# A satellite X of mass m orbits the Earth with a period T. What will be the orbital period of satellite Y of mass 2m occupying the same orbit as X?

## A. T/2 B. T C. (2^0.5)T D. 2T The answer is B, but why isn't it C?

Jun 5, 2018

B is indeed correct

#### Explanation:

Let's start by deriving a formula for the period from what we know.

The first step is to equate centripetal force ($\frac{m {v}^{2}}{r}$) to the gravitational force.

$\frac{{m}_{\text{X" v^2)/r = (G m_"X" m_"E}}}{r} ^ 2$

v = sqrt((Gm_"E")/r

Since $t = \frac{d}{v}$, and the orbit around the earth will be $2 \pi r$, we get that

$P = \frac{2 \pi r}{\sqrt{\frac{G {m}_{\text{E}}}{r}}}$

$P = 2 \pi \sqrt{{r}^{3} / \left(G {m}_{\text{E}}\right)}$

As you can see, all that the period depends on is the mass of the Earth, the orbital radius and the Gravitational constant. This proves that mass of the satellite has no bearing on the orbital period, therefore the orbital period remains T (answer B).

Hopefully this helps!