Answer:
Step-by-step explanation:
The force of gravity acting on an object depends on its mass and the distance from the center of the gravitational body (in this case, the Earth). The force of gravity is inversely proportional to the square of the distance between the centers of the two objects.
Let's assume the mass of the satellite remains constant.
Given that the force of gravity on the satellite when it is on the Earth's surface is 2440 N, and it is transported three Earth radii away from the surface, we need to calculate the new force of gravity.
The force of gravity on the satellite at its new distance can be found using the formula:
�
=
�
×
�
×
�
�
2
F=
r
2
G×M×m
where:
F is the force of gravity,
G is the gravitational constant (approximately 6.674 × 10^-11 N m²/kg²),
M is the mass of the Earth,
m is the mass of the satellite, and
r is the distance between the center of the Earth and the satellite.
Since we are assuming the satellite's mass remains constant, we can ignore it in this context. We are interested in the new force (F') of gravity on the satellite, which occurs when the satellite is three Earth radii (3r) away from the surface. So, the new distance (r') is:
�
′
=
3
×
Earth’s radius
=
3
×
�
r
′
=3×Earth’s radius=3×r
Now, we can find the new force of gravity (F') on the satellite:
�
′
=
�
×
�
(
3
�
)
2
F
′
=
(3r)
2
G×M
�
′
=
�
×
�
9
�
2
F
′
=
9r
2
G×M
Finally, we know that the force of gravity on the Earth's surface is 2440 N, so we can set up the following equation:
2440
N
=
�
×
�
9
�
2
2440 N=
9r
2
G×M
Now, we can solve for the new force of gravity (F'):
�
′
=
2440
×
9
�
2
�
×
�
F
′
=
G×M
2440×9r
2
Plug in the values for G, M, and solve for F':
�
′
=
2440
×
9
×
(
Earth’s radius
)
2
6.674
×
1
0
−
11
×
Earth’s mass
F
′
=
6.674×10
−11
×Earth’s mass
2440×9×(Earth’s radius)
2
The exact value of the Earth's radius and mass is not given in the question, so you'll need to substitute those values to find the exact force of gravity on the satellite at its new distance.