Answer:F
′
=4F
So, if the masses of the bodies are doubled and the distance between their centers is reduced to half, the gravitational force will become four times the original gravitational force.
Explanation:The gravitational force between two objects is given by Newton's law of universal gravitation:
�
=
�
⋅
�
1
⋅
�
2
�
2
F=
r
2
G⋅m
1
⋅m
2
Where:
�
F is the gravitational force,
�
G is the gravitational constant (
6.674
×
1
0
−
11
N
⋅
m
2
/
kg
2
6.674×10
−11
N⋅m
2
/kg
2
),
�
1
m
1
and
�
2
m
2
are the masses of the two objects, and
�
r is the distance between the centers of the two objects.
If the masses of the bodies are doubled and the distance between their centers is reduced to half, the new gravitational force (
�
′
F
′
) can be calculated as follows:
�
′
=
�
⋅
(
2
�
1
)
⋅
(
2
�
2
)
(
0.5
�
)
2
F
′
=
(0.5r)
2
G⋅(2m
1
)⋅(2m
2
)
�
′
=
�
⋅
4
�
1
⋅
4
�
2
0.25
�
2
F
′
=
0.25r
2
G⋅4m
1
⋅4m
2
�
′
=
4
�
⋅
�
1
⋅
�
2
0.25
�
2
F
′
=
0.25r
2
4G⋅m
1
⋅m
2
�
′
=
4
⋅
�
⋅
�
1
⋅
�
2
�
2
×
4
F
′
=
r
2
4⋅G⋅m
1
⋅m
2
×4
