Question

derivation of height of geostationary satellite

Answer 1

The above derivation gives the heightof the Geostationary orbit. Now, please note that the above heightincludes radius of Earth which is 6,384 km. When we deduct it from the calculated height we get 35916 Kilometers. The precise height isaltitude of 35,786 km (22,236 mi) above ground.

Answer 2

Hey Dear,

◆ Answer -

h = 35889 km

● Explanation -

# Given -

G = 6.67×10^-11 Nm^2/kg^2

M = 6 × 10^24 kg

R = 6400 km

T = 24 hrs = 86400 s

# Solution -

Time period of satellite is given by -

T = 2π √(r^3/GM)

T^2 = 4π^2.r^3/GM

r^3 = GM.T^2 / 4π^2

r^3 = 6.67×10^-11 × 6×10^24 × 86400^2 / 4×3.142^2

r^3 = 7.563×10^22

r = 4.229×10^7 m

r = 42289 km

Height of geostationary satellite is thus -

h = r - R

h = 42289 - 3600

h = 35889 km

Therefore, height of geostationary satellite should be 35889 km.

Thanks dear. Hope this helps.