<p>This is a partial answer. It is partial because this is an active area of research, with this very topic as one of the prime questions, second I've only chased down the estimates from one method; microlensing, because this method is not biased toward large (in size and mass) planets in close orbits around small stars.</p>

<p>The microlensing method is biased toward more massive planets in Jupiter like orbits i.e. cold planets. It is biased toward distant planets about stars much closer toward the galactic center. This is important because stars there have lower concentrations of heavy elements need to make planets. It is equally sensitive to planets round all sorts of stars, and even free floating planets. It can detect down to Earth mass planets.</p>

<p>Here is a link to a technical summary of the method. The part you are most interested in is section 4.1.3 pages 23. <a href="https://www.mdpi.com/2076-3263/8/10/365/pdf-vor" rel="noreferrer">Microlensing Searches for Exoplanets Yiannis Tsapras</a>
This poster paper has a summary plot Fig 3 of planet occurrence rates from various methods <a href="http://www.mpia.de/homes/ppvi/posters/2K018.pdf" rel="noreferrer">Poster: Planet frequency from microlensing observations Arnaund Caasan</a>
There is also a link to an archive of papers on the subject: <a href="https://exoplanetarchive.ipac.caltech.edu/docs/occurrence_rate_papers.html" rel="noreferrer">NASA archive: Planet Occurrence Rate Papers</a></p>

<p>I do a quick summary of the main results: (microlensing perspective).
Estimating the biases, combined with actual detections it is possible to estimate (or put limits on) the numbers of planets and how theoccurence depends on mass, distance from star.
Snow line == distance from star where water remains frozen. In our solar system it is between Mars and Jupiter. Jupiter's moons have lots of ice. Dimmer stars this is closer in.
1 AU = Earth-Sun distance</p>

<p>Number of planets beyond snow line (Jupiter and beyond in our solar system) is 7 times greater than close in hot planets. In the distance range 0.5 to 10 Au of 20% of stars have Jupiters. 50% have Neptunes, 60% have super earths. There are many stars with more than one planet. So there is about one planet for every star in the galaxy. At least!. About 1/6th of stars with planets have a solar analog (massive planets like Jupiter and Saturn with room for small rocky planets close in). </p>

CC BY-SA 4.0
2018-12-21T05:20:30.280Z
2018-12-21T05:20:30.280Z
TazAstroSpacial
<p>As far as I've been able to determine, it appears there are some significant  limitations on our ability to detect exo-planets that are below certain sizes or beyond certain distances from their stars.  </p>

<p>It seems that Uranus and Neptune are about as small as we can detect unless the planet is relatively close to its star, and Earth is near the lower size limit we can detect, regardless of proximity to the star.   </p>

<p>In other words, our bias toward detecting large planets, and planets close to their stars, means I have been able to find reasonably good data regarding how many of those kinds of planets are generally present in a system.  But since we can't seem to tell (by direct observation) how many small planets are generally present in a system, or how many planets are present that are just too far from their star for us to detect, I'm struggling to find data regarding how many plants of those types are common in planetary systems.  </p>

<p>For example: our system has 8 planets, 4 rocky, 2 gas giants, 2 ice giants.  But chances are that if we were observing (with current technology) our own Solar system from some other solar system, we'd probably only see 2 to 6 of them.  We'd almost certainly see Jupiter and Saturn, and we'd almost certainly NOT see Mercury or Mars (they're just too small), Venus and Earth "might be" close enough to the sun for us to see them even though they are on the small end of what we can detect, and Uranus and Neptune also "might be" detectable, even though they are small-ish for their distance from the sun.  </p>

<p>My specific question:  <strong>How many planets are in a 'normal' or 'average' planetary system, according to humanity's best scientific theories available so far?</strong>(beyond what we can simply detect.)  In other words, where can I find <strong>reasonable scientific research data sets, models, estimates, theories, evidence, etc.</strong>, that describe the likelihood of "undetectable" (or very hard to detect) planets being present in a planetary system?</p>

<p>This is my first question on Astronomy stackexchange, so please be gentle, but don't hesitate to provide constructive criticism if I'm doing anything wrong.</p>

