If a satellite orbits the Earth with a period of 120 minutes, determine its altitude above the Earth’s surface. Show all work and answer to three significant digits.

Question

If a satellite orbits the Earth with a period of 120 minutes, determine its altitude above the Earth’s surface.  Show all work and answer to three significant digits.

anonymous · Answer

You can calculate the speed of a geosynchronous orbit of a satellite with the following formula:
$$V = \sqrt{\frac{ Gm_E}{ r }}$$
and the orbital speed knowing the circumference of a sphere is 2(pi)R and T as the period so the orbital speed is given by: $$\frac{ 2\pi r }{ T }$$

Setting them equal to each other and solving for T, period, you know have:
$$T = 2 \pi \sqrt{\frac{ r^3 }{ Gm_E }} $$
That formula should be familiar now and you can solve for r the radius of earth+ atmosphere/altitude of satellite. You will need radius of the Earth to subtract it from the answer for r that you find. 
I believe the Earth's radius is:$$6.38 \times 10^6 m$$

Keep watch for units.

anonymous · Answer

i manipulated to get r=(T^2GmE/2π)^1/3 
and plugged in the values =[(7200s)^2(6.67x10^-11)/2π]^1/3
an i got 0.0819 which seems wrong to me
@johnbc

anonymous · Answer

You forgot to also square the 2 pi.

anonymous · Answer

@lolo123

anonymous · Answer

thank u so much!

anonymous · Answer

My pleasure