotation rate of the sun. This has been done before with a different telescope and the paper is here.

It should also be noted that if you don't find an adequate experiment just seeing the sun thru your telescope makes a profound impact on the viewer. One writer wrote that " I watched with a mix of awe and fear. Ever since that time, I've seen the Sun not so much as a sunny companion but as a star to be reckoned with."
Reference is here. That link and this one discuss viewing the doppler effect using an H-alpha telescope.


The image scale is a bit small, but I can see the constellation of Lyra just above center. The bright star Deneb (in the constellation of Cygnus) is left of center, and the star Altair (in the constellation of Aquila) is at the bottom (just right of center). Thus, your photo does not include Sagittarius. Sagittarius is off to the bottom right. The Scutum star cloud is the bright patch toward the right corner.

It would be helpful if you include the time of the photograph and location (latitude and longitude).


Gravity is a fictitious force, actually, much like centrifugal force.  In a free falling frame of reference it disappears.  In general relativity (GR) gravity is just a result of (differential) geometry: space-time curvature.  The inverse square law is just the low energy approximation, but the actual equation for gravity derived from GR is more complex than that.  The massive success of Newtonian gravity tells us that any model of gravity must be approximated by the classical inverse square law at low energies.

Whether GR does that by (Einstein's) design or something else is a matter of personal opinion.  Einstein definitely knew he had to get approximately Newtonian gravity at low energies, so he would have discarded or modified any ideas that failed this criterion.  However, there are standard arguments for why gravity must obey an inverse square law, at least in low energy situations.

Now in GR a lot more than just mass contributes to the gravitational field.  Spin and electric charge, for example, and quite importantly: energy (the famous $E=mc^2$ tells us how to express a mass as energy, so we can treat these things on a common footing).  So, yes, all forces and particles contribute to gravity.  Even photons.

GR itself makes no predictions (or requirements) for the existence of any new particles outside of the standard model, such as gravitons.  GR and quantum mechanics (QM) are famously incompatible: in extreme situations where both GR and QM are relevant (neutron stars and black hole formation, for example), they stop making sense rather quickly.  Especially GR.  "Gravitons" and assorted variations are hypothetical particles that are proposed to resolve this issue by creating a quantum theory of gravity.  The only "evidence" we have for them at this stage is that our two most massively successful theories about the workings of the universe, GR and QM, are so painfully incompatible.  So we know these theories are flawed (aka wrong) and that some other theory is necessary that can handle these situations, while also incorporating all of the successes of QM and GR—they're amazingly accurate when only one of them is particularly relevant, after all.

Exactly what that theory is is an ongoing and substantial research area.


Our eyes and brains make them blue.

Stars are (close to) a black body, they emit a broad band of radiation. The hottest stars will emit most of their radiation in the ultraviolet but they will still be very bright in visible light.

As they get hotter, they emit even more ultraviolet, and more visible light but the mixture of wavelengths in visible light doesn't change much.

This mixture is interpreted by our brains as being a sort of light blue. No matter how hot the star gets, it will still be emitting lots of visible light in a mixture that looks "light blue".  It will never look purple.

Purple can only be seen if either a single short-wavelength visible light is being emitted, or a mixture of short and long wavelengths (red and blue). Neither of the mixtures can occur in light emitted from a black body.

So stars can appear red, orange, yellow, white or light blue, but never green or purple.


Why Earth's perihelion occurs 3rd January rather than 1st?

Back in 1246 CE, the perihelion coincided with the December solstice. The Earth was at perihelion at 1 Jan in 2005 and will be on 6 Jan in 2096, GMT time. The drift is not monotonic, but it does progress overall throughout the centuries. Eventually, it will drift towards the March equinox and beyond, to come back to the winter solstice in around twenty thousand more years. This is primarily due to Milanković cycles of Earth's eccentricity and precession index.

But the problem isn't just effectively unfixable; it's just not a problem in the first place. The apsides were seldom a concern for calendars. The practice of 1 Jan as the new year may have begun with the Romans, but it was not continuously practiced throughout Europe, e.g., the early medieval new year began at several different days from early to late March at different times in history, and sometimes at Christmas.


Do primary mirrors in large observatories undergo regular removal and re-coating of the aluminum? Why?

This might not be the type of telescopes your are thinking about, but as IACTs (Imaging Atmospheric Cherencov Telescopes) in the end also measure light in (or near) the optical range, their mirrors are of similar build.

The important arrays (H.E.S.S., VERITAS and MAGIC) have, at least partially, mirrors made of glass or with a glass surfaces, coated on
the front surface with aluminium (Al) and an additional single protective layer (e.g. SiO$_2$ , Al$_2$O$_3$ ). But as they are exposed to the environment the whole time without any luxury such as protecting domes or similar, the coating degenerates pretty fast.

In the case of H.E.S.S., which is located in the Khomas Highland of Namibia, the mirrors have to endure all kinds of environmental factors, beginning with the sand from the dessert, extreme temperature changes between day and night to curious birds picking at their reflected images. So after five years the optical efficiency of the mirrors was so bad, that one could actually see ones hand through from the mirror. To prolong the lifespan of the instrument, the mirrors were refurbished with a slightly different aluminium coating. In the following image the time of the mirror recoating is marked with the blue shaded area.

Image source: https://www.mpi-hd.mpg.de/hd2012/pages/presentations/Stegmann.pdf

The degeneration for the mirrors of the other observatories mentioned above where of similar timescales and they also did some recoating campaigns.

For further information see for example the following papers, which contain some overview about the different possible techniques:

http://www.brera.inaf.it/~canestrari/pubblicazioni/pubbl44.pdf
https://arxiv.org/pdf/1406.0622

If you ever happen to be in Namibia, go visit the World's largest optical telescope:

Image source: https://www.lsw.uni-heidelberg.de/projects/hess/HESS/hessmultnu.phtml


Given the angular diameter $a$ in radians and the distance $d$ in Mpc, you can get the actual diameter $D$ from:
$$D = d\tan{a}$$

Using the small angle approximation, you get:
$$D = da$$

$a$ is in radians, so to get the distance in Mpc from the angular diameter in arc seconds you'd need to convert the angle in arc seconds to the angle in radians: $a = \frac{2\pi A}{360\times3600}$, where the factor $3600$ is used to convert arc seconds to degrees, and $\frac{2\pi}{360}$ to convert from degrees to radians:

To get the diameter in kpc:
$$D = 1000\times d \frac{2\pi A}{360\times3600}$$
$$D = d \frac{\pi A}{648}$$
$$D \approx \frac{dA}{206} $$

where $d$ is in $\textrm{Mpc}$, $D$ is in $\textrm{kpc}$, and $A$ is in $\textrm{arcsec}$.

Here $D$ is the diameter for round objects (even for disk galaxies seen at an angle). If the object is not round then this would normally be the maximum diameter.

[EDIT (see answer and comments from HDE 226868)] For irregular galaxies you may also need to have more information (viewing angle) to find the real maximum diameter of the galaxy. But that information is (I think) only available for galaxies in the local group.


How does Hawking Radiation work exactly?

... but how does the other know how to take energy from the black hole?

In order to understand this, you need to be familiar with the essence of this picture$^1$ including negative energy states inside the horizon, creation of virtual particle-antiparticle pairs, and conservation of energy.$^2$ I try to intuitively answer your question with simple words.
Assume that a virtual particle-antiparticle pair is created near the black hole's horizon. According to the principle of conservation of energy, the total energy of the pair particles must be zero. So, one of the particle has positive energy and the other one has negative energy. On the other hand, it can be shown that there exist negative-energy states inside the horizon of a static black hole and the negative-energy particles can occupy these states. In order to have a pair of real particles with zero total energy, the only physical possibility is that the positive-energy particle can escape to infinity, while the negative-energy particle falls into the black hole. In this way, the strong gravitational field of the black hole can convert a virtual particle–antiparticle pair into a pair of real particles with zero total energy. This is the reason why the virtual particle that's sucked in always get negative energy.

Does it just know to take energy from the black hole or does the antiparticle fall in, and the blackhole loses mass?

