Question

Find the speed of a satellite in a circular orbit around the earth with a radius 4.03 times the mean radius of the earth. (radius of earth = 6.37×103 km, mass of earth = 5.98×1024 kg, g = 6.67×10-11 nm2/kg2.)

Answer 1

we will equate the earth's grav force to the centrip force acting on the satellite

GMm/r^2=mv^2/r

where M is the mass of the earth, v the speed of the satellite, r the distance from the center of the Earth, m the mass of the satellite, and G the newtonian grav cst

this gives us:

v^2=GM/r
v=sqrt[GM/r] =
sqrt[6.67x10^(-11)(6x10^24)/(3.67xR)] =
4137.5 m/s

(where R is the radius of the Earth=
6.37x10^6m)