# How do I calculate a planets mass?

1. Aug 6, 2011

### Vetmora

Hi all,

I have just joined this forum to see if anyone here can help me out.

First off, I am creating fictional planets that orbit fictional stars.

I have given all of my planets a diameter and a distance from their sun. From this, I have managed to calculate their orbital periods and orbital speeds using Kepler's third law.

So using this criteria is it possible to calculate the mass of the planet?

Also, if possible, I would like to calculate their gravity as well.

2. Aug 7, 2011

### IsometricPion

No, the diameter and orbital radius do not provide enough information to determine the mass or gravity. Both of these values depend on the average density of the planet. However, knowing the mass and diameter of a planet does determine its surface gravity (or vice versa). Specifically (assuming the planet to be spherical), $$M=\frac{\pi{}D^3\rho{}}{6}g=\frac{4GM}{D^2} \Rightarrow{}g=\frac{2\pi{}GD\rho{}}{3}$$.
Where G is the universal gravitational constant, M is the mass of the planet, ρ is its average density, and D is its diameter. So, knowing any two of: mass, diameter, average density, and surface gravity is enough to determine the other two.

3. Aug 7, 2011

### Pengwuino

If you're creating fictional situations, is it possible to create fictional moons? As Isometric said, you can't determine the mass of the planets based off their orbits around the Sun. With moons, however, you can determine the planets mass using the moons orbital characteristics.

4. Aug 7, 2011

### Vetmora

Ah, I figured it wouldn't be possible.

I suppose it would be possible to create fictional moons. Some of the planets already have moons but I haven't worked out any stats for them other than their diameter.

Thanks for the heads up guys.

5. Aug 8, 2011

### Nik_2213

A thought: You will have to watch out for orbital resonances. May be easiest to start from the 'Jupiter' analogue and work backwards.
http://en.wikipedia.org/wiki/Orbital_resonance

6. Aug 15, 2011

### SwiftSpear

Keplers law isn't strictly accurate to a true universal simulation. It is predicated on the star being the sun, and the mass in orbit of that star having zero mass.

formula for acceleration due to gravity
g = GM / (R + h)^2

G is the gravitational constant = 6.67300 * 10-11 m3 kg-1 s-2
M is mass of body
h is height above the body

If that holds true,

g(sun) + g(planet) - (orbital velocity) = 0
(for a perfectly spherical orbit)

for any planet. Under Keplers law, g(sun) should be equal to orbital velocity, since the orbiting objects are massless.

The problem will persist with moons too, you still have to make up average density values (or mass values) for your planets and moons.