Note that, in this picture, when a virtual particle-antiparticle pair is created near the black hole's horizon, each of them may fall into the horizon or may escape to infinity (Always, one of them falls in and the other escapes.) So, it is not correct that only the antiparticle falls into the black hole. This means that a static observer outside the event horizon will observe both the particle and antiparticle spectrums.

In my opinion, you should not take the above argument about virtual particle-anti particle pair etc. too seriously since this picture helps to naively have an intuitive understanding. A rigorous treatment of Hawking radiation using quantization of quantum fields in curved black hole background does not need such a naïve picture.

$^1$There exist more rigorous treatments for understanding the Hawking radiation but I restrict myself to this framework (picture) that you are interested in and ask about.

$^2$ Here, for simplicity, I restrict this discussion to the case of static black holes. The general conclusion is still valid for the rotating black holes.


Requirements to resolve position of Jovian Whistlers up to magnitude of Red Spot with amateur radio equipment?

tl;dr
No, not from Earth.
Because of the ionosphere.
Whistlers are VLF (very low frequency) hundreds to thousands of Hertz. Our ionosphere blocks electromagnetic radiation very reliably below say roughly 10 MHz depending on time of day and solar activity because it's a plasma.
The image below shows peak whistler emissions at about 1 kHz.
You can imagine that the electrons in the ionosphere look more like electrons in a lossy metal to a radio wave in the kHz range; some will bounce off like it's a shiny metal marble, others will be absorbed, but without question None shall pass!
LOFAR works from 10 MHz to 250 MHz.
See also

Why did it take five years to "figure out" how to use astrometric calibration sources to deblur LOFAR images?
What can be learned from low frequency radio astronomy available outside of Earth's ionosphere?

Update!
No, not even from cis-lunar space!
Because the interplanetary electron density is still too high.
@ProfRob's comment on the "What can be learned..." question reminds us:

How low is "low"? The plasma frequency in the interplanetary medium near the Earth is about 100 kHz. https://physics.stackexchange.com/a/519164

and that answer goes into substantial detail on how to calculate the plasma frequency of various media.
The Chinese lunar orbiter Queqiao had a low frequency receiver, and backing up ProfRob's point:

Additionally, this satellite hosts the Netherlands–China Low-Frequency Explorer (NCLE), an instrument performing astrophysical studies in the unexplored radio regime of 80 kilohertz to 80 megahertz. It was developed by the Radboud University in Netherlands and the Chinese Academy of Sciences. The NCLE on the orbiter and the LFS on the lander work in synergy performing low-frequency (0.1–80 MHz) radio astronomical observations.

There are further references in the article.
It seems you must build a spacecraft and fly it into close proximity to Jupiter -- within a few attenuation lengths -- to hear the whistlers.
More
Your reference Strong whistler mode waves observed in the vicinity of Jupiter’s moons links to the Open Access Nature paper Y. Y. Shprits et al. (2018) Strong whistler mode waves observed in the vicinity of Jupiter’s moons which includes Figure 2. shown below.
From Whistlers (radio):

A whistler is a very low frequency or VLF electromagnetic (radio) wave generated by lightning.[1] Frequencies of terrestrial whistlers are 1 kHz to 30 kHz, with a maximum amplitude usually at 3 kHz to 5 kHz. Although they are electromagnetic waves, they occur at audio frequencies, and can be converted to audio using a suitable receiver. They are produced by lightning strikes (mostly intracloud and return-path) where the impulse travels along the Earth's magnetic field lines from one hemisphere to the other. They undergo dispersion of several kHz due to the slower velocity of the lower frequencies through the plasma environments of the ionosphere and magnetosphere. Thus they are perceived as a descending tone which can last for a few seconds. The study of whistlers categorizes them into Pure Note, Diffuse, 2-Hop, and Echo Train types.
Voyager 1 and 2 spacecraft detected whistler-like activity in the vicinity of Jupiter known as "Jovian Whistlers", supporting the visual observations of lightning made by Voyager 1

Figure 2 from the Nature paper linked above.

Comparison of wave power and pitch angle distributions for the encounter on 6 September 1996 (orbital segment G2). a The distance between Ganymede and the Galileo spacecraft, b measurements of the magnetic field, c pitch angle distribution of 527–884 keV electron fluxes, d same as c but normalized by the value of fluxes at 60° local pitch angle, e dynamic spectrogram of electric field very low frequency (VLF) spectral density, f dynamic spectrogram of magnetic field VLF spectral density


According to this website we need another 15 million years to the perigalacticon.

  Recall the Sun's motion ... 30 degrees toward the galactic centre from circular motion, and 23 degrees upward out of the galactic plane. We will be at perigalacticon (closest to the nucleus) in 15 million years. At apogalacticon the Sun is seven percent farther out.

During the galactic year of about 250 million years our solar system isn't orbiting on a Kepler ellipse around the galactic center, but instead oscillating up and down the galactic plane.

  This vertical oscillation cycles at 3.5 times per galactic year.

We are now about 27,000 lightyears away from the galactic center, close to the perigalacticon. The difference between apogalacticon and perigalacticon is a little more than 4,000 lightyears (15% of 27,000 lightyears). The 15% number is calculated from the 7% eccentricity of the orbit by $1.07/0.93=1.15~~$ according to the definition of eccentricity, and Kepler's 1st law.


Effect of particulates on the visibility of stars?

Aerosol physics is actually an old topic - yet still a very vibrant one.
One main factor on the extinction (which sums up scattering and absorption) other than the distance (which is about constant when looking at a a particular zenith distance) is the wavelength $\lambda$ you look at compared to the typical aerosol particle radius $r$ as its ratio affects the scattering regime we look at ($\lambda \gg r, \lambda \approx r, \lambda \ll r$). There's multiple papers on the aerosol influence on observations, like this (Stubbs et al) for PanSTARRS or Patat et al (2018) on extinction over Paranal which also looks at the temporal variability.
Looking at the typical aerosol concentrations (e.g. here by DWD), it seems that the smaller particles are more abundant. Thus we are in the Rayleigh or Mie scattering regimes where the extinction is due to scattering and does not depend much on the actual particle properties other than their size. The actual absorption only becomes important for the larger particles which are the least abundant.
All in all this might only be half an answer, but too long for a comment and maybe gives you leads to follow-up on. If you get a hand on Friedlander's "smoke, dust and haze", it might be a good read, too (especially chapters 5 and 13).


You use Spherical Trigonometry

Given $A_1$ and $A_2$ are the respective azimuthal coordinates of the two objects, and $a_1$, $a_2$ their respective altitudes,

the angular seperation $\theta$ is given by

$$\cos \theta = \sin a_1 \sin a_2 + \cos a_1 \cos a_2 \cos (A_1-A_2)$$


Effect of black coating on the inside of a hobby telescope's tube?

Telescopes have the inner part of the tube blackened to minimize scattered light reaching the eyepiece. Such scattered light reduces contrast, and hence reduces the ability to see very faint objects, or low contrast detail.  A complementary approach for refractor telescopes is to use baffles in the tube. The baffles form a physical barrier to scattered light.  However baffles are costly to make accurately and add to the weight of the telescope.
The more that scattered light is reduced, the better the performance.
Alternatives to super absorbing paint are to attach to the tube, either matt black velvet, or sand paper sprayed with matt black paint.


What will be Supernova SN 2014J's peak brightness?

According to this website the peak visible magnitude will be about 10.5 around February 2nd.
Earlier estimates had been a little brighter around the same date.


Is it possible for a star to return in the main sequence?

The evolution of a star is irreversible process, so strictly speaking, it is impossible to return the star back to its earlier phase (it is impossible to collect all energy it has radiated to space and use it for conversion of helium back to hydrogen).
But it is possible for a star plotted on HR diagram to return to a point corresponding to main sequence phase. These stars are called blue stragglers. They are usually formed when stars merge.


Could dark matter be "inside-out" reality?

As a disclaimer: This answer does not include references, and is mostly based on my first intuition when reading the question. I can see that it can potentially be an interesting question to discuss.

First, we live in a solar system, in a galaxy, in a galaxy cluster. That in itself means that there is a lot of matter around. We are also (at least very likely) living in an overdensity in the universe, meaning that there is extremely much matter where we are compared to the average in the universe.

