Answer:
(a) Acceleration of female astronaut = 9.33*10^-12 m/s^2; Acceleration of male astronaut = 7.56*10^-12 m/s^2
(b) 27.013 days
(c) No, their accelerations would not be constant.
Explanation:
In the given question, we have:
Mass of female astronaut = 60.0 kg
Mass of male astronaut = 74.0 kg
Distance between them (S) = 23.0 m
(a) The free-body diagram is shown in the attached figure.
Using the equations below, the initial accelerations of the two astronauts can be calculated:
Force of gravity (F) =
G = 6.67*10^-11
F = (6.67*10^-11 *60*74)/23^2 = 5.598*10^-10 N
For the female astronaut, her initial acceleration = F/ = 5.598*10^-10/60 = 9.33*10^-12 m/s^2
For the male astronaut, his acceleration = F/ = 5.598*10^-10/74 = 7.56*10^-12 m/s^2
(b) Since the different between their mass is not much, we can deduce that:
= (9.33*10^-12 + 7.56*10^-12)/2 = 8.445*10^-12 m/s^2
Using the equation below, we can calculate the the time:
S = ut + 1/2 (at^2) where u = 0
23 = 1/2 (8.445*10^-12)*t^2
t^2 = 5.447*10^12
t = 2333883.044 s = 27.013 days
(c) No, their accelerations will not be constant. It will increase because their radii would be decreasing.
