Calculate the gravitational potential of a point on the surface of the moon closest to the earth
Mass of Earth : 6 X 1024m
Mass of moon : 7.4 X 1022m
Radius of moon : 1.7 X 106
Dist from centre of earth to centre of moon : 3.8 X 108
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Answer:
Consider gravitational potential from both moon and Earth
We use the formula -Gm/r
From earth,
gravitational potential = - 6.67X10-11 X 6.0X1024 / 3.8X108 = - 1.05X106
From moon,
gravitational potential = - 6.67X10-11 X 7.4X1022 / 1.7X106 = - 2.90X106
since gravitational potential is a scalar, you can add it up
answer = -3.95X106 J/kg
My question...:
Why is it that from earth, I used the dist from the centre of earth to the centre of moon but for moon, I used its radius?
Technically speaking, you will have to consider from centre of earth to surface of moon. Thus, you can take the distance from centre of earth to centre of moon minus radius of moon
However, the difference is extremely minute (100 times difference), and the final answer would not have been much different.
Simplifying like this makes the calculations faster.
