Question

20.) Two astronauts have deserted their spaceship in a region of
space far from the gravitational attraction of any other
body. Each has a mass of 100 kg and they are 100 m apart.
They are initially at rest relative to one another. How long
will it be before the gravitational attraction brings them
1 cm closer together?
(a) 2.52 days
(b) 1.41 days
(c) 0.70 days
(d) 1.41 sec​

Answer 1

Explanation:

Given wo astronauts have deserted their spaceship in a region of

space far from the gravitational attraction of any other

body. Each has a mass of 100 kg and they are 100 m apart.

They are initially at rest relative to one another. How long

will it be before the gravitational attraction brings them

1 cm closer together?

• We are given m1 = m2 = 100 kg, r = 100 m
• Acceleration of 1 st Astronaut
• A1 = Gm1m2 / r^2 x 1/ m1 = Gm2 / r^2
• Acceleration of 2 nd Astronaut
• A2 = Gm1m2 / r^2 x 1/m2 = Gm1 / r^2
• Net acceleration will be
• A = A1 + A2
•   = Gm2 / r^2 + Gm1/r^2
•   = 2 Gm1 m2 / r^2
•   = 2 x 6.67 x 10^-11 x 100 / 100^2
•   = 2 x 6.67 x 10^- 13 m / s^2
• As s = 1/2 at^2
•   Now t = √2s / a
•           t = √2 x 0.01 / 2 x 6.67 x 10^-13
• So t = 1.41 days