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**Homework Statement**

gravitational potential at surface of the earth = -63MJkg-1

gravitational potential at surface of the moon = -2MJkg-1

**The attempt at a solution**

I thought gravitational potential was a scalar, so in which case, you would surely just add up the potential due from both masses at any point along the line between them to show how the 'resultant' potential varies between them

apparently, that isn't the case, and I suppose that does make sense, because the two masses are pulling in opposite direction. Gravitational potential is the amount of energy you would have to put in to escape from the gravitational influence of a particular mass, and if you already have a force 'assisting' you (gravity due from another mass on the other side of you), then you don't require as much energy. Is this way of thinking right?

but I'm really puzzled by the mark scheme:

''Gravitational potential is a scalar quantity. The total potential at any point along a line joining the Earth and Moon is the sum of the potentials produced by the Earth and Moon separately''

doesn't ''sum of'' means you add up the two quantities. So in which case, how would you get a 'peak' in gravitational potential somewhere between the earth and the moon whereby the gravitational potential is at its least negative?

if you add a negative value to a negative value, you get even larger negative value, so I'm slightly confuse