Answer:
The altitude of geostationary satellite is [tex]3.58\times10^{7}\ m[/tex]
Explanation:
Given that,
Radius of moon's orbit [tex]r=3.84\times10^{8}\ m[/tex]
Time period [tex]T=2.36\times10^{6}\ sec[/tex]
We need to calculate the orbital radius of geostationary satellite is
Using formula of time period
[tex]T=\sqrt{\dfrac{4\pi^2}{GM}a^3}[/tex]
[tex]a=((\dfrac{GM}{4\pi^2})T^2)^{\dfrac{1}{3}}[/tex]
Where, G = gravitational constant
M = Mass of earth
T = time period of geostationary satellite orbit
Put the value in to the formula
[tex]a=((\dfrac{6.67\times10^{-11}\times5.97\times10^{24}}{4\times\pi^2})\times(86160)^2)^{\dfrac{1}{3}}[/tex]
[tex]a=4.217\times10^{7}\ m[/tex]
We need to calculate the altitude of geostationary satellite
Using formula of altitude
[tex]h = a-R_{e}[/tex]
Where, R = radius of earth
a = radius of geostationary satellite
Put the value into the formula
[tex]h =4.217\times10^{7}-6.38\times10^{6}[/tex]
[tex]h =35790000\ m[/tex]
[tex]h=3.58\times10^{7}\ m[/tex]
Hence, The altitude of geostationary satellite is [tex]3.58\times10^{7}\ m[/tex]
