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This note is primarily based on Why We Haven't Found Any Earth-Like Planets by Cool Worlds, but if I remember correctly, also contains references I found elsewhere (and don't seem to have properly documented, sorry!). The tl;dr is that we overestimated how easy they would be to find, and then adjusted our definition instead of acknowledging this fault.
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Why We Haven't Found Any Earth-Like Planets
There have been many attempts to estimate values of Eta-Earth, but these are confused by the varying definitions used. I made a graph describing a handful of them, sorted by publication date:
Eta-Earth Estimated Values.png:
Using a wisdom of the crowd approach, the average estimate is 30.218% (+19.87% -6.183%) planets per star (between 24.035% and 50.088%).
Kepler's mission assumptions:
- All star systems have at least one planet.
- In order to see an earth-like planet orbiting a G-type star at a habitable range (based on earth's solar flux), the ecliptic has to pass between the parent star and us. 1/200th are presumed to be edge-on to us.
- At least 170,000 stars would need to be observed to find 50 earth-like planets in habitable zones. Note: This estimate is not limiting us to G-type stars.
- 43 of which are: 6 planets around G2 stars, 7 around G7, 14 around K2, 16 around K7
- The missing 7? Possibly originally thought to be around F7 stars, but later believed unlikely to be seen.
- Additionally, 60 should have been detected around M2 stars, and 7 around M7 stars.
- That's 110 total detections expected.
- Earth-like planets were defined to have a radius 0.9 < R⨂ < 1.2 and a semi-major axis 0.8 AU < a < 1.2 AU.
As of 2022-02-19, there are 7 out of 530,506 observations that match the earth-like planet criteria. One of these is confirmed: Kepler-296 e. Note: In the source video, G-type stars are the only candidates looked at (leading to 3 candidates, all of which are unlikely to be accurate), but I am using all stars with the same approximate solar flux.
(PCM: per cent mille, thousandth of a percent)
0.0647% (64.7 pcm) of observations were expected to return an earth-like planet. 0.00132% (1.32 pcm) of observations did. Assuming we re-calculate what we should expect based on what is now known - the stellar background interference (stellar noise) is much higher than what was expected, we should have seen 13 earth-like exoplanets, or 0.00765% (7.65 pcm). Notice that this expectation is still 580% higher than what was actually observed.
Eta-Earth (ηE, sometimes presented as nE or ηE) is an extremely difficult to define term, because scientists keep redefining it instead of sticking to a consistent definition.
- One of the loosest definitions is used in Drake's Equation: how many planets that support life exist per star with planets. (Most definitions are based on all stars instead of just those with planets.)
- One of the tightest definitions was used in the Kepler mission (above): how many planets with a radius 0.9 < R⨂ < 1.2 and a semi-major axis 0.8 AU < a < 1.2 AU exist per (G-type only?) star.
Sources
- Why We Haven't Found Any Earth-Like Planets by Cool Worlds
- NASA Exoplanet Archive KOI Cumulative Table of Kepler exoplanets
- Eta-Earth Estimated Values
- Accounting for Multiplicity in Calculating Eta Earth by Zink & Hansen (local copy)