If we assume that we do live in an underdensity of the universe, that would mean that there is more matter present in the universe on average compared to where we are. However, if pockets of space in a distribution of regular matter was dark matter, then it sounds like there would be a larger amount of regular matter than dark matter in the universe, something which does not agree with our estimates.

If we assume for a minute that it is the other way around (that we live in an area with a lot of matter, not a lot of space), then this theory will struggle with explaining some of the things that point towards the existence of dark matter. One such thing is the rotation curves of galaxies, which indicate that there is more mass presence than there is seen. I expect that there would not be enough space within a galaxy to create such "pockets" of space. Say, however, that we assume this was possible, then the voids we observe between galaxies and galaxy clusters would be even more gigantic pockets of space, which would mean that there would be an enormous amount of dark matter, which I would think would be inconsistent with what we see from the CMB.


Do the terrestrial planets form later than gas giants in our solar system?

The current ideas are that both terrestrial planets and giant planets start their formation in a similar manner. Dust settles towards the mid-plane of a predominantly gaseous disk, starts to stick together and eventually small (km-sized) planetesimals are formed. This process may be quicker in the outer parts of the solar systems where the gas is colder and the condensed material (ices) is probably "stickier". The planetesimals then interact with each other gravitationally and can grow by merger. The rate of growth is controlled by their spatial densities and their relative velocities, but is thought to occur quite quickly in both the inner and outer parts of the solar system ($\sim$ 1-3 million years, e.g. Righter & O'Brien 2011).

Thereafter, the inner and outer parts of the solar system differ. The gas is cold enough in the outer parts of the solar system to accrete onto rocky cores and build giant planets on timescales of another few million years.
In the inner solar system the gas is too hot to be accreted and instread the next tens of millions of years are characterised by high velocity collisions between planetary embryos and planetesimals. This indeed may be sculpted and influenced by the early migration inwards of Jupiter to about 1.5 au, followed by migration outwards - the so-called "Grand Tack model" (Raymond & Morbidelli 2014).

Overall it probably takes the inner solar system and terrestrial planets of order 100 million years to settle down into its final configuration. The collision that formed the moon may have been several tens of millions of years after the formation of the Sun and certainly long after the giant planets formed.


Calculate the orbital phase when plotting the Radial Velocity data of a transitting exoplanet

The phase as plotted on the graph is constrained in the range [0,1) to plot everything in one orbital cycle (this makes it easier to see the shape of the RV curve). The phase can be obtained by taking the fractional part of the total number of cycles. So the first row in the table with the cycles number 28.677 corresponds to phase 0.677.

Update: As to what the cycles number is, it is a measurement of time since a reference time (usually the transit time), counted in units of the orbital period of the planet. In the case of a transiting planet, the orbital period will be known from the transit interval, so it doesn't need to be derived from the RV curve.

In this case, the first row in Table 1 has time $t = \mathrm{HJD}\ 2455107.37937$, while in Table 2 the transit time is given as $E = \mathrm{HJD}\ 2454967.27571$ and the orbital period as $P = 4.885525\ \mathrm{days}$. So the number of cycles can be calculated as $\mathrm{cycles} = (t-E)/P$ giving 28.677 (to 3 decimal places).


How does the Event Horizon Telescope implement the interferometry?

Assuming I understand your question:

As in actually mentioned in the article, all data collected are stored on hard drives, timestamped with an atomic clock, and then flown to a central location where the interferometry actually takes place.

Further reading:

R2DBE: A Wideband Digital Backend for the Event Horizon Telescop
eventhorizontelescope.org/publications


Can it be inferred that our cosmological horizon has increased over time?

No. Space expansion doesn't slow down, unlike the expansion of cosmic horizon. That means the cosmic horizon actually swallows galaxies as they travel away from us due to space expansion, reducing their number instead of increasing it. Nevertheless, we still haven't gathered all cosmic radiation from Big Bang that occurred within our current event horizon, so it's still a good while before it begins restricting distance of observable universe for us - currently the speed of light (+space expansion rate) vs age of the universe limits it to a considerably smaller radius.
Yes, we discovered more stars and galaxies, but that is due to improvement of technology, which is still quite far (roughly a third of the way) from observing stars near the Hubble Sphere as the universe formed (ones whose light would be observable today; as opposed to these at the space horizon, whose light will reach us eventually, in infinitely distant future.)

Currently we're still quite a bit away from leaning against the cosmological limits of observability. Currently our limit of observability is the budget for building better devices.


How far into intergalactic space would you have to go to see the Milky Way?

We can calculate the distance we need to be from an object in order for it to be any arbitrary angular size using the formula $D=\frac{d}{2\tan(\frac12\delta)}$.  In this case, $D$ is the distance from the object, $d$ is its diameter, and $\delta$ is the angular size.  The Milky Way's diameter is 100,000 light years.  If we want the Milky Way to appear as large as the Sun appears from the Earth (0.5$^\circ$), we would need to be 5,700,000 light years away.  If we want it to appear much larger, we could be closer.  For the Milky Way to be the size of a 1 meter circle held at arm's length (90$^\circ$), we would need to be 50,000 light years away.


Can lightning occur in stars like the Sun?

Stars are not actually gaseous, they are plasmas, i.e., highly ionized. Hence, the entire star is highly conductive and does not easily develop the voltage difference via friction needed for lightning like that in our atmosphere. On the other hand, stellar atmospheres have strong magnetic fields which reconnect, and that causes strong voltage spikes that generate high energy electrons. On the Earth we would call streams of high energy electrons lightning, but on the sun we call them flares.


What causes objects to become tidally locked?

Tidal locking occurs because the planet deforms the satellite into an oval, with long axis pointing towards the planet. If the satellite is rotating the long axis will move away from being pointing towards the planet, and the gravity of the planet will tend to pull it back, slowing the rotation until one face is permanently facing the planet. Tidal locking isn't a result of the formation processes, but a consequence of satellites not being perfectly rigid.

In order to model the effects of tides on the orbits and rotation periods of satellites you need to know several important pieces of information.

First you obviously need to know the size of the planet and the satellite (both in terms of mass and radius) the shape of the orbit and the rotation rate of both planet and satellite. For many objects, these values are well known.

Next, and this is the tricky bit, you need to know how the satellite and planet will be deformed by the other's gravity, and how much tidal heating will occur. These are the so-called "love number" (after Augustus Love) and the dissipation function, Q.

It is hard to estimate these. For the Earth Moon system the ratio k/Q is known to be 0.0011. (but the Earth is a poor model for other planets, which don't have a substantial ocean, or a liquid core)

For other planets the value of Q varies between 10 and 10000, with larger values for the gas giants, and k can be estimated from the rigidity of the bodies.

A simple gravitation model is not able to capture the subtleties of the gravitational interaction between two mutually deforming bodies, indeed for most simulations, the planets are modelled as points, or at most as spheres, and this is good enough for all but the highest precision calculations.

Tidal locking takes a long time (by human standards) but a relatively short time compared with the age of the solar system. The time taken is very strongly dependent (order 6) on the radius of the orbit.

Direct simulation would be more or less impossible: the deformations are too small, and the time scale of locking is too large. It would be possible (though difficult) to model tidal locking in a simulation with unrealistic values for the rigidity of the satellite, and the size of the planet (think jelly world, orbiting a (Newtonian) black hole) so the deformation is greater and the locking time shorter. However modelling the  elastic deformation of a body under gravity is far from trivial.


What are some good telescopes for a programmer?

One project you could work on is an Arduino-based Go-To telescope system. You could use, in theory, any scope that can accommodate the addition for this purpose. Also, it's my understanding that any Go-To system that can be connected to a computer can receive custom scripts you could write. At least, I know it's true for the NexStar system.

In my opinion, it's best to start with a simple Dobsonian telescope from a reputable dealer, without any programmable components. It will force you to learn the sky well before you start observing. And it will serve as an entry-level introduction to the world of telescopes.


Did the earth form outside the solar system?

