The average distance separating Earth and the Moon (center to center) is 384,000
ID: 1967816 • Letter: T
Question
The average distance separating Earth and the Moon (center to center) is 384,000 km. Use the data in the table to find the net gravitational force exerted by Earth and the Moon on a 3.00 104-kg spaceship located halfway between them.
1 N use graph below
Useful Planetary Data
Body
Mass (kg)
Mean Radius (m)
Period (s)
Distance from Sun (m)
T2/r3 (s2/m3)
Mercury
3.18 1023
2.43 106
7.60 106
5.79 1010
2.97 1019
Venus
4.88 1024
6.06 106
1.94 107
1.08 1011
2.99 1019
Earth
5.98 1024
6.37 106
3.156 107
1.496 1011
2.97 1019
Mars
6.42 1023
3.37 106
5.94 107
2.28 1011
2.98 1019
Jupiter
1.90 1027
6.99 107
3.74 108
7.78 1011
2.97 1019
Saturn
5.68 1026
5.85 107
9.35 108
1.43 1012
2.99 1019
Uranus
8.68 1025
2.33 107
2.64 109
2.87 1012
2.95 1019
Neptune
1.03 1026
2.21 107
5.22 109
4.50 1012
2.99 1019
Pluto
~1.4 1022
~1.5 106
7.82 109
5.91 1012
2.96 1019
Moon
7.36 1022
1.74 106
-
-
-
Sun
1.991 1030
6.96 108
-
-
-
Useful Planetary Data
Body
Mass (kg)
Mean Radius (m)
Period (s)
Distance from Sun (m)
T2/r3 (s2/m3)
Mercury
3.18 1023
2.43 106
7.60 106
5.79 1010
2.97 1019
Venus
4.88 1024
6.06 106
1.94 107
1.08 1011
2.99 1019
Earth
5.98 1024
6.37 106
3.156 107
1.496 1011
2.97 1019
Mars
6.42 1023
3.37 106
5.94 107
2.28 1011
2.98 1019
Jupiter
1.90 1027
6.99 107
3.74 108
7.78 1011
2.97 1019
Saturn
5.68 1026
5.85 107
9.35 108
1.43 1012
2.99 1019
Uranus
8.68 1025
2.33 107
2.64 109
2.87 1012
2.95 1019
Neptune
1.03 1026
2.21 107
5.22 109
4.50 1012
2.99 1019
Pluto
~1.4 1022
~1.5 106
7.82 109
5.91 1012
2.96 1019
Moon
7.36 1022
1.74 106
-
-
-
Sun
1.991 1030
6.96 108
-
-
-
Explanation / Answer
The net gravitational force is the difference from the gravitational force from the Earth and the gravitational force from the Moon.
We also know the distance between the ship and the moon equals the distance between the ship and the earth, which is 192000km, or 1.92x10m.
F=Gm1m2 / r²
for the Earth:
F=Gm1m2 / r²
F=(6.67428x10¯¹¹N (m/kg)²)(5.98x10²kg)(3.00x10kg) / [(1.92x10m)²]
F=32.48063x10¹N or 324.8063N;
for the Moon:
F=Gm1m2 / r²
F=(6.67428x10¹¹N (m/kg)²)(7.36x10²²kg)(3.00x10kg) / [(1.92x10m)²]
F=39.97616x10¹ or 3.997616N;
The net gravitational force then would be:
324.8063-3.997616
=320.808684 or 3.20808684x10²N
Assuming all the numbers in the question is given to 3 significant digits, the answer should be rounded to 3 significant digits too, which would be 3.21x10²N.
Final answer: 3.21x10²N towards / from the Earth
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