Question

An artificial satellite circling the Earth completes each orbit in 110 minutes. a.) Find the altitude of the satellite. b.) What is the value of g at the locatioin ofthis satellite?

Answer 1

Period of satellite T = 110 min= 110 x 60 s=6600 sWe know T = 2π √[ r ³ / GM ]r ³ / GM = (T/2π) ²r ³ = GM (T/2π) ²Where G = Gravitational constant= 6.67 x 10 ^-11 N m ² / kg²M = Mass of earth= 5.98x 10 ²⁴ kgSubstitute the values we get r ³ = 4.401 x 10 ²⁰ m ³r = 7.606 x 10 ⁶ m∴Altitide of the satellite h = r -RWhere R = radius of earth= 6.38 x 10 ⁶ mSo, h = 1.226 x 10 ⁶ m(b). The value of g at the locatioin of this satellite g ' = g [ R /r ] ²= g [0.7036] where g = 9.8 m /s ²= 6.89 m / s ²