The orbital period of a moon is calculated using the same equations as for calculating the orbital period for double-planets.

Where:

𝜒

𝜒

As in the previous section, there are times when you’ll know the mass and the orbital period and need to calculate the orbital radius (semi-major axis). Deriving from the above results in the following equation:

*P**S*= period of the moon’s orbit;*R**S*= radius of the moon’s orbit in Earth radii;*M*= mass of the planet in Earth masses;*m*= mass of the moon in Earth masses;𝜒

*= 0.0588*to have*P**S*expressed in days;𝜒

*= 1.4112*to have*P**S*expressed in hoursAs in the previous section, there are times when you’ll know the mass and the orbital period and need to calculate the orbital radius (semi-major axis). Deriving from the above results in the following equation:

So, let’s say Arada has a moon called Haimoxa at the second ordinal, with the same mass as Jupiter’s moon, Ganymede (

Arada mass:

Orbital period:

Mass of Haimoxa:

Constant: 𝜒

So Haimoxa’s orbital radius is:

*M**S**= 0.025*terran).Arada mass:

*M**P**= 272.16*terranOrbital period:

*P**S**= 1.367*Earth daysMass of Haimoxa:

*M**S**= 0.025*terranConstant: 𝜒

*= 0.0588*(since*P**S*is expressed in days)So Haimoxa’s orbital radius is:

… just over 55 Earth-radii.

It is

We have not yet specified a radius for Arada, but we have an equation from which we can determine one:

It is

*vital*to remember that the value returned by this equation is in terms of*Earth-radii*. To be truly useful, the number will have to be converted to be expressed in terms of the radius of the parent planet.We have not yet specified a radius for Arada, but we have an equation from which we can determine one:

To use this equation, we’ll need to determine a density (

Arada’s mass falls into the Jovean range, which has a mass range of 140 – 500 terran. Thus we can calculate Arada’s place in this range by:

*ρ*) value for Arada.Arada’s mass falls into the Jovean range, which has a mass range of 140 – 500 terran. Thus we can calculate Arada’s place in this range by:

… and multiply this value by the maximum density listed in the table to get a density for Arada:

We now use Arada’s mass and density to calculate its radius:

… just less than 14 times the radius of the Earth, and 3.95% smaller than Uranus.

Dividing Haimoxa’s orbital radius by the radius of Arada gives us the orbital radius in Arada-radii:

Dividing Haimoxa’s orbital radius by the radius of Arada gives us the orbital radius in Arada-radii:

… just shy of 4 times the radius of the planet.

Just for fun, let’s calculate the Roche limit for Haimoxa orbiting Arada:

Arada radius: 13.962 terran

Density of Arada: 0.100 terran

Density of Haimoxa: 0.351 terran (same as Ganymede)

Just for fun, let’s calculate the Roche limit for Haimoxa orbiting Arada:

Arada radius: 13.962 terran

Density of Arada: 0.100 terran

Density of Haimoxa: 0.351 terran (same as Ganymede)

Converting from Earth-radii to Arada-radii:

Thus:

Haimoxa orbital radius: 4.491 Arada-radii

Haimoxa Roche limit: 1.606 Arada-radii

Haimoxa orbital radius: 4.491 Arada-radii

Haimoxa Roche limit: 1.606 Arada-radii

So, Haimoxa is orbiting Arada 2.797 times farther out than its Roche limit.

Should you need/desire to do so, you would calculate Haimoxa’s orbital speed in the same way as calculating the orbital speed of a double-planet system, as described above.

Should you need/desire to do so, you would calculate Haimoxa’s orbital speed in the same way as calculating the orbital speed of a double-planet system, as described above.