Question

1. which of these factors does the orbital velocity of a satellite depend on?

i. the mass of the satellite
ii. the mass of the planet
iii. the separation distance

Explanation:

Step1: Write the formula for orbital velocity

The formula for the orbital velocity \(v\) of a satellite is \(v = \sqrt{\frac{GM}{r}}\), where \(G\) is the gravitational constant, \(M\) is the mass of the planet, and \(r\) is the separation distance (distance from the center of the planet to the satellite).

Step2: Analyze the dependence on each factor

• For the mass of the satellite (\(m\)): It does not appear in the formula \(v = \sqrt{\frac{GM}{r}}\), so the orbital velocity does not depend on the mass of the satellite.
• For the mass of the planet (\(M\)): It is in the numerator of the formula. As \(M\) changes (while \(r\) is constant), \(v\) changes. So the orbital velocity depends on the mass of the planet.
• For the separation distance (\(r\)): It is in the denominator of the formula. As \(r\) changes (while \(M\) is constant), \(v\) changes. So the orbital velocity depends on the separation distance.

Answer:

II and III.