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## Homework Statement

A 1,000 kg satellite traveling at speed "v" maintains an orbit of radius, "R" around the earth. What should be its speed if it is to develop a new orbit of radius "4R" ?

## Homework Equations

Gravitational force equation (F) = (Gmems)/r^2

G (universal gravitational constant) = 6.67 x 10^-11 N*m^2/kg^2

me = mass of earth

ms = mass of satellite

r= distance between the centers of me and ms

Centripetal force equation (Fc) = (ms*v^2)/r

ms = mass of satellite

v^2/r = centripetal acceleration

r = radius of orbit for satellite

## The Attempt at a Solution

The satellite and the earth both exert a mutual attraction for each other through the gravitational force equation and the earth exerts a centripetal force to the satellite, so these two forces can be set equal to each other, since the gravitational force provides the centripetal force necessary for the satellite to orbit the earth.

The speed of satellite "v" when radius is "R"[/B]

⇒(Gmems)/R^2 = (ms*v^2)/R

⇒(G*me)/R = v^2

⇒v = √(Gme)/R

New speed of satellite "v*" when radius is "4R"

⇒(Gmems)/R^2 = (ms*(v*^2)/4R

⇒(4Gme)/R = v*^2

⇒v* = 2√(Gme)/R

since speed of satellite "v" when radius is "R" is equal to √(Gme)/R, substitute this into v* equation,

∴ v* = 2v

However my solution is wrong, and I don't understand why. I would like to know conceptually as well as mathematically the reason why. Any help would be great, thanks!

I have trouble with this problem. Please correct my approach and if my understanding of the concept is wrong. Thanks!