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 19.0mapart

Part A

Find his initial acceleration.

Part B

Find her initial acceleration.

Part C

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.)

Part D

Would their acceleration, in fact, remain constant?

Explanation / Answer

The gravitational force acting on the astronauts is

Fg = m a

where Fg = G m1 m2 / d2

where m1 = mass of her = 66 kg

m2 = mass of his = 72 kg

Part A:

Fg = m2 a

==> G m1 m2 / d2 = m2 a2

==> a2 = G m1 / d2

= 6.673 x 10-11 x 66 / 19 x 19

= 1.219 x 10-11 m/s2

Part B:

Fg = m1 a

==> G m1 m2 / d2 = m1 a1

==> a1 = G m2 / d2

= 6.673 x 10-11 x 72 / 19 x 19

= 1.330 x 10-11 m/s2

Part C

If the want to reach each other one astronaut has to trave the 19 m i.e. X1 = X2 + d

X1 = ut + 0.5 a1t2 and  X2 = ut + 0.5 a2t2

initial velocity is zero. So, we get

0.5 a1t2 = 0.5 a2t2 + d

   a1t2 = a2t2 + 2d

substitute values

1.219 x 10-11 t2 = - 1.330 x 10-11 t2 + 2 * 19

  t2 = 38 / 2.55 x 10-11   

==> t = 1.220 x 105 s = 33.90 hr = 1.412 days

Part D

Their acceleration will increases.

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