Answer:
The force of gravitation between two objects can be calculated using the formula for universal gravitation:
�
=
�
⋅
�
1
⋅
�
2
�
2
F=
r
2
G⋅m1⋅m2
Where:
�
F is the force of gravitation
�
G is the gravitational constant (
6.67430
×
1
0
−
11
m
3
kg
−
1
s
−
2
6.67430×10
−11
m
3
kg
−1
s
−2
)
�
1
m1 and
�
2
m2 are the masses of the two objects
�
r is the distance between the centers of the two objects
In this case, one of the objects is the Earth and the other is the rocket. The mass of the rocket doesn't really matter in this context because the problem only involves the gravitational force acting on the rocket.
Given that the force of gravitation on the rocket when it's 400 km from the center of the Earth is 900 N, and we're looking to find the force when it's 800 km from the center of the Earth, we can set up the following relationship:
�
1
�
2
=
�
2
2
�
1
2
F
2
F
1
=
r
1
2
r
2
2
Where:
�
1
F
1
is the initial force (900 N when the rocket is 400 km from the Earth's center)
�
2
F
2
is the force we want to find
�
1
r
1
is the initial distance (400 km from the Earth's center)
�
2
r
2
is the new distance (800 km from the Earth's center)
Plugging in the values:
�
2
900
N
=
(
800
km
)
2
(
400
km
)
2
900N
F
2
=
(400km)
2
(800km)
2
Solving for
�
2
F
2
:
�
2
=
900
N
⋅
(
800
km
)
2
(
400
km
)
2
F
2
=900N⋅
(400km)
2
(800km)
2
Calculating this gives:
�
2
=
3600
N
F
2
=3600N
So, when the rocket is 800 km from the center of the Earth, the force of gravitation on the rocket would be 3600 N.