Question

5. A satellite of mass M travels in a circular orbit of radius R about the earth. If the mass of
the satelite is doubled, but the velocity stays constant, the new orbital radius will be
a. 4R
b. R/2
c. unchanged
d. 2R

Answer 1

Are you given an equation or some other reference material on the relationship of a satellite's mass and velocity to its orbital radius?

Answer 2

This is an important question.

Think about a mass m in orbit about a larger mass M. If it is in a steady circular orbit, then the force of gravity exactly equals the required centripetal force for that orbit.

When you write down the equations, you find that the quantity m cancels.

Answer 3

Therefore, the mass of the satellite is irrelevant. Given that, what is the answer to your question?

Answer 4

Force of gravity = -GMm/r^2 in the direction of the radial vector.
Centripetal force = -mv^2/r in the direction of the radial vector

Hence
\[ -\frac{GMm}{r^2} = -\frac{mv^2}{r} \ \ \implies \ \ \frac{GM}{r^2} = \frac{v^2}{r} \]