I Perigee and apogee

Who says they are? I'm not even sure what you are talking about as it doesn't seem to make sense.

 

As Phinds said ... that didn't make a lot of sense

do you understand what the definitions perigee or apogee are ?
Describe what you think they are and we can work from there


D

 

I hope this thread doesn't turn into the guessing game "maybe the OP means..."

 

The radius of the orbit is not 22,236 miles. Take a trip to Google and look up what reference point that 22,236 figure is measured from.

Now, to determine the radius of the orbit from the period, you need to know two formulas:

The centripetal force required to keep a body in circular motion: ##f=\frac{mv^2}{r}## where m is the mass of the object, v is its velocity and r is its distance from the center of the earth.

The force of gravity: ##f=\frac{GmM}{r^2}## where G is Newton's universal gravitational constant, M is the mass of the Earth, m is the mass of the object and r is the distance of the object from the center of the earth.

Solve these two equations for the radius at which gravity is exactly equal to the required centripetal force.
[Hint: the orbital velocity is easily found from the orbital radius and period.]
[Hint: pick a consistent set of units (e.g. meters, kilograms, seconds) and use that]
[Hint: keep everything symbolic until you have a formula for the quantity you are after in terms of things that you know]

 

Perhaps reading about orbital period [1] and geo-synchronous orbits [2] may help.

[1] https://en.wikipedia.org/wiki/Orbital_period
[2] https://en.wikipedia.org/wiki/Geostationary_orbit