# How does mass affect orbital speed?

Mar 18, 2018

Assuming we are talking about the mass of the satellite (and not the mass of the body being orbited), mass does not affect the orbital speed.

#### Explanation:

Kepler's 3rd Law of Planetary Motion says that

${T}^{2} = \frac{4 \cdot {\pi}^{2} \cdot {r}^{3}}{G M}$

$T$ is the period of the orbit. That and the radius of the orbit determine the orbital speed.

The terms $\frac{4 \cdot {\pi}^{2}}{G}$ from that equation are constants. I will assume you want to compare masses without changing radius, so I will assume that the entire expression $\frac{4 \cdot {\pi}^{2} \cdot {r}^{3}}{G}$ is to be considered constant.

It is unclear which mass you are asking about. There is the mass of the satellite and the mass of the body being orbited to be considered.

I will first assume you are asking about the mass of the satellite. The mass of the satellite is not part of the expression $\frac{4 \cdot {\pi}^{2} \cdot {r}^{3}}{G M}$. Therefore we can conclude that mass of the satellite does not affect orbital speed.

Now I will assume you are asking about the mass of the body being orbited. The mass of that body is the $M$ in the expression $\frac{4 \cdot {\pi}^{2} \cdot {r}^{3}}{G M}$. Therefore if $M$ increases, the value of $T$ will decrease indicating that the speed has increased.

I hope this helps,
Steve