A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.75 104 m/s, and the radius of the orbit is 5.00 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 8.75 106 m. What is the orbital speed of the second satellite?

v = 1.32 10² m

Explanation:

In this case we are going to use the universal gravitation equation and Newton's second law

F = G m M / r²

F = m a

In this case the acceleration is centripetal

a = v² / r

The force is given by the gravitational force

G m M / r² = m v² / r

G M/r = v²

Let's calculate the mass of the planet

M = v² r / G

M = (1.75 10⁴) ² 5.00 10⁶ / 6.67 10⁻¹¹

M = 2.30 10²¹ kg

With this die we clear the equation to find the orbit of the second satellite

v = √ G M / r

v = √ (6.67 10⁻¹¹ 2.30 10²¹ / 8.75 10⁶)

v = 1.32 10² m