Why do two masses move towards each other under gravity?

[Kyoma]

Homework Statement

This picture represents the gravitational field lines for a pair of masses. The problem I have with this picture is that it seems to indicate that the 2 masses would not move towards each other, which is surely wrong since gravity would cause two masses to move towards each other. Is there an explanation for this? Much help appreciated. Thanks!

 

[haruspex]

The problem I have with this picture is that it seems to indicate that the 2 masses would not move towards each other, which is surely wrong since gravity would cause two masses to move towards each other.

A point mass is not subject to the field lines it generates. If you want to consider each body as a mass distributed over a volume then you would need to take into account the forces that maintain the structure of each body.

 

[Kyoma]

A point mass is not subject to the field lines it generates. If you want to consider each body as a mass distributed over a volume then you would need to take into account the forces that maintain the structure of each body.

Let's us ignore point masses. So, I presume you're saying that if I have two masses, m1 and m2, whereby m2 is significantly larger than m1, m1 will move towards m2 whereas if I have two masses of equal mass and assuming no other external forces, they will not move towards each other?

 

[Dadface]

Homework Statement

This picture represents the gravitational field lines for a pair of masses. The problem I have with this picture is that it seems to indicate that the 2 masses would not move towards each other, which is surely wrong since gravity would cause two masses to move towards each other. Is there an explanation for this? Much help appreciated. Thanks!

Where did you get the picture from? It resembles the field pattern you would get from two equal strength repelling particles/objects, not what you would get from attracting objects such as masses.

 

[haruspex]

Let's us ignore point masses. So, I presume you're saying that if I have two masses, m1 and m2, whereby m2 is significantly larger than m1, m1 will move towards m2 whereas if I have two masses of equal mass and assuming no other external forces, they will not move towards each other?

No, that's not what I was saying at all.
The diagram you show is quite correct for a third body (a 'test' mass) exposed to the combined field. But it treats the two bodies in the picture as point masses, and you want to understand what happens if you consider them instead as aggregates.
That gets complicated because you now have to consider the field inside the body. Right in the middle, of course, the field due to that body cancels out, and you only feel the field due to the other body. Elsewhere inside the body, there is some field due to it, but integrating over the whole body it will still cancel. Therefore the body taken as a whole does not feel its own field, and the diagram is not relevant to this case.