Exoplanet Stats

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In another thread, Pale blue dot thread, the catalog presented from another paper, here, presents an extensive list of exoplanets in the HZs (both OHZ and CHZ). The OHZ is the Optimistic zone that extends to an Early Venus position to allow consideration of exoplanets that may have once had liquid water, I think. It also extends to a Mars for the outer OHZ.

This broadens the HZ, of course, so more exoplanets will be found.

One area I would like explanation is that the list is based on extensive formulations done in 2014 where the Early Venus and the Mars parameters were limited to a mass of 1 Earth. The coefficients vary as mass changes, and the list includes very massive objects that would seem to me, at least, not be ones that could be used for those limited formulations.

With that in mind, I elected to simply adjust (fudge) the inner and outer zones a little but limit the exoplanet mass to under 13 Earth masses. As noted in a prior post, I also tweaked their 2017 Radius => Mass equation to fit today's better data. This is important since their HZ formulae require both radius and mass. I could extend the list to the more Jupiter-like exoplanets, as they did, but I don't have reliable coefficients, nor do I think there is great hope for an Earth-like Jupiter-mass exoplanets to be found, for that matter.]

Notice that their method produces only 4 HZ exoplanets with reasonable masses.

View: https://imgur.com/LUhhw7C
 
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As of today (10/25), the count is 5225, with an extra one found in the HZ (115 total), but it doesn't fall into the selected size of 0.5 to 1.8 Earth Radii. So the table of results above is the same, essentially.
 
There is a more sophisticated method for calculating the HZ, as mentioned earlier. I can't say if it is actually more reliable in predicting HZ planets, but I hope to be able to present all reasonable models for everyone's consideration. Better telescopes, especially the JWST, should tweak these models.

Notice how there are now more Earth-sized exos in this model than shown before. This is a corrected model. I found an incorrect mass multiplier in my program, which is now corrected.

The green highlight are the exoplanets about the size of Earth.

The percentages shown in the 2nd column are where the exoplanet is aligned from the middle of the HZ. A 0% value means it is in the middle of the HZ. A negative percentage means it is closer to the star from the model (hence a little hotter).

View: https://imgur.com/RwVelrh
 
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Helio, the results and data are very interesting. I would be interested in going through and using some of this data on my website and of course if I do I would credit you for anything I use.

Being an avid astrophotgrapher I wonder if exoplanets are completely beyond my reach in photographic terms. I think so.
 
Helio, the results and data are very interesting. I would be interested in going through and using some of this data on my website and of course if I do I would credit you for anything I use.
There is no need to credit me for my use of the free exoplanet catalogs. If you have Excel, I can send you my programs (vba), which allows you to adjust variables such as planet size. Just send me your email in my private message.

Being an avid astrophotgrapher I wonder if exoplanets are completely beyond my reach in photographic terms. I think so.
They are too far awayand too small for even most large scopes.

At least one possible amateur endeavor exists. The new scopes, like the JWST, can tickle the exoplanet spectrum out of the star’s spectrum. This exo spectrum will reveal the exo’s color if someone were to go to the trouble to use it. I invented a device (asterochromograph) that takes a reference white light and adjust its spectrum to the given exo’s spectrum by using a prism and a mask. I never completed building it as there was very little data at the time, and not much interest in it back then.

The color of exo’s change with their rotation. This would reveal a water world to have continents, like Earth.
 
The real magic will happen when we can build telescopes large enough to see fauna & cities? on exoplanets. Until then this is great! Thanks for sharing

This is quite a ways off. The nearest star is 4 light years away. If we wanted to make a telescope that could resolve a city, say 100 km across, using visible light at 500 nm, the mirror would have to be 200 km in diameter.

Four light years is 4e16 meters. A 100,000 meter object at that distance subtends an angle of 100,000 divided by 4e16 or 2.5e-12 radians.

Mirror diameter = wavelength divided by angle

Diameter = 500e-9 / 2.5e-12 = 200 kilometers

This would best be done with a number of smaller mirrors forming an interferometer. We currently have visible light interferometers at 85 m (Keck) and 86 m (Palomar) with plans for one of 400 meters. 200,000 meters is a long way off.
 
