Can Distance Alone Prove Gravitational Binding?

[wolram]

Can the distance between two bodies be calculated to prove they are gravitationally bound?

Use two bodies with known mass.

 

[Wallace]

You need to know velocity as well as distance in order to know this. If you took a snapshot of the Earth and the Moon you wouldn't know whether the Moon was in orbit, moving away from the Earth at sufficient velocity to escape or indeed plunging straight towards it!

Edit: you would also need to know that masses, since that will tell you what velocities would indicate stable orbits. So that's three things, position, velocity and mass.

 

[wolram]

Thankyou Wallace.

From that i guess there is no way the milky way and its motion towards the great attractor could be proven by calculation to be cause by gravity?

 

[Wallace]

No, since we can get an estimate of the masses of the bodies involved and measure velocities via redshift, hence we have (to some level of precision) the three things I mentioned.