Question

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?

Answer 1

Answer:

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