CC BY-SA 4.0
2018-11-14T17:05:53.557Z
As you note, all our planet detection methods are biased towards finding large planets in close orbits around small stars.  Solar system like ours, with a medium-sized star, smallish planets in ~ 1 year orbits and large planets in distant orbits, are much harder to identify (impossible on the timescales we have been observing so far).  We know that solar systems unlike ours are reasonably common, but AFAIK we can't really say that solar systems like ours aren't even more common.
antlersoft
CC BY-SA 4.0
2018-11-14T21:21:56.487Z
@RobJeffries  Thanks for the heads up.  Most of the question marks are in an effort to explain what type of information I'm hoping for, they are not intended to be separate questions in and of themselves.  I've re-arranged the post, and added a final summary with an attempt at wording the actual single question.  If you have suggestions for additional improvement to the question, please let me know.
Harthag
CC BY-SA 4.0
2018-11-14T21:38:23.007Z
RobJeffries is right. You might not be aware of this, but this is an extremely wide range of topics. Every detection methods has other biases to discuss those would take a whole lecture. Better google "exoplanet detection bias correction". For example, to derive and correct the transit bias is relatively simple, while already for radial velocity planets it's not.
AtmosphericPrisonEscape
CC BY-SA 4.0
2018-11-14T22:32:32.820Z
@AtmosphericPrisonEscape  Wow, that was an incredibly helpful search suggestion.  A couple of good examples from that search, in the form of an answer, would probably have been (and still might be) the answer I accepted
Harthag
CC BY-SA 4.0
2018-11-14T22:32:43.200Z
@RobJeffries  better?
Harthag
CC BY-SA 4.0
2018-11-15T08:07:31.130Z
@RobJeffries In the current form of the question, I see only a single one. Although it might be considered too broad, I think it is not yet (what the currently accepted most realistic estimation say, I think it is enough clear).
peterh
CC BY-SA 4.0
2018-11-22T05:09:15.050Z
It always bothers me that only positive results are published. Sometimes "null results" where we could have detected something can be helpful to the understanding also.
Jack R. Woods
CC BY-SA 4.0
2018-11-26T19:17:40.253Z
@JackR.Woods: You have to distinguish between scientific and journalistic publication. In the scientific literature null results are published, even the comparison of detection biases to what theory would say would be impossible without those.
AtmosphericPrisonEscape
CC BY-SA 4.0
2018-11-27T23:36:14.757Z
I think there's two approaches to making a very rough estimate.   The majority of solar systems that Kepler has gotten a good look at are close, based on where most of the planets have been found.  https://en.wikipedia.org/wiki/Exoplanet#/media/File:Distribution_of_exoplanets_by_distance.png  If you wanted to download from here: https://en.wikipedia.org/wiki/List_of_exoplanets_discovered_using_the_Kepler_spacecraft#Table to a spreadsheet and filter by distance you might get a rough idea of a low estimate.   I'd make this an answer if my excel was working and if I had the time work it out.
userLTK
<astrophysics><observational-astronomy><exoplanet><planetary-formation>
Estimates for "undetectable" planets in extra-solar systems
Harthag
# Estimates for "undetectable" planets in extra-solar systems

(Asked by: username_0 on 2018-11-14)

As far as I've been able to determine, it appears there are some significant limitations on our ability to detect exo-planets that are below certain sizes or beyond certain distances from their stars.

It seems that Uranus and Neptune are about as small as we can detect unless the planet is relatively close to its star, and Earth is near the lower size limit we can detect, regardless of proximity to the star.

In other words, our bias toward detecting large planets, and planets close to their stars, means I have been able to find reasonably good data regarding how many of those kinds of planets are generally present in a system. But since we can't seem to tell (by direct observation) how many small planets are generally present in a system, or how many planets are present that are just too far from their star for us to detect, I'm struggling to find data regarding how many plants of those types are common in planetary systems.

For example: our system has 8 planets, 4 rocky, 2 gas giants, 2 ice giants. But chances are that if we were observing (with current technology) our own Solar system from some other solar system, we'd probably only see 2 to 6 of them. We'd almost certainly see Jupiter and Saturn, and we'd almost certainly NOT see Mercury or Mars (they're just too small), Venus and Earth "might be" close enough to the sun for us to see them even though they are on the small end of what we can detect, and Uranus and Neptune also "might be" detectable, even though they are small-ish for their distance from the sun.

My specific question: **How many planets are in a 'normal' or 'average' planetary system, according to humanity's best scientific theories available so far?**(beyond what we can simply detect.) In other words, where can I find **reasonable scientific research data sets, models, estimates, theories, evidence, etc.**, that describe the likelihood of "undetectable" (or very hard to detect) planets being present in a planetary system?

This is my first question on Astronomy stackexchange, so please be gentle, but don't hesitate to provide constructive criticism if I'm doing anything wrong.

