6.1 Mastery Check You and your brother are pushing a 2400 kg car with a dead battery. You push with a force of 20 N and your brother pushes with a force of 25 N in the same direction. There are no other forces acting on the car. What is the acceleration of the car?

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

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 satelliteR is the radius of the satellite's orbitv 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 constantM_p is the mass of the planetm_s is the mass of the satelliteR 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.