Functions
This function calculates the surface acceleration of a planet. The mass is in units of solar masses, the radius in terms of km, and the acceleration is returned in units of cm/sec2.
This function returns the boiling point of water in an atmosphere of pressure ‘surface_pressure_bar’, given in bars. The boiling point is returned in units of Kelvin. This is Fogg’s eq.21.
Given the surface temperature of a planet (in Kelvin), this function returns the fraction of cloud cover available. This is Fogg’s eq.23. See Hart in “Icarus” (vol 33, pp23 - 39, 1978) for an explanation. This equation is Hart’s eq.3. It was modified slightly by using constants and relationships from Glass’s book “Introduction to Planetary Geology”, p.46. The ‘CLOUD_COVERAGE_FACTOR’ is the amount of surface area on Earth covered by one Kg. of cloud.
Fogg’s information for this routine came from Dole “Habitable Planets for Man”, Blaisdell Publishing Company, NY, 1964. From this, he came up with his eq.12, which is the equation for the base_angular_velocity below. Going a bit further, he found an equation for the change in angular velocity per time (dw/dt) from P. Goldreich and S. Soter’s paper “Q in the Solar System” in Icarus, vol 5, pp.375-389 (1966). Comparing to the change in angular velocity for the Earth, we can come up with an approximation for our new planet (his eq.13) and take that into account.
This is Fogg’s eq.19. The ecosphere radius is given in AU, the orbital radius in AU, and the temperature returned is in Kelvin.
The mass passed in is in units of solar masses, and the orbital radius is in units of AU. The density is returned in units of grams/cc.
This function implements the escape velocity calculation. Note that it appears that Fogg’s eq.15 is i/ncorrect. The mass is in units of solar mass, the radius in kilometers, and the velocity returned is in cm/sec.
Convert solar mass to Earth mass
This function calculates the surface gravity of a planet. The acceleration is in units of cm/sec2, and the gravity is returned in units of Earth gravities.
This is Fogg’s eq.20, and is also Hart’s eq.20 in his “Evolution of Earth’s Atmosphere” article. The effective temperature given is in units of Kelvin, as is the rise in temperature produced by the greenhouse effect, which is returned.
Note that if the orbital radius of the planet is greater than or equal to R_inner, 99% of it’s volatiles are assumed to have been deposited in surface reservoirs (otherwise, it suffers from the greenhouse effect).
This function is Fogg’s eq.22. Given the volatile gas inventory and planetary radius of a planet (in Km), this function returns the fraction of the planet covered with water.
Given the surface temperature of a planet (in Kelvin), this function returns the fraction of the planet’s surface covered by ice. This is Fogg’s eq.24. See Hart[24] in Icarus vol.33, p.28 for an explanation.
The orbital radius is expected in units of Astronomical Units (AU). Inclination is returned in units of degrees.
The temperature calculated is in degrees Kelvin.
Returns the radius of the planet in kilometers. The mass passed in is in units of solar masses, the orbital radius in A.U. This formula is listed as eq.9 in Fogg’s article, although some typos crop up in that eq. See “The Internal Constitution of Planets”, by Dr. D. S. Kothari, Mon. Not. of the Royal Astronomical Society, vol 96 pp.833-843, 1936 for the derivation. Specifically, this is Kothari’s eq.23, which appears on page 840.
This function returns the smallest molecular weight retained by the body, which is useful for determining the atmosphere composition. Orbital radius is in A.U.(ie: in units of the earth’s orbital radius), mass is in units of solar masses, and equatorial radius is in units of kilometers.
This function returns the dimensionless quantity of optical depth, which is useful in determining the amount of greenhouse effect on a planet.
This function, given the orbital radius of a planet in AU, returns the orbital ‘zone’ of the particle.
Separation - Units of AU between the masses returns the period of an entire xorbit in Earth days.
The surface temperature passed in is in units of Kelvin. The cloud adjustment is the fraction of cloud cover obscuring each of the three major components of albedo that lie below the clouds.
This implements Fogg’s eq.18. The pressure returned is in units of bars. The gravity is in units of Earth gravities, the radius in units of kilometers.
This is Fogg’s eq.16. The molecular weight (usually assumed to be N2) is used as the basis of the Root Mean Square velocity of the molecule or atom. The velocity returned is in cm/sec.
This implements Fogg’s eq.17. The ‘inventory’ returned is unitless.
The mass passed in is in units of solar masses, and the equatorial radius is in km. The density is returned in units of grams/cc.
The mass is in units of solar masses, and the density is in units of grams/cc. The radius returned is in units of km.