The chance happenstance that Earth happened to be floating along and got captured is minuscule. How did Earth wind up floating through space? There's no established mechanism for terrestrial planets to form on their own. As far as we know, they need a host star to form around. So if our Sun captured Earth, it must've formed around another Star, got ejected somehow, and then came under the influence of our Sun where it was captured and nicely placed at its current position. This is all highly, highly unlikely. I'm not going to run through the math, but you probably have a better chance of getting struck by lighting at the exact moment you buy a winning lottery ticket (twice).
Aside from a statistical argument, you can look at it from the vantage point that the composition of the Earth properly matches everything else in our solar system. People have made a very close study as to the physical composition of Earth, the Moon, and the other planets and bodies in our solar system. We would have noticed if there was a large disparity in composition or something just didn't match up. As it is, Earth matches up pretty darn well, especially with our Moon. The close resemblance in composition between our Moon and Earth gives strong evidence that the Moon was formed from the Earth. If Earth was captured, so too was the Moon which makes point 1 even less likely.
Many people have spent a lot of time simulating the formation of our solar system, from the start up until now. There are a few open questions (such as why Jupiter resides where it does), but by and large, people agree that a planet should form about where Earth is. So if Earth wasn't here during formation and was later captured, why isn't there an extra planet that did form where Earth is? All simulations suggest such a planet should exist. The most likely scenario is that Earth is that planet!
It is believed that basic life (i.e., single celled organisms) started on Earth around 3.8 to 4.1 billion years ago. Earth itself has been reliable dated to about 4.53 billion years old. This means life was forming a mere 400-700 million years after Earth first formed. Life requires very very specific conditions (as we know it) to start forming and that can't happen in the dead of space. Earth had to be around a star from the beginning. Any time spent drifting through space until it was captured would have delayed the onset of the formation of life.

I'm sure there are plenty of arguments that could be added to the list, but that's a good start I think.

Edit: I didn't expect such a spirited debate in response to this answer. First off, I want to say that none of my arguments above are bullet-proof. I'm going to incorporate some of the comments below to help round out this answer. This will be easier than creating a long conversation of comments.

Matthew Whited - [It] is possible that other rouge planets could have formed outside of their own solar systems. It is also possible that they could form within solar systems and be ejected.

This is certainly true. One cannot soundly reject the hypothesis that Earth formed elsewhere (be it in free space or around another star) and was later captured by our Sun. My arguments are mostly ways to point out that the chance of such an occurrence is diminishingly small due to the unlikely circumstances that must occur for that hypothesis to be true. The betting man would not side with the hypothesis that the Earth formed outside our solar system and was later captured.

Rob Jeffries - Almost the only way Earth could be captured is during the clustered star formation stage (well established theoretical possibility). In which case it would have the same age and metallicity as if it had formed around the Sun. So age and metallicity are weak arguments.

I don't know if they're as weak as that. If the Earth did come from another stellar system, it would of course come from a nearby one, which would of course have a similar metallicity as our Sun. But I think a point which makes the above arguments stronger is the specific composition of the Earth. If it formed around a star which was slightly different in nature (say an M Dwarf) or at a different distance from the star I think we'd notice that the Earth seemed "out of place" in our solar system. As it is, its iron content agrees quite well with it forming where it currently resides. Again, none of this is bullet-proof, but it cast's doubts on the validity of Earth forming elsewhere.

Rob Jeffries - Planet capture in the nascent cluster also nullifies arguments 2 (since the Moon would have to be formed after capture) and 4.
jwenting - The moon argument isn't a valid one. The moon could have been formed out of the earth after capture. Which doesn't make that capture a more likely scenario of course.

I wouldn't say nullifies. In fact, I would think it makes them a bit stronger. The process of the Earth forming elsewhere, being flung out of its stellar system and captured by ours (and put in its proper place), then forming a Moon and life, requires that these events happened extremely quickly. While not impossible, it is improbable, especially when you add in your argument for the Earth being in a very precise orbit unlikely to have been achieved if it had been captured. If you argue that the Moon/Life formed after capture you're really limiting the time and chances that the Earth didn't form in our system.


Why don't we see more supernovae in our galaxy?

So from this I can only come to the conclusion that supernovae did in
  fact happen in the Milky Way in the last two centuries, but that we
  didn't see any of them.

  But now I'm confused. I read about supernovae that have happened in
  galaxies billions of light-years from here that lit up as the
  brightest source of light in the sky for days. Surely we would be able
  to see all of the supernovae that happen in our Milky Way

One problem with estimating how many supernovae have happened in the Milky Way in the last two centuries, is that the remnant from a supernova is far dimmer than the nova itself and far harder to find. Several supernovae could have happened in the Milky Way in the last 2 centuries and remain undiscovered — and just for clarity, we define the date of a supernova by the date the light from the explosion reaches the Earth, so saying saying a nova "happened" in the last 200 years refers to the date the light from the event reached Earth, not the actual date of the event, which you probably already know, but just to clarify.

So for argument's sake, let's say that a supernova's light reached the Earth about 50 years ago, but it took place on the far side of the galaxy. To find that, we'd have to look for a nebula on the far side of the galaxy and that's a hard thing to see. Similar to looking for the theoretical Planet Nine, finding old supernova remnants on the other side of the Milky Way takes a lot of looking. Even with modern telescopes, it's still a needle in a haystack, and especially if the view is blocked by dust like much of the Milky Way is.

A Milky Way supernova remnant was discovered in 1985, supernova remnant G1.9+0.3. It was thought to have "happened" around 1868, though it went unobserved and probably wasn't visible to the naked eye at the time.   There's probably been several others more recent than that one.  G1.9+0.3 would have been visible if not for interstellar dust. From article above:

  It was a type Ia supernova believed to have exploded about 25,000
  years ago, and the signal began reaching Earth around 1868. The light
  from the supernova would have been visible to 19th century
  astronomers, had it not been obscured by the dense gas and dust of the
  Galactic Center.

I'm not sure the 4.6 supernovae per century from your article is accurate. It might be, but the number I'm used to hearing is about one per century. But regardless of which number is actually correct, it still doesn't imply high mathematical improbability because many Milky Way novae would have gone unnoticed if they were far enough away. In short, I agree with what you said here:

  I can only come to the conclusion that supernovae did in fact happen in the Milky Way in the last two centuries, but that we didn't see any of them.

Here's a related article on Milky Way visibility.

Observation of a distant galaxy nova is possible if we have telescopes looking in that direction. A nova is much more detectable at the time it goes nova.  Much less so, years later.

Today, however, with neutrino detection in 7 locations around the globe, I think it's virtually impossible that we'd miss a supernova in the Milky Way, so we have a good chance of seeing one in our lifetime and it's likely that none have occurred since somewhere around 1980. A supernova was detected in the Andromeda galaxy in 1987 by that method, and our neutrino detection has improved since then to give us early warning and pinpoint location.

As far as visibility, size matters, but what matters more is how close and how much dust is in the way. Most of the recorded supernovae were quite bright and fairly noticeable to someone who was familiar with the stars in the sky (list of known supernovae).

Eight Milky Way novae have been recorded by history and observed by the naked eye in the last 2,000 years, well below the number that should have happened in that time. Five of those eight had brightness greater than $-3$, which is brighter than Jupiter and would have been immediately noticed by anyone familiar with star charting. Two others had magnitudes around zero, which is still brighter than most stars. SN386 was less bright, but is still easily visible and recorded by Chinese astronomers. And finally, Cassiopeia A was quite dim, but it was still observable. Only about 10% (ballpark estimate) of the Milky Way is close enough and unobstructed enough to provide supernovae that would visibly get noticed.  Most would have gone unnoticed until recently.

Hope that's not too wordy, I can try to clean up if needed.


Colossus telescope, trying to outsmart aliens?

The real reasoning has nothing to do with some civilization "deliberately" hiding its radio emissions. Rather, the problem is that we can not expect some other civilization to do something we would not do ourselves.

It makes no sense whatsoever to radiate large amounts of energy into space when there exist other, more economical alternatives. Radio transmitters circa 1911 required whole dedicated dynamo machines to run at abysmally low efficiency - these days we are using tiny battery powered devices with directed radio beam steering and adaptive power minimization as to not transmit a single joule more than absolutely necessary to get the data through to intended destination.

