Question

The mass of a planet can be calculated if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of the following would not be required in this calculation?

i. the mass of the satellite
ii. the radius of the satellite's orbit
iii. the period of the satellite's orbit
iv. all of these are required

Answer 1

i. the mass of the satellite will not be required in this calculation

Step-by-step explanation:

When a satellite is orbiting a planet, it experiences two forces. The centripetal force and the gravitational force that the planet exerts on the satellite. In order for the satellite to keep in orbit, the centripetal force and the gravitational force must be equal.

The expression for the centripetal force is:

F_c = (m_s)v² / R

where

• m_s is the mass of the satellite
• R is the radius of the satellite's orbit
• v is the velocity that the satellite travels with around the planet

The expression for the Gravitational force is:

F_g = (G M_p m_s) / R²

where

• G is the universal gravitational constant
• M_p is the mass of the planet
• m_s is the mass of the satellite
• R is the radius of the satellite's orbit

Thus, equating the two forces together, we get:

(G M_p m_s) / R² = (m_s)v² / R

We can cancel out m_s since it is a common factor on both sides.

Thus,

(G M_p) / R² = v² / R ⇒ M_p = v²R / G

Therefore, the mass of the satellite is not required to calculate the mass of the planet.