<p>Exactly what is meant by &quot;Earth-like&quot; or &quot;habitable zone&quot; can vary from paper to paper. So the exact number of 1 in 5 depends on what those definitions are.</p>
<p>The basic statistic comes from analysis of <em>observed</em> exoplanets discovered by the transiting method - mainly by Kepler. The definition of &quot;Earth-like&quot; will be based on the radius of the exoplanet inferred from the depth of the transit (e.g. it might be <span class="math-container">$0.5 &lt; r/r_{\rm Earth} &lt; 2$</span>).</p>
<p>Of course, transiting planets are rare, so the fraction of stars for which a transiting &quot;Earth-like&quot; planet has been found in the &quot;habitable zone&quot; is <em>far</em> lower than 1 in 5 - given that Kepler found a few thousand exoplanetary candidates from a target list of a few hundred thousand stars, the observed &quot;Earth-like&quot; exoplanet fraction is <span class="math-container">$&lt;1$</span>%.</p>
<p>The key point is that the observational biases against the detection of such &quot;Earth-like&quot; planets are reasonably well understood and involve quite reasonable assumptions - e.g., we assume that the orientation of exoplanet orbital planes is random in space, so you can estimate what fraction of such exoplanets would actually transit.</p>
<p>As long as you have <em>some</em> sensitivity to the region of parameter space that you are interested in then you can apply some sort of forward-modelling approach, whereby you simulate a population of exoplanets with particular parameters, observed with the particular instrument you have (including all the sensitivity, noise properties, observation cadence etc.) and then see what fraction of the exoplanets are detected (or &quot;recovered&quot;). Hence you can then correct your raw observed frequency to a true frequency.</p>
<p>Relevant: <a href="https://physics.stackexchange.com/questions/633661/is-our-solar-system-really-that-odd/633693#633693">https://physics.stackexchange.com/questions/633661/is-our-solar-system-really-that-odd/633693#633693</a></p>

CC BY-SA 4.0
2021-06-10T16:35:54.157Z
You seem to know everything! :) Won't the orientations of the orbits lie in the plane of the galaxy (if the galaxy is flat)?
Deschele Schilder
CC BY-SA 4.0
2021-06-10T16:40:53.640Z
@Berbierium our solar system doesn't and there isn't any evidence for non-randomness. I believe there is a Q about this somewhere. See https://astronomy.stackexchange.com/questions/40277/do-the-axes-of-rotation-of-most-stars-in-the-milky-way-align-reasonably-closely https://astronomy.stackexchange.com/questions/21191/detection-of-exo-planets
ProfRob
CC BY-SA 4.0
2021-06-10T16:52:48.977Z
Thanks for the links. I understand that only a small fraction of planes will make it possible for us to detect the planets. The bigger the stars the more chance of seeing a planet pass between us and the star. Doesn't that mean we should observe no planets around most stars (assuming all planets to orbit in the same plane)?
Deschele Schilder
CC BY-SA 4.0
2021-06-10T16:55:47.407Z
@Barbierium Yes. There are a few thousand exoplanetary candidates in the Kepler dataset. Kepler observed a few *hundred* thousand stars. So the fraction of stars with an observed exoplanet is something like 1%.
ProfRob
CC BY-SA 4.0
2021-06-10T17:00:15.460Z
So that observation confirmes the idea that most planetary systems don't "spin" in alignment with the spin of the entire milky way? (I don't think planets outside the milky way have been found)
Deschele Schilder
CC BY-SA 4.0
2021-06-10T17:17:13.387Z
@Barbierium although the transit chance due to geometry goes up if the star is bigger, the transit depth goes *down* (since transit depth $\sim(R_p/R_*)^2$ and so it gets more difficult to detect above the noise (see e.g. [this explanation](https://lweb.cfa.harvard.edu/~avanderb/tutorial/tutorial.html)). This is why the majority of the smallest planets found by transit are around small M dwarf stars
astrosnapper
CC BY-SA 4.0
2021-06-10T16:27:48.333Z
2021-06-10T16:58:06.910Z
2021-06-10T16:58:06.910Z
ProfRob
<p>When reading the question about the first use of the term exoplanet (about which Giordano Bruno and Isaac Newton already speculated but they didn't use that term for them, I think), I searched a surfed a bit along and found this on Wikipedia:</p>
<blockquote>
<p>An exoplanet or extrasolar planet is a planet outside the Solar System. In several cases, multiple planets have been observed around a star. About 1 in 5 Sun-like stars have an &quot;Earth-sized&quot; planet in the habitable zone.</p>
</blockquote>
<p>I'm not sure how this estimate is made. Is it based on observation? Is there one Earth-like planet observed for every five stars? That is, planets with more or less the same mass as the Earth, orbiting at about the same distance from the star as we orbit the sun? Is it based on a calculation?<br />
Are planets that have a higher mass and circle around a higher mass star considered as Earth-like too (the &quot;only&quot; difference being that a higher gravity is present)?</p>

<exoplanet>
Why does one presume that there is at least one Earth-like exoplanet around one in five stars?
Deschele Schilder
# Why does one presume that there is at least one Earth-like exoplanet around one in five stars?