Another problem arises from the fact that most of the "radio SETI" effort to date was concentrated around the "cosmic waterhole" (the frequency of interstellar hydrogen emission). This is a reserved frequency here on Earth, so nobody broadcasts on it. Common sense suggests that aliens would probably do the same - after all, we expect them to have developed radio astronomy as well. Unfortunately, listening on any other frequency will probably pick up locally generated broadcasts first and completely mask the weak alien signal.

Given the above, what choices are we left with? One would be to construct a large radio telescope somewhere Earth radio emissions can not reach - the far side of the moon or even a trans-solar location on the Earth orbit come to mind. Unfortunately, such project, while doable, is hugely expensive.

The other approach is to develop "distributed" telescopes which can be built gradually on low budget and to develop techniques to cancel the local noise. For low frequency radio telescopy such project is already ongoing:

http://en.wikipedia.org/wiki/LOFAR

For infrared, we've got this "Collosus" proposal, but place our hopes on JWST (http://www.jwst.nasa.gov/).

And we don't expect to see much in visible light for all the obvious reasons.


The principle is almost exactly the same as a watch or clock, but instead of three concentric axles, you need 9 for the planets.

Have a google for Orrery kit - there are loads available. It is really all simple maths - you just need to know relative orbital periods in order to calculate cog sizes.

(picture from curiousminds.co.uk)
For moons, you do add a little complexity in the form of a transmission to support the Earth, so that the difference in movement can move the Moon.


How does a physical distance $rR_0$ comes into play in the angular diameter distance, because from its definition ...

The manner you choose to calculate it is explained on Wikipedia's "Angular diameter distance" webpage:

The angular diameter distance is a distance measure used in astronomy. It is defined in terms of an object's physical size, $x$, and $\theta$ the angular size of the object as viewed from earth.

$$d_{A}={\frac {x}{\theta}}$$

The angular diameter distance depends on the assumed cosmology of the universe. The angular diameter distance to an object at redshift, $z$, is expressed in terms of the comoving distance, $r$ as:

$$d_{A}={\frac {S_{k}(r)}{1+z}}$$

Where $S_{k}(r)$ is the FLRW coordinate defined as:

$$S_{k}(r)={\begin{cases}\sin \left({\sqrt {-\Omega _{k}}}H_{0}r\right)/\left(H_{0}{\sqrt {|\Omega _{k}|}}\right)&\Omega _{k}<0\\r&\Omega _{k}=0\\\sinh \left({\sqrt {\Omega _{k}}}H_{0}r\right)/\left(H_{0}{\sqrt {|\Omega _{k}|}}\right)&\Omega _{k}>0\end{cases}}$$

Where $\Omega _{k}$ is the curvature density and $H_{0}$ is the value of the Hubble parameter today.

In the currently favoured geometric model of our Universe, the "angular diameter distance" of an object is a good approximation to the "real distance", i.e. the proper distance when the light left the object. Note that beyond a certain redshift, the angular diameter distance gets smaller with increasing redshift.

See also Wikipedia's "Distance measures (cosmology)":

$$\begin{array}{l}
\text{Comparison of cosmological distance $\qquad\quad\;\,$ Comparison of cosmological distance} \\
\text{measures, from redshift 0 to redshift 0.5. $\qquad$ measures, from redshift 0 to redshift 10K.} \\
\hline
\qquad\text{The background cosmology is Hubble parameter 72 km/s/Mpc, $\Omega_\Lambda=0.732$,} \\
\qquad\text{$\Omega_{\rm matter}=0.266$, $\Omega_{\rm radiation}=0.266/3454$, and $\Omega_k$ chosen so that the sum of} \\
\qquad\text{Omega parameters is 1.}
\end{array}$$

Notice how, even at a small $z$, the choice of cosmological model is important for full accuracy.

The book "Astrophysics in a Nutshell: Second Edition" was published Feb 23, 2016, the first edition was published on Dec 4, 2011. The first edition is old (and 25% of the cost of), the second edition is not new.

Wikipedia explains the Lambda-CDM model:

  The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parametrization of the Big Bang cosmological model in which the universe contains a cosmological constant, denoted by Lambda (Greek Λ), associated with dark energy, and cold dark matter (abbreviated CDM). It is frequently referred to as the standard model of Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos:

  the existence and structure of the cosmic microwave background
  the large-scale structure in the distribution of galaxies
  the abundances of hydrogen (including deuterium), helium, and lithium
  the accelerating expansion of the universe observed in the light from distant galaxies and supernovae

  The model assumes that general relativity is the correct theory of gravity on cosmological scales. It emerged in the late 1990s as a concordance cosmology, after a period of time when disparate observed properties of the universe appeared mutually inconsistent, and there was no consensus on the makeup of the energy density of the universe.

  The ΛCDM model can be extended [tweaked to fix it, depending on what you are doing] by adding cosmological inflation, quintessence and other elements that are current areas of speculation and research in cosmology.

  Some alternative models challenge the assumptions of the ΛCDM model. Examples of these are modified Newtonian dynamics, modified gravity, theories of large-scale variations in the matter density of the universe, and scale invariance of empty space.

The reason to nitpick about a tiny difference of opinion is because the distances involved are so enormous, and the difference really isn't so small either. Depending on the distance the amount of time that has passed means that the space through which the light is passing changes somewhat throughout it's lifetime.

See also: "Scale invariant cosmology III: dynamical models and comparisons with observations" (19 May 2016) by André Maeder:

  The basic equations of cosmology are modified, showing an acceleration of the expansion after a certain initial period, the duration of which depends on the mean density of the Universe. Another major consequence of the scale
  invariance is that the laws of conservation of matter-energy show some dependence on the cosmic time. This dependence is very weak for models with a non-zero matter density, but at the conceptual level this is not a minor effect.

  We do think it is worth to undertake the present exploration for two main reasons. One is that the recent cosmological results suggest that a totally unknown form of matter-energy, the dark energy, dominates the energy content of the Universe. This is a major problem. The other main reason is that scale invariance is not a kind of adjusted trick to make things work. But it is a basic physical change, that responds to the fundamental wish (Dirac 1973) that the equations expressing basic laws should be invariant under the widest group of transformations.

The newer paper "An alternative to the LCDM model: the case of scale invariance" (14 Jan 2017), by André Maeder contains the calculations ($d_M = R_0 r_1$, $d_A = d_M/(1+z)$, on pages 13 and 14) and the following graph:

Figure 5. The angular diameter distance $d_A$ vs. redshift $z$ for flat scale invariant models (continuous red lines) compared to flat ΛCDM
models (broken blue lines). The curves are given for Ωm = 0, 0.1, 0.3, 0.99, from the upper to the lower curve in both cases (at $z$ > 3).

Please refer to that paper for details on the derivation of the calculations.


It might seem like the way to figure this out would be to test the composition of micrometeorites and see what objects this matches up with. This, however, is not a viable technique, as Genge et al. (2008) explains:

  In interplanetary space dust particles are inherently transported sunwards by P-R light drag (Dohnanyi 1967) and once captured by the Earth their deceleration occurs at high altitudes allowing fragile micrometeoroids to survive atmospheric entry (Love and Brownlee 1991). The parent bodies of MMs, therefore, are likely to differ from those of meteorites.

It is, however, possible to analyze micrometeorites and group them in various categories, and determine the parent bodies. The two main types of parent bodies are thought to be comets and asteroids. Distinguishing between the micrometeorites of these two groups, however, can be difficult. Many large micrometeorites are from main-belt asteroids (see Genge & Grady (2002)). However, Nesvorny et al. (2010) suggests that many micrometeorites (and large amounts of cosmic dust in general) are from comets.


Read Edwin Abbot's book Flatland.

In this story we visit a vision of a two dimensional "Universe" embedded in a higher dimensional space. Now by analogy we may suppose that our Universe is embedded in a higher dimension space with plenty of room for other (3+1)-Universes.

I do not claim this is a viable model of "reality" just a thought experiment to show "where" other universes might be if there are indeed multiple universes. Also Flatland is a fun read.


The relation between the light of full moon and the distance between the sun and the earth

The strength of the light from the Sun scales with the inverse square of distance [note 1]. That means that we would need to have the Earth-Moon system at $\frac{1}{\sqrt{2}}$ (approx 0.7) AU for the full Moon to be twice as bright [note 2].

