<p>For orbiting objects, gravitational wave intensity depends on the second time derivative of the quadrupole moment of an isolated system's stress–energy tensor (which for the wimpy objects in our vicinity is proportional to the mass times the line of sight acceleration) and drop off with the distance. So you can easily estimate the GW intensity of any object.  Hint: It's <em>small</em> for nearby objects.</p>

<p>As requested, I have tried to estimate the GW amplitude and I found the numbers somewhat surprising.  I looked at the Moon, Jupiter, Io, the LIGO neutron star and a pair of supermassive BHs if they were at the Galactic center.</p>

<p>I got the mass of each object in Suns, the orbital radius in miles, the orbital period in years and the distance in AU.  The angular acceleration is computed as r * omega<sup>2</sup>. Multiply by mass to get GW radiation at source. Divide by distance to get GW amplitude observed at Earth. (All units relative and arbitrary.)</p>

<pre><code>Object             Acceleration   Mass*Acceleration  Est. amplitude
Moon               3 x 10**7      1                  4 x 10**2
Jupiter            3 x 10**6      3 x 10**3          7 x 10**2
Io                 1 x 10**10     5 x 10**2          1 x 10**2
LIGO Neutron star  1 x 10**19     3 x 10**16         4 x 10**6
Supermassive BHs   1 s 10**9      2 x 10**15         3 x 10**6
</code></pre>

<p>(The supermassive BH numbers are really quite arbitrary, since you can assume any separation you like and pretty much any mass.  I picked 1 AU and 1,000,000 suns mass.  You can easily get much larger numbers, but the frequency will typically be too low to be seen by LIGO.)  </p>

<p>The other <strong>really important</strong> thing to remember is that in spite of Io being about as bright as the sources LIGO <em>has</em> observed, the frequency of Io's radiation is about 10<sup>-5</sup> Hz. LIGO is only really sensitive in the 10-1000Hz range and has no chance at all of ever seeing IO or Jupiter or the Moon or even a pair of supermassive BHs that are not in the last milliseconds of merger.  If eLISA gets built, it can probably see at least some supermassivs BH pairs.</p>

CC BY-SA 4.0
2018-06-05T13:39:46.573Z
GW detectors are sensitive to wave amplitude which falls as the reciprocal of distance.
ProfRob
CC BY-SA 4.0
2018-06-05T15:24:05.170Z
*small* and *wimpy* are kind of vague terms in this context:  I know there is a widespread confusion (that appears to be reflected in this question) that things like tides are caused by gravity waves from the sun and the moon.  This answer might clear that up with more finality if someone that could do the math compared the wave amplitudes.
antlersoft
CC BY-SA 4.0
2018-06-05T17:38:01.227Z
@antlersoft, unless you're referring to **wimps**  https://en.wikipedia.org/wiki/Weakly-interacting_massive_particles
Carl Witthoft
CC BY-SA 4.0
2018-06-05T18:20:12.437Z
That gives a very deep idea of gravity wave topology, i'm surprised that the moon doesn't provide the highest amplitude waves,  if the moon is at the zenith or the antizenith,  it would generate the loudest waves.  Perhaps a gravity interferometer would have to be a different size to see that kind of wavelength,  like a radio antenna?
bandybabboon
CC BY-SA 4.0
2018-06-05T12:18:59.080Z
2018-06-05T20:48:33.740Z
2018-06-05T20:48:33.740Z
Mark Olson
<p>Now that we know that gravity waves exist,  we can consider to design a new unit of measurement,  i.e.  deciGravs (from dB) and we can predict what the backround noise of dG's is locally and in space. </p>

<p>Consider a theoretical high-res LIGO that can graph gravity waves here and far away,  we can ffwd the record to represent the dG's at human timeframes. </p>

<p>What are the loudest local waves? Can we see the moon as the loudest local wave,  followed by other planets and moons,  are local bodies much louder than local bh waves? </p>

<p>There is an expected 3D wave map type locally and in deep space that we can model with graphical animations? Can we draw it easily in 2D/3Dusing 5 lines of code for every body and lots of processing?</p>

<p>Perhaps it makes sense to define a frequency chart of dG's and astroHz and a bit like the electromagnetic waves,  and chart gravity-waves,  amplitude and frequency trends and types?</p>

<p>Perhaps supernovas and solar flares and many background waves appear on graviCharts.  Can we know what graviCharts and backround noise of gravity resembles here and far away?</p>

<gravitational-waves>
What does gravity-wave noise resemble locally?
bandybabboon
# What does gravity-wave noise resemble locally?

