Celestia Forums

Okay,

i am just going to rebuild some parts of my addons and will try to be a little be more astrophysically correct then last time.
Now i have looked up some information, but am not completely sure that i got those things right.

The planets have been quite easy, but with the moons i have a bit problems.
Okay first of all everything is fictious, from a series, but i have data on the planets, like gravity in g and the diameters.

Now i started out with the following equations:

(1) t(m) = 2*PI*sqrt(R??/?µ) t(m) = period in seconds; R = orbitalradius of the moon
(2) ?µ = m*gravitational constant m = mass of planet
(3) m=surface acceleration*r(p)??/gravitational constant r(p) = radius of planet

from (2) and (3) i get

(4) ?µ = surface acceleration*r(p)??

put into (1) results in

(5) t(m) = 2*PI*sqrt[R??/(surface acceleration*r(p)??)]

If i want to be correct i need also to take into account the Roche-Limit beyond which there can be no moons, right?

How do i get this one?

I found something, but am not sure if it right.

(6) Roche = 2.423*r(p)*density(p)/density(m) p = planet; m = moon

Now i don't know the density of my planets, so after some playing around i came up with

(7) Roche = 2.423*g(p)*density(earth)/density(m) g(p) = surface acceleration of the planet in times of earthnormals (e.g. 2 = 19.62 m/s??)

Did i do this correct? And what are typical values for the density of moons?

Do i have to take other things also into account when creating moons? Things that are not too complicated to calculate?

Regards,

Guckytos

Well, it's generally easier if you just start from scratch.

You know the radius and you know the gravity. So you can calculate the volume, density and the mass from that. Make sure you use units of metres, kilograms and seconds to keep everything consistent - then you can convert to earth masses or years or whatever afterwards.

Gravity (m/s^2) = (G*Mass)/(radius^2) where G = 6.672559e-11 (gravitational constant) so:

Mass = (Gravity * (radius^2))/G. This gives you mass in kg - if you want that in Earth Masses divide it by 5.9736e24 kg.

To find the density, you need the volume:

Volume = (4/3)*PI()*(radius^3). Make sure you use metres for radius to keep everything consistent.

Density (kg/m^3) = Mass (kg) /Volume (m^3).

If you want to know the orbital period of an object (planet or moon) then you'll need to know the mass of the primary they orbit and the semimajor axis of the orbit:

Orbital period (s) = SQRT[(a^3)*(4*(PI()^2))]/(G*M)

where a = semimajor axis of orbit (m), G = gravitational constant, M = mass of primary in kg.

That gives a period in seconds. Divide that by 86400 to get it in earth days, or divide it by 31557600 to get it in earth years.

Roche limit is estimated by:

Roche Limit = 3 * [(density of planet/density of satellite)^(1.3)]

Within this distance, a satellite would be destroyed by tidal forces. Outside it, the satellite is stable.

You might also want to calculate the Hill Sphere limit, which is the maximum distance you can find a satellite orbiting a planet. For this, you need to know the mass of the primary star that the planet orbits (m1), and the mass of the planet orbiting the star (m2). Note that you don't use the mass of the satellite itself in this equation:

?µ = [m2/(m1+m2)]

Hill Limit (in metres) = (?µ/3)^(1/3)

Did i do this correct? And what are typical values for the density of moons?

Any good astronomy text book will list the values of densities for moons. But as a rule of thumb, icy moons (eg the small moons of Saturn) will have low densities of around 1000-1500 kg/m3. Rock/Ice moons (eg Titan, Ganymedem Callisto, Triton) will have densities between 1500 - 2000 kg/m3. Rocky moons (eg Luna, Io, Europa) will have densities between 3000-3500 kg/m3. Rock/Iron moons (no examples in the solar system) would have densities more like 4000-5500 kg/m3 - but these are unlikely. It rather depends on a lot of things like their size, history, differentiation, location in the system, etc.

Thanks for the answer Malenfant.

didn't know about that Hill-Radius. Will have to take it into account too.
You are probably right with the advice of starting from scratch. Will do that once again.

With the densities of the moons, i will have to play a bit around. Seeing where i will place which one. Thanks for the rough values.

Regards,

Guckytos