This is related to Semi-Empirical Stellar Equations. I have had some questions easily answered, and others which are difficult or impossible to get the kind of accuracy I want.

I’m going to order what I’ve learned by the order I am planning to use these equations, marking equations loosely based on empirical data with an asterisk, and double asterisks for things I’ve completely made up to simplify calculation.

- Radius of Surface* (R
_{surface}):

5500km mean, 1550km standard deviation - Density* [based on common rock types] (D
_{planet}):

4.7g/cm^{3}mean, 0.55g/cm^{3}standard deviation - Volume [assumes a perfect sphere] (V
_{planet}):

4/3 * π * R_{surface}^{3} - Mass (M
_{planet}):

D_{planet}* V_{planet} - Surface Gravity (g
_{surface}):

6.673×10^{-11}Nm^{2}kg^{-2}* M_{planet}/ R_{surface}^{2} - Surface Area [assumes a perfect sphere]:

4 * π * R_{surface}^{2} - Atmospheric Pressure Reduction Rate** (P
_{r}):

P_{r}[unit: none] = -0.00011701572 [unit: s^{2}/ m^{2}] * g_{surface} - Atmospheric Halving Height** (h
_{d}):

h_{d}[unit: m^{-1}] = ln(2) / P_{r} - Atmospheric Volume at Constant Pressure** (V
_{sim}):

(4/3 * π * (R_{surface}+ h_{d})^{3}– V_{planet}) * 2 - Surface Atmospheric Pressure (P
_{surface}):

P_{surface}[unit: kPa] = ??? - Lowest Safe Orbital Height** (h
_{0}):

h_{0}[unit: m] = ln(1.4×10^{-11}/ P_{surface}) / P_{r} - True Atmospheric Volume (V
_{atm}):

4/3 * π * (R_{surface}+ h_{0})^{3}– V_{planet}

V_{sim} exists to support a simulation of an entire planet’s atmospheric contents using my simple fluid simulation mechanic. The magic constant used to calculated P_{r} is based on Earth’s atmosphere, it can be changed to set an exact “atmospheric height” while maintaining other properties of this simulation.

- Atmospheric Pressure at Altitude** (P
_{altitude}):

P_{altitude}[unit: kPa] = P_{surface}* exp(P_{r}* m_{altitude}) [P_{r}may be -P_{r}, I don’t remember]

This post is obviously incomplete, but it’s been a while since I posted anything here, and I felt like I should go ahead and share what I’ve been up to.