Question

A satellite of mass m and speed v moves in a stable, circular orbit around a planet of mass M. What is the radius of the satellite's orbit? Plz, answer quickly!! I will mark the best answer as Brainlest!!! :D NO SPAMMING OR ELSE I WILL REPORT!!

Answer 1

Equate the centripetal force that is mv^2/r to the gravitational force between the satellite and the planet GMm/r2. Then from this u will get v^2= GM/r^2. By further simplifying this by transposing terms, r is the whole root of GM/v^2.

Answer 2

Given:

• Mass of satellite = m, velocity of satellite = v.
• Mass of planet = M

To find:

• Radius of orbit of satellite ?

Calculation:

When the satellite is revolving around the planet, the gravitational force is providing the centripetal force.

• The distance of separation between M and m be 'r'. That will also be the radius of orbit.

$\therefore \: F_{g} = F_{c}$

$\implies \: \dfrac{GMm}{ {r}^{2} } = \dfrac{m {v}^{2} }{r}$

$\implies \: \dfrac{GMm}{ r } = m {v}^{2}$

$\implies \: {v}^{2} = \dfrac{GM}{ r }$

$\implies \: r= \dfrac{GM}{ {v}^{2} }$

So, radius of orbit is GM/v².