Question

Question 9 ListenWhen a satellite is at a distance d from the center of the Earth, the force due to gravity on the satellite is F. What would the force due to gravity on the satellite be when its distance from the center of the Earth is 3d?F9F

Answer 1

F/9

Step-by-step explanation:

F = GmM/ d² where F is the force due to gravity, F₂ = is the force due to gravity when d in meters, the distance from the center of the earth is 3d and G is gravitional constant in Nm²/kg²

F₂ = GmM / (3d)² = GmM/ 9d²

make d² subject of the formula in the first formula

d² = GmM/ F

substitute this into the second formula

F₂ = GmM / 9( GmM / F) = GmM × (F /9GmM)

cancel GmM

F₂ = F/9

Answer 2

F/9

Step-by-step explanation:

There's Newton formula for attraction force between 2 objects with mass and a distance between them:

`F_G = G(M_1M_2)/(d^2)`

where G is the gravitational constant.
`M_1,M_2` are the masses of the 2 objects. and d is the distance between them.

Consider that the distance variable is squared and in the denominator of the formula. So in the case where the distance is tripled to 3d, the masses stay the same, the gravitational force would be reduced by
`3^2 = 9` times

So the new force would be F/9