Calculating distance

Question

An astronaut on a spacewalk outside a spaceship with a mass of 3.16x10⁸ kg far from any other massive bodies leaves a wrench floating outside the ship. The wrench feels an acceleration of 6.43x10^-7 m/s² toward the spaceship. What is the distance between the centre of the wrench and the centre of the spaceship?

Answer 1

Gravitation Force between two bodies is

F= G Mm/d²

G = Gravitational Constant ( fixed every where)

M= Mass of spaceship =3.16* 10⁸

Force = mass *acceleration =m*a , where a = Acceleration of wrench

m = mass of wrench

a = G*m/d²

^{d = √ ( G*M/a)}

Now plug in values given

and G= 6.67259 x 10 -11 N m 2 /kg 2.

M = 3.16* 10⁸ kg and a= 6.43*10 ^-7 m/s²

You get your answer in m ( Distance between two centers)