Note 1: The fact that the Sun is not a point source of light has only a very minor effect on the scaling.
Note 2: Technically, it will be slightly brighter because more of the absorbed radiation will be radiated away in the visible spectrum. This is however also a negligible effect.


How many Moon's Topocentric Conjunction occurs per lunar month?

Let's double-check @barrycarter's conclusion:

Ignoring the rest of the solar system and even the Moon's non-negligible mass, the velocity of the Moon's motion around the Earth is on average roughly 1 km/sec per $v=\sqrt{GM_E/a_M}$ (the vis-viva equation).

The Earth is about 12760 km in diameter, so the Moon traverses the Earth's projection in about 3.5 hours.

A topographic point traverses the Earth's projection in 12 hours with a tangential velocity that's never more than 0.47 km/sec.

That means that the moon's projected position always "moves" faster than a topographic location, so there can never be more than one topocentric superior conjunction per lunar month.

Hopefully there will never be any inferior topocentric conjunctions for this Earth at least.


Could we see planets around active Stellar Mass Black Hole?

Stellar Black Holes (SBHs) are really really hard to find. If there's a free-floating one in space with no companion, our chances of finding it are almost nil. However, observations have more or less ruled out the possibility that space is freely floating with huge quantities SBHs. This was one of the proposed sources of Dark Matter, namely MACHOs. We don't believe MACHOs exist at this point because lensing observations towards the galactic core suggest they don't exist in any significant quantity.

The list of known and candidate SBHs contains less than 30 entries. The reason SBHs are hard to find is that, as stated above, they don't seem to be too common, and also that they can only really be observed indirectly through their interactions with a binary companion. Often, one observes the X-ray radiation coming from infalling matter around the black hole, taken from the binary companion, rather than observing the black hole itself.

  Is there too few active Stellar Mass BH close enough for us to have a chance the system's plan is well aligned with us?

The answer to this is probably yes.

  Do we only see Stellar Mass BH when they have a stellar companion feeding them, and this discards to possibility for close-by planets?

Again yes, we can only "see" the SBHs when they have a companion feeding them. This doesn't count the three cases where we've found SBHs through gravitational wave observations though, but all of those were far outside our galaxy. Whether a planet could exist in such a violent binary system is up for debate. There's only one known case that I know of where a planet is orbiting a similar system and that is PSR B1620-26. This is a white dwarf, pulsar pair with a planet around it. This would be completely analagous to an X-ray binary system with a black hole if only the pulsar were a bit more massive. So certainly it seems possible for a planet to be around such a system, but probably not very likely.

  Or is it because the light we can see from them is too fast-changing for a wobble or transition to be observable with today telescopes?

This certainly plays a part too. Even if you find a binary system with an SBH that is active and producing X-rays, you're still going to have a hard time teasing out an exoplanet signal, especially if that exoplanet is small (i.e., smaller than Jupiter). The transit method would be difficult due to the natural variability and hence noise in the X-ray emissions and the radial velocity method may not be sensitive enough to small planets. Such a measurement would be really hard.

As it turns out though, astronomers are thinking about these things. There was recently a paper published almost on this very topic. Check out Irma & Stefano (2017) where they discuss trying to find planets around X-ray binaries that may potentially house a SBH.


The site in-the-sky.org has a wide variety of functions and options. In Planetarium mode, I chose a random city at about 24N and in the middle, which helps to get the correct UTC + 05:30 India Time Zone, and then just put in the time and date and turned on alt/az grid.

So it is likely to have been Jupiter, as you suspect. Below are two screen shots - 20:00 and 23:00 local time, with Jupiter climbing from 41 to about 73 degrees above the horizon.


How long between the moment a meteor is first visible and the moment a meteorite hits the ground?

I'm a researcher at Curtin University working on the Desert Fireball Network. The DFN is the largest fireball observation network in the world, and our primary goal is to recover meteorites with orbital information attached.
The traditional rule of thumb for meteorite-dropping events is a final luminous height below 35 km and a final luminous velocity below 10 km s-1
So when I refer to the luminous part of the trajectory, I am referring to the portion in which ablation is occurring and optical light is emitted. As you said, this portion typically lasts a few seconds depending on the initial size, strength, speed, and slope of the meteoroid. After this, if the object still has mass left, the speed continuously decreases. We call this portion of the trajectory the "dark-flight" (as opposed to the "bright-flight" which is the luminous part) because we can longer observe the meteoroid.
During the dark flight, the rock goes from <10 km s-1 to tens to a few hundred m s-1 when it finally impacts the ground as a meteorite. This part of the trajectory can be greatly affected by wind as seen below from the dark flight modeling done for the recovered Dingle Dell meteorite:

So, in total, from first becoming a meteor to impacting the surface, you should expect about tens of seconds to minutes to pass. Of course, this is dependent on things I have mentioned like mass, speed, and slope notably.


Why do pre-main sequence stars show lithium in absorption?

As pre-main sequence (PMS) stars contract towards the main sequence, their cores become hotter.

Lithium is turned into helium by proton capture reactions. These are initiated in the core at temperatures of around 3 million K, so much lower than for hydrogen burning.

At the same time, PMS stars, or at least the type of low-mass pre-main sequence stars that are being referred to here, are fully convective and this mixes material inside the star rapidly and effectively.

Thus the sequence of events is that the PMS star contracts; the core reaches $3\times 10^{7}$ K at some point before the main sequence; Li is destroyed by proton capture; the Li-depleted is completely mixed with the rest of the star.

In this way Li can be rapidly and totally destroyed on a timescale that depends on the mass of the PMS star. It is as short as 10 Myr for a star like the Sun, increasing to about 100 Myr for a star of $0.1 M_{\odot}$.

That is the basic picture, but there is a wrinkle for stars with $M>0.4M_{\odot}$, where the core becomes radiative rather than convective before they reach the main sequence, but after Li burning has commenced. The radiative core pushes outwards and its  base then drops below $3\times 10^{6}$ K. This means that although Li destruction runs to completion in the core, at least some Li can be preserved in the outer layers of such stars.

Li is therefore an extremely complicated function of age and mass. But for the purposes of identifying low-mass PMS stars we can clearly say that anything that shows strong lithium signatures is probably younger than 100 million years if it is below about $0.5 M_{\odot}$ (or equivalently is a K- or M-type star).

If you want much more detail, see my review article on Pre-main sequence Lithium depletion.

The H$\alpha$ emission of PMS stars is connected with their youth. It can arise in two ways. The first is associated with accretion from a circumstellar disc. This is caused by gas falling from the disk onto the star and heating up. The H alpha emission can be very strong and very doppler broadened ($>300$ km/s). As pre-main sequence discs only survive for 10 million years or less, then this is a very clear signature of a pre main sequence star.

On the other hand, young stars that have lost their discs also show strong (though not as strong as accretion-related emission) H$\alpha$ emission that is caused by non-radiative, magnetic heating of their chromospheres. This magnetic activity is associated with convective, rapidly rotating stars. Pre main sequence stars possess both these properties. Thus PMS stars must exhibit H$\alpha$ emission of some sort.


Motion of the sun as observed from mercury

Both effects combined.

Day being longer than year would just have retrograde motion of the Sun on sky, but no direction change.

Variation of the distance alone happens on Earth, and we have no such effect.

But the combination of both factors, in the precise amount they have on Mercury, makes this effect happen.


Trisolar syzygy and it's effects on the planet

Is it just for the spoiler?

My guess is that the 3 suns aligned create a sufficient gravity field for the outermost parts - less well attached - of the planet (atmosphere, people, buildings) to be in the Roche Limit of the system, causing them to be sucked out spiraling inwards.

Here is a funny vid I found to illustrate:  https://www.youtube.com/watch?v=6e5yyIcq40o .

Hope this helps.


Singularities/ringularities and their properties

You need to be a bit cautious about statements like: A black hole contains a singularity at its center. It is a zero-dimensional point, and it's where all its mass is located. What you are referring to is a mathematical structure called the Schwarzschild metric. This is indeed a solution to the Einstein equations for a static black hole, but this particular solution takes an infinite time to form. So given that the universe is only a shade under 14 billion years old we can be confident that as I type this there are no Schwarzschild black holes in the universe.