**Tags:** astrophysics, observational-astronomy, exoplanet, planetary-formation

> **Comments:**
> **username_1**: As you note, all our planet detection methods are biased towards finding large planets in close orbits around small stars.  Solar system like ours, with a medium-sized star, smallish planets in ~ 1 year orbits and large planets in distant orbits, are much harder to identify (impossible on the timescales we have been observing so far).  We know that solar systems unlike ours are reasonably common, but AFAIK we can't really say that solar systems like ours aren't even more common.  
> **username_0**: @RobJeffries  Thanks for the heads up.  Most of the question marks are in an effort to explain what type of information I'm hoping for, they are not intended to be separate questions in and of themselves.  I've re-arranged the post, and added a final summary with an attempt at wording the actual single question.  If you have suggestions for additional improvement to the question, please let me know.  
> **username_2**: RobJeffries is right. You might not be aware of this, but this is an extremely wide range of topics. Every detection methods has other biases to discuss those would take a whole lecture. Better google "exoplanet detection bias correction". For example, to derive and correct the transit bias is relatively simple, while already for radial velocity planets it's not.  
> **username_0**: @username_2  Wow, that was an incredibly helpful search suggestion.  A couple of good examples from that search, in the form of an answer, would probably have been (and still might be) the answer I accepted  
> **username_0**: @RobJeffries  better?  
> **username_3**: @RobJeffries In the current form of the question, I see only a single one. Although it might be considered too broad, I think it is not yet (what the currently accepted most realistic estimation say, I think it is enough clear).  
> **username_4**: It always bothers me that only positive results are published. Sometimes "null results" where we could have detected something can be helpful to the understanding also.  
> **username_2**: @JackR.username_4: You have to distinguish between scientific and journalistic publication. In the scientific literature null results are published, even the comparison of detection biases to what theory would say would be impossible without those.  
> **username_5**: I think there's two approaches to making a very rough estimate.   The majority of solar systems that Kepler has gotten a good look at are close, based on where most of the planets have been found.  https://en.wikipedia.org/wiki/Exoplanet#/media/File:Distribution_of_exoplanets_by_distance.png  If you wanted to download from here: https://en.wikipedia.org/wiki/List_of_exoplanets_discovered_using_the_Kepler_spacecraft#Table to a spreadsheet and filter by distance you might get a rough idea of a low estimate.   I'd make this an answer if my excel was working and if I had the time work it out.  

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## 1 answers

### Answer by username_6 on 2018-12-21. Score: 5

This is a partial answer. It is partial because this is an active area of research, with this very topic as one of the prime questions, second I've only chased down the estimates from one method; microlensing, because this method is not biased toward large (in size and mass) planets in close orbits around small stars.

The microlensing method is biased toward more massive planets in Jupiter like orbits i.e. cold planets. It is biased toward distant planets about stars much closer toward the galactic center. This is important because stars there have lower concentrations of heavy elements need to make planets. It is equally sensitive to planets round all sorts of stars, and even free floating planets. It can detect down to Earth mass planets.

Here is a link to a technical summary of the method. The part you are most interested in is section 4.1.3 pages 23. [Microlensing Searches for Exoplanets Yiannis Tsapras](https://www.mdpi.com/2076-3263/8/10/365/pdf-vor)
This poster paper has a summary plot Fig 3 of planet occurrence rates from various methods [Poster: Planet frequency from microlensing observations Arnaund Caasan](http://www.mpia.de/homes/ppvi/posters/2K018.pdf)
There is also a link to an archive of papers on the subject: [NASA archive: Planet Occurrence Rate Papers](https://exoplanetarchive.ipac.caltech.edu/docs/occurrence_rate_papers.html)

I do a quick summary of the main results: (microlensing perspective).
Estimating the biases, combined with actual detections it is possible to estimate (or put limits on) the numbers of planets and how theoccurence depends on mass, distance from star.
Snow line == distance from star where water remains frozen. In our solar system it is between Mars and Jupiter. Jupiter's moons have lots of ice. Dimmer stars this is closer in.
1 AU = Earth-Sun distance

Number of planets beyond snow line (Jupiter and beyond in our solar system) is 7 times greater than close in hot planets. In the distance range 0.5 to 10 Au of 20% of stars have Jupiters. 50% have Neptunes, 60% have super earths. There are many stars with more than one planet. So there is about one planet for every star in the galaxy. At least!. About 1/6th of stars with planets have a solar analog (massive planets like Jupiter and Saturn with room for small rocky planets close in).


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