Satellite 1, which has mass M1, orbits earth at a semi major axis r1. Satellite 2 has a mass of 6m1 and orbits at 2r1. What is the ratio of the gravitational force by earth on satellite 2 to the gravitational force by earth in satellite 1?

This states that the gravitational force of attraction, F between two masses m₁ and m₂ is directly proportional to the product of their masses and inversely proportional to the square of their distance apart, r.

So, F = Gm₁m₂/r² where G = universal gravitational constant = 6.67 10⁻¹¹ Nm²/kg²

Gravitational force on satellite 1

Now, for Satellite 1 with mass M₁ and at a distance r₁ from the earth, the gravitational force of attraction between the earth of mass M and the satellite is

F₁ = GMM₁/r₁²

Gravitational force on satellite 2

Also, for Satellite 2 with mass M₂ = 6M₁ and at a distance r₂ = 2r₁ from the earh, the gravitational force of attraction between the earth of mass M and the satellite is

F₂ = GMM₂/r₂²

F₂ = GM6M₁/(2r₁)²

F₂ = 6GMM₁/4r₁²

Ratio of gravitational forces

So, the ratio of the gravitational force by earth on satellite 2 to the gravitational force by earth in satellite 1 is

F₂/F₁ = 6GMM₁/4r₁² ÷ GMM₁/r₁²

F₂/F₁ = 6/4

F₂/F₁ = 3/2

So, the ratio of the gravitational force by earth on satellite 2 to the gravitational force by earth in satellite 1 is 3/2

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