Question

A satellite is in a circular orbit about the earth (ME = 5.98 x 1024 kg). The period of the satellite is 1.04 x 104 s. What is the speed at which the satellite travels

Answer 1

we know the formula

F=GMm/r²................1)

force that is helping in circular motion of the satellite around the earth is centripetal force

so F=mv²/r........2)

equating both the equations we get

GMm/r²=mv²/r

v²=GM/r.........3)

we know that speed=distance/time

here s= circumference=2pir and time=T

v=2pir/T

r=Tv/2pi

substituting the value of r in eqn 3

v²=2piGM/Tv

v³=2piGM/T

v===6.22*10³m/s

so answer is 6.22*10³m/s. ( if this is incorrect try 6223m/s or 6222 m/s or 6.223*10³ m/s or 6.222*10³m/s)