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/cm³ mean, 0.55g/cm³ standard deviation
• Volume [assumes a perfect sphere] (V_planet):
  4/3 * π * R_surface³
• Mass (M_planet):
  D_planet * V_planet
• Surface Gravity (g_surface):
  6.673×10^-11Nm²kg^-2 * M_planet / R_surface²
• Surface Area [assumes a perfect sphere]:
  4 * π * R_surface²
• Atmospheric Pressure Reduction Rate** (P_r):
  P_r [unit: none] = -0.00011701572 [unit: s² / m²] * 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** (h₀):
  h₀ [unit: m] = ln(1.4×10^-11 / P_surface) / P_r
• True Atmospheric Volume (V_atm):
  4/3 * π * (R_surface + h₀)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.