Show how gravitational potential varies between the earth and the moon

[question dude]

Homework Statement

gravitational potential at surface of the Earth = -63MJkg-1
gravitational potential at surface of the moon = -2MJkg-1The 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 into 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

 

[voko]

The potential is a scalar, but not constant, at any point it is inversely proportional to the distance from its source. It is always negative, approaching zero infinitely far away.

 

[BruceW]

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

Yep. That's correct.

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

Yes. So the gravitational potential is going to be negative. What is wrong with having a 'peak' that is still less than zero?

 

[question dude]

Yep. That's correct.


Yes. So the gravitational potential is going to be negative. What is wrong with having a 'peak' that is still less than zero?

so at the point where the two masses' gravitational field strength cancel, say if the gravitatiional potential due from one mass was -60MJkg-1 and the gravitational potential due from the other mass is -40MJkg-1, the resultant potential at this point would be -100MJkg-1?

 

[BruceW]

yeah, that's it. I haven't worked out the values for this specific problem, but, yes, that is the right idea.