Question

Two satellites orbit Earth at altitudes of 5700 kmand 1.8×10⁴ km.Which stellite is faster and by what factor?

Answer 1

Ans :-

  v = sqrt(GM/R)
v = velocity in m/s
G = 6.673e-11 Nm²/kg²
M is mass of central body in kg
R is radius of orbit in m
earth radius 6,371,000 m

divide the two and we get
V1 is speed of sat at 5700 km
V2 is speed of sat at 18000 km

V2/V1 = sqrt(GM/R2) / sqrt(GM/R1)
V2/V1 = sqrt(R1/R2)
but this is distance to the center of the earth, not altitude. We have to add 6371 km
V1/V2 = sqrt[ (18000+6371) / (5700+6371) ]
V1/V2 = sqrt[ (24371) / (12071) ]
V1/V2 = 2.02
1^st satellite is faster which velocity is faster ie V1 by 2.02 factor