Indeed, it is far from clear that a Schwarzschild black hole could ever form, even given infinite time, because black holes evaporate. This point is pursed in the question Why does Stephen Hawking say black holes don't exist?

Incidentally, the Schwarzschild black hole doesn't have all its mass at the centre. In fact it is a vacuum solution and contains no matter at all. The mass of the Schwarzschild black hole is actually a geometrical property called the ADM mass.

We run into the same problems with the spinning black hole. The structure with the ring singularity is the Kerr metric, and again while it's a perfectly valid solution to Einstein's equations, like the Schwarzschild metric it also takes an infinite time to form. Actually the Kerr metric is more troublesome still, because it is uncertain whether the structure is stable with respect to perturbations. It seems very likely that real collapsing stars would not form a structure resembling the Kerr metric. More precisely the region outside the event horizon would be well described by a Kerr metric, the region near the singularity would be different.

But if we put these doubts aside and return to what you asked, the answer is that in the Kerr metric the ring singularity really is a ring and not a collection of points.


How long after the Big Bang would CMB radiation have been between 273 and 373 K?

The temperature of the cosmic microwave background scales as the inverse of the cosmic scale factor $a$. i.e. When everything was at half the separation it is now, then the CMB was twice the (absolute) temperature. The scale factor in turn is reciprocally related to the redshift by $a/a_0 = (1 +z)^{-1}$, where $z$ is the redshift and $a_0$ is the present-day scale factor, usually taken to be 1.

From this we see that
$$T(z) = T_0 (1+z),$$
where $T(z)$ is the temperature at redshift $z$ at some time in the past and  $T_0 = 2.73$K is the temperature of the CMB now. For the range of temperatures you specify requires redshifts in the range $99< z< 136$.

Getting from a redshift to a time in the universe since the big bang is not so simple. The answer depends on what you take to be the "cosmological parameters" - i.e. the values of the cosmic matter density, the dark energy density and so on.

However, we can avoid looking "under the hood" and use a cosmology calculator. The one I have linked to is for a "flat" universe and has default values for what are currently good estimates for the matter density and present-day Hubble parameter. For the range of $z$ I found above, this corresponds to an age of between 10.8 and 17.3 million years after the big bang.

I guess you are perhaps thinking about these ideas that life could have been around about 15 million years after the big bang.


How would Special relativity explain past-present-future if thinking about 13-billion-light-years distanced objects

First off, if Earth were point B, and you were an observer at point A looking at it with the most magnificent telescope ever imagined, you would still not see the Earth, because it didn't exist 13 billion years ago.  I assume you picked 13 billion years because it is roughly the age of the universe, so you'd see the universe as it existed then, but that doesn't get you what I think you want.  I will instead pick 4.5 billion years ago (or objects A and B 4.5 billion light years apart), because then you will have an actual Sun and Earth to look at but long before life evolved.

We'll also wave our arms over the tracking software of your telescope being able to locate Sun and Earth in their orbits over the course of 4.5 billion years as seen from point B.

Yes.  You would have to wait 4.5 billion years to see the observer at point A looking back at you through his telescope.  You would now be looking at a cooling hunk of molten rock with no moon or oceans.
No.  If you waited 4.5 billion years and saw Observer A, he would have been dead for 4.5 billion years by the time you see him.  In fact, his Sun would likely be expanding to the point of burning his planet to a cinder if not engulfing it entirely.  But of course, you would have to wait another 4.5 billion years to see that.  You would be observing the photons that bounced off Observer A all that time ago and have been traveling ever since.  It is important to note that this is not him, and does not mean he still exists.

Hopefully this answers your question, though it doesn't have much to do with Special Relativity, it's still good blow-your-mind stuff.  It's just speed of light stuff which we really knew and measured (albeit inaccurately) long before Einstein.


This is an opinion based question and so I don't think there is an objective answer.  For example what constitutes a wealthy person?
However, in his book "Celestial Objects for Common Telescopes", first published in 1859, the author, Thomas Webb, writes: Instruments quite sufficient for the student's purpose are far less expensive than formerly; a trifling outlay will often procure them, of excellent quality, at second-hand
This suggests to me that telescopes had become reasonably available by the mid 19th C.


Why do most of the myths behind constellations originate from Greek?

Ptolemy was Greek.  He wrote an important book called the Almagest. In it, he lists and describes the constellations as used in Greece in the 4th century BC. Naturally, the Greeks used elements from Greek Mythology in their sky culture, just as Chinese sky culture uses elements from Chinese legend and myth.

Ptolemy's Almagest and Greek sky culture influenced the Hellenistic world, and through Rome, it influenced the whole of Western Europe.  Then through European expansion, it came to influence the whole world.

There are several additions to Ptolemy's system: The Southern Sky was divided into constellations by Europeans in the 15th century, and there are several additions to the Northern sky, such as Coma Berencies (Hair of Berenice II of Egypt) and Camelopardalis, the giraffe, (added in the 15th century)


Quantum Mechanics after the detection of Gravitational Waves

No more than the observation of light waves disproves quantum mechanics.

Light has properties of both a particle and a wave. At low energies, the particle nature of light is hard to detect: radio waves are made of photons, but individual radio wave photons are pretty hard to detect. I'm not sure that we have directly detected individual photons with energies below the infrared band.

Gravitational waves (probably) also have both a wave and a particle nature. The gravitational field is probably quantised. But at the frequencies and sensitivity at which LIGO operates, individual quanta cannot be measured. So this detection does not prove the ascendency of GR over QM.

If anything, understanding extreme events like black hole mergers might lead to a theoretical understanding of the quantum nature of gravity.


You can't, not with that information. However if you also have the date and time, you'll be good to go: there are plenty of sites in the web with this information, such as: RA and DEC to ALT and AZ


Why wasn't there any oxygen in the beginning of the Earth?

The 1200 C temperature is a big clue, given the auto-ignition temperatures of most "stuff". https://en.wikipedia.org/wiki/Autoignition_temperature

Any "free" oxygen would immediately "burn" with carbon and just about anything else, yes.


Is it possible that the Sun and all the nearby stars formed from the same nebula?

There are three main reasons why we can tell that local stars did not, for the most part, form from the same molecular cloud that the Sun formed from.
The first is that unless stars are born in a very tightly bound system such as a globular cluster (which the Sun is definitely not in), they will drift apart from their birth companions over time in slightly different orbits in the Milky Way galaxy. The Sun has gone around the center of the galaxy about twenty times since it was born; this is more than enough time for its initial cluster to become completely scrambled in azimuth (the angle in the plane of the galaxy). To see how this would work, imagine two stars with very similar orbits, one with a period of 200 million years and the other with a period of 210 million years. If they start off right next to each other, then after 2 billion years, the first star has made 10 complete orbits, while the second has made about 9.5 -- meaning it will now be on the other side of the galaxy from the first star.
You can also take the current velocities of nearby stars, and see that they can be rather different, which tells you they are not on very similar orbits. Alpha Centauri is moving about 20 km/s in our direction, while Barnard's star has a velocity in our direction of over 100 km/s (in both cases, they also have movement in perpendicular directions; they're not moving directly toward us). So these are stars which happen to be near each other now, but are on different orbits and therefore were almost certainly not near each other at any given time in the past.
The second reason is the one that David Hammen pointed out: stars born from the same clouds should have very similar chemical compositions ("metallicities" in astronomical parlance).
The third reason is that stars born from the same cloud should have the same age (to within a few million years, anyway), since molecular clouds tend to be disrupted by the star-formation process and don't keep forming stars for hundreds of millions or billions of years.
Looking at some of the very nearest stars: the Sun has what we define as "solar metallicity" and is about 4.6 billion years old. The stars of Alpha Centauri are slightly more metal-rich than the Sun and probably several hundred million years older. Barnard's Star is more metal-poor than the Sun (maybe only 1/3 the iron fraction), and about 5 billion years older. Sirius is significantly more metal-rich than the Sun (its iron fraction is about three times that of the Sun) and is only about 250 million years old.
So you can see that the Sun and the nearby stars are a heterogeneous group, and clearly not all born at the same time from the same patch of interstellar gas.


What would happen if a body were to fall into a neutron star?

