A satellite will travel indefinitely in a circular orbit around the earth if the

Question

A satellite will travel indefinitely in a circular orbit around the earth if the normal component of its acceleration is equal to g(R/r)^2 , where g = 9.81, R = the radius of the Earth, and r is the distance from the center of the earth to the satellite. Find the speed of a satellite traveling in a circular orbit 480 km above the surface of the Earth NOTE: Be careful with the distances here! One is from the surface of the Earth and one is from the center. Also make sure to use consistent units in the ratio R/r.

A satellite will travel indefinitely in a circular orbit around the earth if the normal component of its acceleration is equal to g where g 9.81 m (r) the radius of the Earth, and ris the distance from the center of the earth to the satellite. Find the speed of a satellite traveling in a circular orbit 480 km above the surface of the Earth NOTE: Be careful with the distances here! One is from the surface of the Earth and one is from the center. Also make sure to use consistent units in the ratio R/r.

Explanation / Answer

Centripetal force = m*v^2/r

mg(R/r)^2 =m*v^2/r

v = sqrt(gR^2/r)

=sqrt(9.8*(6371*10^3)^2/(6371+480)*10^3))

=7619.8 m/s

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