Answer:
a). F = 3.376 N, θ = 59.18°
b). W = 1.3x
J
Explanation:
We know
Gravitational constant, G = 6.673 x
N-
/
Mass of the earth, M = 5.97 x
kg
mass of the moon, m = 7.35 x
kg
Mass of the satellite,
= 1250 kg
Distance between the objects, r = 3.84 x
km
= 3.84 x
m
Now
The force on the satellite due to moon


= 0.0415 N ( in the positive x direction )
The force on the space craft due to the earth


= 3.377 N ( at 60° to x axis )
Now component of force of earth along x axis

= 3.377 x 0.5
= 1.6885 N
Now component of force of earth along y axis

= 3.377 x 0.86
= 2.90 N
∴ Net force on the space craft due to earth and moon along x axis
=
cos 60+
= 1.3885+0.0415
= 1.73 N
Net force on the space craft due to earth and moon along y axis
= 
= 2.90 N
Therefore, total force F = 
F = 
F = 3.376 N
∴ Magnitude of the net gravitational force on the space craft is 3.376 N
Direction of net force on the space craft is given by


°
Therefore this direction is 59.18° from the line joining earth and the space craft.
b).
∴ Gravitational potential energy of the space craft is given by



E = 1312769385 J
E = 1.3 x
J
Therefore minimum work done is 1.3x
J