No detailed calculations, but a qualitative answer: Depending on the trajectory of the impactor, the results will vary a bit, but it's clear, that the potential energy of the impactor will be transformed into a high amount of kinetic energy before the impact happens. The kinetic energy will then be transformed mainly into heat during the impact, transforming a substantial part of the mass of the impactor into x-rays and gamma rays.

The remnants of the impactor will be transformed into a plasma, with most of the electrons moving independently of their former nuclei, and dispersed mainly into the atmosphere (a thin layer of a few millimeters) of the neutron star. The energies will be high enough to trigger nuclear fusion as well as fission, together with other high-energy particle reactions. Part of the energy will be transformed into magnetic fields, which can also be very strong on neutron stars.

No much intermixing with the interior of the neutron star is to be expected in the first instant for small impactors due to the high inertia and density of the inner parts of the neutron star.

In some cases the impact could trigger the collapse of the neutron star into a black hole, depending of the mass of the neutron star, and the mass of the impactor.

More on the inner structure of neutron stars on Wikipedia.
("Matter falling onto the surface of a neutron star would be accelerated to tremendous speed by the star's gravity. The force of impact would likely destroy the object's component atoms, rendering all its matter identical, in most respects, to the rest of the star.")

More about the Chandrasekhar limit of neutron stars.


The temperature in the heliosphere is about one million Kelvin, lower (but still very hot) in the outer regions of the heliosphere, higher close to the sun.
But the density of the plasma is very low, so you wouldn't feel the heat (except close to the sun).

Within Earth's exosphere, reaching up to 10,000 km, the temperature is lower, roughly 1,000 to 1,500 C.

In interstellar space there exist hot (e.g. 10,000 K) and cold gas clouds.

Due to the very low density, hot and cooler fractions can penetrate each other, such that there doesn't need to be a uniquely defined temperature.

The large-scale average temperature of outer space should be 2.7 K (about -270.5 C), close to the CMB black body temperature.


Firstly, if you're planet spotting, don't worry too much about light pollution. The planets are some of the brightest objects in the sky and some (especially Jupiter) can easily be observed even with a full Moon - the full Moon (along with the Sun!) is the biggest contributor to light pollution!

Take a look at the list of brightest stars ( https://en.wikipedia.org/wiki/List_of_brightest_stars ), which also contains estimates for the brightness of the Sun, Moon and major planets. There aren't typically any stars brighter from Earth than Venus, Jupiter, Mars and Mercury and precious few brighter than Saturn. I'm going to suggest you probably have seen many of the planets - but just didn't recognise them.

+1 for Stellarium ( http://www.stellarium.org/en_GB/ ). It's free, intuitive and very visual to use. You can put in your local viewing location and it gives you a view for any time of the night, future or past. At the time of writing (23 July 2017), Saturn and Jupiter should be looking good for the Southern Hemisphere. This rotates throughout the year, and Stellarium will help with this.

Do a web search for "the sky at night in the southern hemisphere" and you'll find a number of examples of websites with highlights to look for when you get out.

Couple of final suggestions:

Do allow plenty of time to let your eyes adjust to the darkness - it takes me a good 20-30 minutes to get going. You'll see many more stars then
Do be aware that local conditions (houses / trees etc) might restrict visibility of things near the horizon. In any case, you find items over-head are much clearer
Refractors (yours included) come with an 'erecting prism'. Despite the name, the real benefit isn't that you see the image the right way up (that isn't really an issue in astronomy), the prism just allows you a more sensible and comfortable viewing position - you'll understand when you get going
Don't restrict yourself to planets. When you get going, learn about the deep sky objects too. For instance, the southern hemisphere has access to the famous Magellenic Clouds which we cannot see from the northern hemisphere!


Would dropping a white dwarf or a "still-hot" stellar core into a large planet or brown dwarf create a star?

The issue is not whether the dense core can fuse, but what fusion processes can occur on its surface. Remember that novas happen when gas accumulate on the surface of white dwarf stars: the high temperature and density is enough to trigger runaway fusion.
Hence this method, where you to magically make a dense core appear inside a gas giant or somehow drop it onto the core, would likely produce a nova effect. Fusion starts, heats up the hydrogen, this speeds up fusion and increases the temperature, and then the whole thing blows up. Likely not enough for a supernova, but not really creating a star as much as just burning up the planet.
The exception may be a low mass star core, where the gravitational gradient and temperature may be mild enough to allow gradual burning. Here unfortunately a lot depends on the assumed magic making the dumping happen, which presumably makes the answer ill defined.


What's the theoretical maximum density of a galaxy?

As a general rule, galaxies aren't very dense at all, though precise numbers are impossible, rough estimates can be made.

Mass of the Milky-way:  with it's dark matter halo, about 6 x 10^42 kg

Volume of the Milky-way (per Wikipedia) about 3.3 × 10^61 cubic meters, or, 3.3 x 10^52 cubic km.

That gives us a rough density of the milky way of about 1 kg for every 5 billion cubic km.   That's obviously not very dense.   There are probably denser galaxies out there and larger galaxies, but the overall density is going to be very low, even for the densest galaxies.   Space is, generally speaking, mostly empty.

Even in regions that are so called "densely packed with stars", if you measure the density in the traditional way, mass to volume, you end up with very low density, 1 kg per thousands if not millions of cubic km.   On earth, that density of air would essentially be a vacuum.


Is there a limit to how hot an object an get?

First, let's get a bit of background. "Absolute hot" is the concept that a maximum temperature exists. It describes your question exactly. For a long time, no one was able to figure out whether an absolute hot exists, but in the 20th century major revolutions in theoretical physics gave us answers.

"Absolute hot" isn't the name of the hottest temperature, but it's the concept that one exists. So what is our answer — is there a highest possible temperature that fits the concept of an "absolute hot"? Well, yes. But first we must talk about heat and temperature.

Photons act both like particles and waves. As we add more energy, the photon's wavelength decreases, and its frequency increases. Thus, the wavelength of the light emitted by hot objects generally depends on the temperature of the object. Hotter objects will emit more energetic photons with shorter wavelengths.

According to modern physics, a Planck length is the smallest meaningful length in the Universe (the reason for that is an entirely different question). If we keep raising the temperature of our object, nonstop, the wavelength of the photons it emits will decrease until it reaches a Planck length. Our object would reach a temperature called Planck temperature. That's about $1.417×10^{32} \; \mathrm{K}$.

Planck temperature is theoretically the hottest possible temperature. At that point, the object could not theoretically get any hotter, as the photon's wavelength cannot decrease beyond a Planck length.

But what happens if we were to add more energy to the object? Would it go beyond Planck temperature? Well...God knows. At that point, we wouldn't even call it temperature anymore. Nobody knows what exactly would happen, but it certainly wouldn't match the definition of temperature.


Is it possible for particles to be accelerated FTL inside BH travelling towards the singularity?

It's a little hard to follow the question.

The short answer is: No it doesn't move faster than light.

First off from the perspective of the outside observer, the particle doesn't reach the Schwartzchild radius, due to gravitational time dilation. From the viewpoint of the distant observer (the best kind to be when black holes are involved) the particle's clock slows to a stop as it nears the event horizon.

Your velocity is a relative and a local property, if you want to talk about the velocity you need to say what it is relative, and when black holes are involved you need to be careful about which metric you are measuring the velocity in. From the point of view of the infalling particle, it enters and crosses the event horizon. It may then be falling faster than the speed of light relative to people on the outside, but it is behind the event horizon, and can not return to them. It is not moving faster than light relative to any point which it can return to. So this doesn't break causality, nor does it allow for high-speed transport.

All that is certain is that in a short time (as the particle sees it) it will reach a singularity and then time and space will cease to exist for it, and all you are left with is mass.

Hadrons might become some kind of quark gluon plasma on their way in, but this doesn't make it lose mass, nor does it have any effect on the whether it moves faster or slower than light.


How far above the Earth's surface does interplanetary space begin?

It it wherever is convenient for the article you are writing. There is no single consenus definintion of "interplanetary space".  If you are in orbit around a planet then you are not in interplanetary space, if you are between planets, then you are.  But there is no substantial change in the matter filling space as you move from planetary orbit to interplanetary trajectory

So you can use any reasonable point that fits the article you happen now to be writing