A couple of astronauts agree to rendezvous in space after hours. Their plan is t

Question

A couple of astronauts agree to rendezvous in space after hours. Their plan is to let gravity bring them together. She has a mass of 66.0kg and he a mass of 72.0kg , and they start from rest 25.0m apart.

1- Find his initial acceleration.

2- Find her initial acceleration.

3- If the astronauts' acceleration remained constant, how many days would they have to wait before reaching each other? (Careful! They both have acceleration toward each other.)

4- Would their acceleration, in fact, remain constant?

Explanation / Answer

force on each = G M m / r^2 = 6.67x10^-11*72*66/25^2 =

= 5.071 x 10^-10 Newtons

Her acc = force/mass = 7.68 x 10^-12 m/s^2

His acc = force / mass = 7.043 x 10^-12 m/s^2

The distance each travels is given by

d = (1/2) a t^2

The sum of their distances is 25 m so

25 = (1/2) a t^2 for him + (1/2) a t^2 for her

or

t^2 = 50 / (his a + her a) = 50 / (7.68 + 7.043) x 10^-12 = 3.396 x 10^12

t = 1842824 seconds = 21.33 days

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