# What is the difference in speed between my two moons?

The planet in my current project is orbited by two moons, which like Mars' are relatively small and irregularly shaped. The largest moon orbits closer to the planet and the smaller one orbits farther away. My question is, which is faster? I know the closer one should orbit the fastest, but since it's larger, I imagine that would slow it down. My current understanding is that the smaller, farther moon would orbit slightly faster, would that be accurate scientifically?

For the sake of simplicity we can say that the second moon is half the size of the first one and the second moon is exactly as far from the first moon as the first moon is from the planet. If it's at all relevant, I also imagine that this planet is smaller than Earth and orbits its star slightly slower and closer than Earth does.

• The radius of the orbit determines the orbital speed and the duration of a revolution. The mass of the satellite is irrelevant. Commented Feb 23, 2023 at 0:32
• The mass of the satellite is not entirely irrelevant, but if it's not a a noticeable fraction of the planet's mass, it can be safely ignored for fictional worldbuilding purposes in the orbital speed calculations. Ultimately, though we'll need a lot more information to answer what the actual speed difference can be; minimally the mass of the planet, semi-major axes and eccentricates of the moons' orbits. Commented Feb 23, 2023 at 1:11
• Please research basic orbital mechanics. Such as: equal area is swept in equal time for orbiting bodies, Where the sweep line is the line connecting the two bodies. Commented Feb 23, 2023 at 1:17
• You say your two moons resemble Mars's satellites, Phobos and Deimos. Then look at their orbital velocities and what differences they have. Commented Feb 23, 2023 at 8:11

If I drop a feather and a hammer at the same time and at the same height, assuming there is no air resistance, which hits the ground first? At first thought, you may say that the hammer has more weight, which means force of gravity on it is stronger, so it should fall faster. On the other hand, the hammer also has more mass, so more force needed to accelerate is larger, so it should fall slower. In truth, as I am sure you know, these two factors cancel each other out perfectly, and the feather and hammer will hit the ground together. As long as two objects start at the same height, they will hit the ground at the same time.

The same thing happens with orbits. To calculate a satellite's orbit, all you need is its velocity and current position. The mass ends up not mattering. For circular orbits, the equation is actually super easy:

$$V = \sqrt(GM/r)$$

where V is the velocity of the moon,G is Newton's constant, M is the mass of the planet, and r is the radius of the circular orbit. Since the small moon is twice as far from the planet as the large moon, the small moon travels $$1/\sqrt(2)$$ as fast as the first moon.

For more information for why the mass ends up not mattering, go here or here.

• Answers my question perfectly, thank you!
– INPU
Commented Feb 24, 2023 at 0:21