Astrophysics- Calculate the altitude of a geosynchronous orbit

[sleepyhead212]

a)Calculate the altitude of a geosynchronous orbit (an orbit that has an orbital period of one sidereal day)(altitude is measured from the surface of the earth/ The "r" in gravitational equations is always measured from the center of mass of an object. one may assume a circular orbit.)

b) how does the altitude of this geosynchronous satellite compare to the average 354 km altitude of the International Space Station?

c) Calculate the orbital period of the international Space Station (assume circular Orbit)



this was my attempt

a= (mu*(1/(2pi))^2)^(1/3)
a= (398600(1/(2pi))^2)^(1/3)
a=21.6

but for b) I am not sure if my prof. wants a word explanation or to solve the actual difference so i provided a word explanation

then for c)

T = ((2\pi)/(mu)a^(3/2))^(1/3)
but am unsure what mu would be.

i'm not sure if what I'm doing is correct because we never went over this in class so i tried do this based off internet research. any help would be appreciated

 

[mgb_phys]

The equation you have is Keplers third law (ignoring the mass of the satelite)
( period / 2pi )^2 = radius^3 / GM
If you plugin G and M=mass of the Earth you should get the right answer, be careful of the units.

 

[sleepyhead212]

can this equation be used for both part a and c?

 

[mgb_phys]

The law describing their behaviour is the same, you simple have to find radius in one case given the period and the period in the other case given the radius.