Question

An artificial satellite circling the Earth completes each orbit in 104 minutes.

(a) Find the altitude of the satellite.
-----------m

(b) What is the value of g at the location of this satellite?
--------m/s²

Answer 1

from the kepler's third law of circular orbits we have

T²=4pi²r³/GM_e

G=6.67*10^-11Nm²/kg² Me=5.97*10²⁴kg, T=104 mins=6240 sec

r³=T²GMe/4pi²

r³=(6240s)²(6.67*10^-11Nm²/kg²)²*(5.97*10²⁴kg)²/4pi²

=39.32*10¹⁸

r=(39.32*10¹⁸)^1/3

r=13.12*10⁶ m

when we subtract the radius from the earth radius we get the satellite altitude (Re=6.731*10⁶m)

altitude=13.12*10⁶m-6.731*10⁶m=6.39*10⁶m

so a) 6.39*10⁶m

b) g=GM_e/r²

g=6.67*10^-11Nm²/kg²*5.97*10²⁴kg/(6.39*10⁶)²

g=6.23m/s²

so b) 6.23m/s²