(Asked by: username_0 on 2018-06-05)

Now that we know that gravity waves exist, we can consider to design a new unit of measurement, i.e. deciGravs (from dB) and we can predict what the backround noise of dG's is locally and in space.

Consider a theoretical high-res LIGO that can graph gravity waves here and far away, we can ffwd the record to represent the dG's at human timeframes.

What are the loudest local waves? Can we see the moon as the loudest local wave, followed by other planets and moons, are local bodies much louder than local bh waves?

There is an expected 3D wave map type locally and in deep space that we can model with graphical animations? Can we draw it easily in 2D/3Dusing 5 lines of code for every body and lots of processing?

Perhaps it makes sense to define a frequency chart of dG's and astroHz and a bit like the electromagnetic waves, and chart gravity-waves, amplitude and frequency trends and types?

Perhaps supernovas and solar flares and many background waves appear on graviCharts. Can we know what graviCharts and backround noise of gravity resembles here and far away?

**Tags:** gravitational-waves


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## 1 answers

### Answer by username_1 on 2018-06-05. Score: 1

For orbiting objects, gravitational wave intensity depends on the second time derivative of the quadrupole moment of an isolated system's stress–energy tensor (which for the wimpy objects in our vicinity is proportional to the mass times the line of sight acceleration) and drop off with the distance. So you can easily estimate the GW intensity of any object.  Hint: It's small for nearby objects.
As requested, I have tried to estimate the GW amplitude and I found the numbers somewhat surprising.  I looked at the Moon, Jupiter, Io, the LIGO neutron star and a pair of supermassive BHs if they were at the Galactic center.
I got the mass of each object in Suns, the orbital radius in miles, the orbital period in years and the distance in AU.  The angular acceleration is computed as r * omega2. Multiply by mass to get GW radiation at source. Divide by distance to get GW amplitude observed at Earth. (All units relative and arbitrary.)
Object             Acceleration   Mass*Acceleration  Est. amplitude
Moon               3 x 10**7      1                  4 x 10**2
Jupiter            3 x 10**6      3 x 10**3          7 x 10**2
Io                 1 x 10**10     5 x 10**2          1 x 10**2
LIGO Neutron star  1 x 10**19     3 x 10**16         4 x 10**6
Supermassive BHs   1 s 10**9      2 x 10**15         3 x 10**6

(The supermassive BH numbers are really quite arbitrary, since you can assume any separation you like and pretty much any mass.  I picked 1 AU and 1,000,000 suns mass.  You can easily get much larger numbers, but the frequency will typically be too low to be seen by LIGO.)  
The other really important thing to remember is that in spite of Io being about as bright as the sources LIGO has observed, the frequency of Io's radiation is about 10-5 Hz. LIGO is only really sensitive in the 10-1000Hz range and has no chance at all of ever seeing IO or Jupiter or the Moon or even a pair of supermassive BHs that are not in the last milliseconds of merger.  If eLISA gets built, it can probably see at least some supermassivs BH pairs.

> **Comments:**
> **username_2**: GW detectors are sensitive to wave amplitude which falls as the reciprocal of distance.  
> **username_3**: *small* and *wimpy* are kind of vague terms in this context:  I know there is a widespread confusion (that appears to be reflected in this question) that things like tides are caused by gravity waves from the sun and the moon.  This answer might clear that up with more finality if someone that could do the math compared the wave amplitudes.  
> **username_4**: @username_3, unless you're referring to **wimps**  https://en.wikipedia.org/wiki/Weakly-interacting_massive_particles  
> **username_0**: That gives a very deep idea of gravity wave topology, i'm surprised that the moon doesn't provide the highest amplitude waves,  if the moon is at the zenith or the antizenith,  it would generate the loudest waves.  Perhaps a gravity interferometer would have to be a different size to see that kind of wavelength,  like a radio antenna?  

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