# Gravitation Question

## Homework Statement

A satellite is to be put into an equatorial orbit with an orbital period of 12 hours.
Given: 12 Hours = 12 X 60 X 60 seconds

What is the orbital speed?
How many times a day will the satellite be over the same point on the equator if the satellite orbits in the same direction of the Earth's rotation? If it orbits in the opposite direction?

## Homework Equations

r= (GMT^2)/(4pi^2 )^1/3
G = Gravitational Constant = 6.67 X 10^-11 N m^2/kg^2
M = Mass of earth 5.98 X 10^24 kg
T = time

## The Attempt at a Solution

Well I started with the radius equation and plugged everything in

r= ((6.67×10^(-11) N∙m^2∕kg^2 × 5.98×10^24 kg × (12×60×60 s)^2)/(4pi^2 ))^(1/3)

However I had trouble working it out. Then the other problems just went over my head.

You already stated that the orbital speed is $$\sqrt{\frac{GM_{earth}}{r}}$$