(Asked by: username_0 on 2021-06-10)

When reading the question about the first use of the term exoplanet (about which Giordano Bruno and Isaac Newton already speculated but they didn't use that term for them, I think), I searched a surfed a bit along and found this on Wikipedia:

> An exoplanet or extrasolar planet is a planet outside the Solar System. In several cases, multiple planets have been observed around a star. About 1 in 5 Sun-like stars have an "Earth-sized" planet in the habitable zone.

I'm not sure how this estimate is made. Is it based on observation? Is there one Earth-like planet observed for every five stars? That is, planets with more or less the same mass as the Earth, orbiting at about the same distance from the star as we orbit the sun? Is it based on a calculation?  
Are planets that have a higher mass and circle around a higher mass star considered as Earth-like too (the "only" difference being that a higher gravity is present)?

**Tags:** exoplanet


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## 1 answers

### Answer by username_1 on 2021-06-10. Score: 4

Exactly what is meant by "Earth-like" or "habitable zone" can vary from paper to paper. So the exact number of 1 in 5 depends on what those definitions are.

The basic statistic comes from analysis of *observed* exoplanets discovered by the transiting method - mainly by Kepler. The definition of "Earth-like" will be based on the radius of the exoplanet inferred from the depth of the transit (e.g. it might be $0.5 < r/r\_{\rm Earth} < 2$).

Of course, transiting planets are rare, so the fraction of stars for which a transiting "Earth-like" planet has been found in the "habitable zone" is *far* lower than 1 in 5 - given that Kepler found a few thousand exoplanetary candidates from a target list of a few hundred thousand stars, the observed "Earth-like" exoplanet fraction is $<1$%.

The key point is that the observational biases against the detection of such "Earth-like" planets are reasonably well understood and involve quite reasonable assumptions - e.g., we assume that the orientation of exoplanet orbital planes is random in space, so you can estimate what fraction of such exoplanets would actually transit.

As long as you have *some* sensitivity to the region of parameter space that you are interested in then you can apply some sort of forward-modelling approach, whereby you simulate a population of exoplanets with particular parameters, observed with the particular instrument you have (including all the sensitivity, noise properties, observation cadence etc.) and then see what fraction of the exoplanets are detected (or "recovered"). Hence you can then correct your raw observed frequency to a true frequency.

Relevant: <https://physics.stackexchange.com/questions/633661/is-our-solar-system-really-that-odd/633693#633693>

> **Comments:**
> **username_0**: You seem to know everything! :) Won't the orientations of the orbits lie in the plane of the galaxy (if the galaxy is flat)?  
> **username_1**: @Berbierium our solar system doesn't and there isn't any evidence for non-randomness. I believe there is a Q about this somewhere. See https://astronomy.stackexchange.com/questions/40277/do-the-axes-of-rotation-of-most-stars-in-the-milky-way-align-reasonably-closely https://astronomy.stackexchange.com/questions/21191/detection-of-exo-planets  
> **username_0**: Thanks for the links. I understand that only a small fraction of planes will make it possible for us to detect the planets. The bigger the stars the more chance of seeing a planet pass between us and the star. Doesn't that mean we should observe no planets around most stars (assuming all planets to orbit in the same plane)?  
> **username_1**: @Barbierium Yes. There are a few thousand exoplanetary candidates in the Kepler dataset. Kepler observed a few *hundred* thousand stars. So the fraction of stars with an observed exoplanet is something like 1%.  
> **username_0**: So that observation confirmes the idea that most planetary systems don't "spin" in alignment with the spin of the entire milky way? (I don't think planets outside the milky way have been found)  
> **username_2**: @Barbierium although the transit chance due to geometry goes up if the star is bigger, the transit depth goes *down* (since transit depth $\sim(R_p/R_*)^2$ and so it gets more difficult to detect above the noise (see e.g. [this explanation](https://lweb.cfa.harvard.edu/~avanderb/tutorial/tutorial.html)). This is why the majority of the smallest planets found by transit are around small M dwarf stars  

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