planets

To build a planet, designate its mass (M⊕) or radius (R⊕) and density (ρ⊕) relative to Earth’s.

distance from star

The distance of a planet from its star can be determined by the sunlight intensity it receives. A sunlight intensity (S) of 1 is equivalent to Earth’s sunlight intensity. Habitable planets must have a 0.53–1.1 sunlight intensity.

Pdist = L☉ / S

mass

Mass (M⊕) is the amount of matter in a body

M⊕ = R⊕3 / ρ⊕

radius

A planet’s radius is the distance from its centre to its surface

R⊕ = cubeRoot(M⊕ρ⊕)
R⊕(km) = R⊕ * 6731.009

circumference

The circumference (C) is the distance around a closed curve. Note that unless your planet is perfectly spherical, its circumferences will differ around its poles and its equator

C⊕ = 2πR⊕

gravity

G = M⊕ / sqrt(R⊕)

temperature

The average planetary temperature (T) is a factor in the planet’s habitability.

T = 374 * G * (1 - A) * Psunlight0.25

escape velocity

A planet’s escape velocity (ve) refers to the minimum speed required for an object to escape its gravitational pull

ve = (2.365 * 10-5) * Rm * sqrt(pKgm)
ve = sqrt((2GM☉) / Rm)

molecular velocity

Gas constant

vescJean = ve / 6
f(x) = sqrt((3RT) / x)

distance to horizon

To determine how far an observer with a height of h (in metres) can see into the horizon, assuming a perfectly flat* terrain:

dh = sqrt(h * (2 * Rm + h))

obliquity

Obliquity (ε) is the angle between a planet’s rotational axis at its poles and a line perpendicular to its orbital plane. This angle is a factor in the planet’s seasons and temperature regions.

λA = 90 - ε
λT = ε

angular diameter of primary

The apparent size (δ) of the planet’s primary

δ = 57.3 * (d☉ / Pdist)