Question

An alien spacecraft is out in space leaving an unknown planet. It detects the pull of gravity due to this unknown planet to be 100 N. Later the Alien rechecked the pull on their spacecraft and detects it to be 33 N. By what factor has their distance changed as they left the unknown planet?

Answer 1

We know that gravitational pull on a object is given by:

F = G*m1*m2/R^2

m1 = mass of planet

m2 = mass of spaceship

G = Gravitational constant = 6.674*10^-11

R = distance between both planet and spaceship

Suppose when spaceship is at R1 distance from planet, then

F1 = G*m1*m2/R1^2 = 100 N

And when spaceship is at R1 distance from planet, then

F2 = G*m1*m2/R2^2 = 33 N

So, divide both equation

(G*m1*m2/R1^2)/(G*m1*m2/R2^2) = 100/33

(R2/R1)^2 = 100/33

R2 = R1*sqrt (100/33)

R2 = 1.74*R1

So their distance has been changed by a factor of 1.74 as they left the unknown planet

Let me know if you've any query.