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I am a high school student beginning a simple independent project to calculate the equilibrium temperature of exoplanets. I'm curious to see how many exoplanets have a similar equilibrium temperature to Earth's 255K and was looking for some guidance. I found this formula on a few online resources:

$$ T_p = T_\odot(1-a)^{1/4}\sqrt{\frac{R_\odot}{2D}}$$

I was hoping someone could tell me where I can find the relevant public data on known exoplanets to calculate their equilibrium temperature. I looked through NASA Exoplanet Archive Kepler Database and found some data that listed planets' "Stellar Radius" (unit is solar radii), "Stellar Effective Temperature" (unit is Kelvin) and "Planet Star Distance over Star Radius" (not sure what the unit is). Are these data points what I use for the formula? Additionally, I am not sure where I can locate the albedo for the specific planets, is there another database I should use?

I realize there is a column in the database that lists the "Equilibrium Temperature" for the planets, but I was hoping to attempt the calculations on my own to learn to use it and see if I am able to get the same results. Any info would be very much appreciated, I am not sure I am taking the right approach, I would love some input.

screenshot of Exoplanet Archive table

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$R_\odot$ and $T_\odot$ should be replaced with the stellar radius and stellar effective temperature respectively. $D$ is the planet-star distance, which you can get from multiplying the appropriate column by the stellar radius.

Note that the radii are given in solar radii, so need to be multiplied by the solar radius in SI units.

The albedo $a$ is unknown for most exoplanets. You can probably work out what value of $a$ has been assumed in this table (somewhere between zero and one).

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I've actually been writing a python app to look for exoplanets in stars' light curves and simulate their atmospheric temperature.

As others have pointed out, we struggle to even estimate albedo or other factors that influence temperature for exoplanets, so we're mostly stuck with guessing and simulating for now. ProfRob has already given the answer you were looking for, but if you'd like to play around with my python app to learn more about exoplanets, you can install the script [here][1].

This is how I calculate the temperature in there:

  1. First, get the stellar irradiance received by the planet:

    $I = \sigma T^4 \frac{R_p^2}{D^2} $

  2. Scale down the irradiance based on possible atmospheric factors of various weights:

$T_1 = \frac{I(1 - Co2 - CH4)}{4R_p^2\sigma}^{1/4}$

$T = T_1 \frac{(1 + (Co2 + CH4) P)}{\rho Q}$

Where Co2 and CH4 are carbon dioxide and methane in part per million, $P$ is pressure, $\rho$ is density and $Q$ is the specific heat.

This might be more confusing than you were hoping for, but in the app you can play around with different atmospheric conditions and get some sort of estimate for the temperature, albeit rough.

I would also love some feedback on the app in general if you end up giving it a try, I'm not a programmer and it's the first time I mess around with GUIs and stuff like this. It's just a personal project, nothing to sell here. [1]: https://github.com/Britishterron/exoplanet_finder

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