Question

Two satellites revolve around the Earth. Satellite A has mass m and has an orbit of radius r. Satellite B has mass 6m and an orbit of unknown radius rb. The forces of gravitational attraction between each satellite and the Earth is the same. Find rb.

Answer 1

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Step-by-step explanation:

M = Mass of the Earth

m = Mass of satellite

r = Radius of satellite

G = Gravitational constant

`F=G(Mm)/(r^2)`

`F=G(M6m)/(r_b^2)`

`G(Mm)/(r^2)=G(M6m)/(r_b^2)\\\Rightarrow (1)/(r^2)=(6)/(r_b^2)\\\Rightarrow (r_b^2)/(r^2)=6\\\Rightarrow (r_b)/(r)=√(6)\\\Rightarrow r_b=2.44948r`

`r_b=2.44948r`