Question

Two satellites, X with a mass of m and Y with a mass of 2m, orbit the same planet at the same height. If the orbital velocity of X is v, what is the orbital velocity of Y?

a) v

b) 2v

c) v/2

d) 4v

Answer 1

The orbital velocity of satellite Y is 2 times the orbital velocity of satellite X.

Step-by-step explanation:

The orbital velocity of satellite Y can be determined using the concept of conservation of angular momentum. The angular momentum of a satellite is given by the equation:

L = mvr

where L is the angular momentum, m is the mass of the satellite, v is the orbital velocity, and r is the radius of the orbit. Since both satellites are at the same height, the radius of their orbits would be the same. Therefore, the angular momentum of satellite Y would be:

LY = 2m * v * r

Using the equation for angular momentum of satellite X (LX = m * v * r), we can compare the two angular momenta:

LY / LX = (2m * v * r) / (m * v * r) = 2

Since angular momentum is conserved, the ratio of the angular momenta is equal to the ratio of the masses. Therefore, the orbital velocity of satellite Y would be equal to 2 times the orbital velocity of satellite X. So the correct answer is b) 2v.