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This is quite a ways off. The nearest star is 4 light years away. If we wanted to make a telescope that could resolve a city, say 100 km across, using visible light at 500 nm, the mirror would have to be 200 km in diameter.

Four light years is 4e16 meters. A 100,000 meter object at that distance subtends an angle of 100,000 divided by 4e16 or 2.5e-12 radians.

Mirror diameter = wavelength divided by angle

Diameter = 500e-9 / 2.5e-12 = 200 kilometers

This would best be done with a number of smaller mirrors forming an interferometer. We currently have visible light interferometers at 85 m (Keck) and 86 m (Palomar) with plans for one of 400 meters. 200,000 meters is a long way off.
Yes. There was a recent article of a space-based interferometer that would have incredible resolution, if it could actually work.
 
The real magic will happen when we can build telescopes large enough to see fauna & cities? on exoplanets. Until then this is great! Thanks for sharing
There was a new instrument design that would allow astronomers to see color variations for any exoplanet as they rotated. Thus, oceans and lands would be revealed, but not with any great resolution. It's called the asterochromograph, which was originally designed to help determine star colors, especially the Sun's.

Astronomers can, amazingly, tickle out the spectrum of an orbiting planet from the spectrum of the star. But each spectrum will produce a net color, so as the planet rotates and exposes more land & water, the color will shift.

It's likely that the better plan is to use the actual exoplanet's spectrum to better define these variations rather than draw conclusions on just the color, hence this instrument was never developed beyond a crude prototype. Still, color graphics adds real sizzle to any exoplanet article. It's why you never, essentially, see a white Sun -- it's real color -- since it's too plain.
 
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This is quite a ways off. The nearest star is 4 light years away. If we wanted to make a telescope that could resolve a city, say 100 km across, using visible light at 500 nm, the mirror would have to be 200 km in diameter.

Four light years is 4e16 meters. A 100,000 meter object at that distance subtends an angle of 100,000 divided by 4e16 or 2.5e-12 radians.

Mirror diameter = wavelength divided by angle

Diameter = 500e-9 / 2.5e-12 = 200 kilometers

This would best be done with a number of smaller mirrors forming an interferometer. We currently have visible light interferometers at 85 m (Keck) and 86 m (Palomar) with plans for one of 400 meters. 200,000 meters is a long way off.
What about light pollution? & How much time you spend observing/collecting light from the same exoplanet? May be 200km, but I'm pretty damn confident you can get away with less if you place it far enough away from the sun & spend enough time observing the planets 1 by 1. Perhaps as little as 100 "star"ship launches would do if in situ resources can be utilized. Besides a 100km city may be rather large by Earth standards, but there is no proof other civilizations wouldn't build them larger. After all it is estimated that more than 75% of nearby civilizations in space are more advanced than Earth life, perhaps as much as 90%. But ofcourse, this remains speculation based on mathematical models of approximation derived from what we know about life as we already know it.
 
This analysis assumes no light pollution. It is based on the best case, perfect optics, no interfering light. It is the best that any 200 km mirror can possibly do at 500 nm wavlength. If you want to see at a resolution smaller than 100 km you must either shorten the wavelebgth or make the mirror wider.
 
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This analysis assumes no light pollution. It is based on the best case, perfect optics, no interfering light. It is the best that any 200 km mirror can possibly do at 500 nm wavlength. If you want to see at a resolution smaller than 100 km you must either shorten the wavelebgth or make the mirror wider.
Impossible or just unpractical?
 
Somehow, one would have to maintain a mirror surface with no area higher or lower than about 100 nanometers from the mean over 200 kilometers. It is not ruled out but there is no way we know of to do this. Maybe some day.
 
No change in the number of exos in the HZ and about the size of Earth.

But, there has been more interest, apparently, in allowing for increasing the HZs to allow for orbital migration. These increases that are added the the HZ width are called the optimistic zones and are surprisingly large.

So, I have bumped the HZ by only 5% in the following run to allow for a little of the "optimistic" effect, as well as, the inherent inaccuracy of the equations we use today.

View: https://imgur.com/CxVvUwb
 

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