Potential energy of gravitation

[pixelpuffin]

I was writing a script to help me calculate gravitation and various other things when i noticed i don't know how to calculate this
I need to calculate the kinetic energy of an object being pulled towards a second object until they meet knowing only the weight of the objects, the distance of the objects, and the distance at which they meet and thus stop accelerating towards each other
with a very large object like Earth accelerating a small object like a football you can assume gravity to be constant, but in this case the distance will change to a small fraction of what it was
I'd appreciate if you also knew if this equation translates to other forces

 

[mikeph]

Newton's law of gravitation will give you the weights, you do need to know their masses and their separation distance.

To calculate the kinetic energy you must solve the differential equation to find the positions and velocities of the two objects. This is because the force on the first body depends on the position of the 2nd body (and vice versa) so you have two coupled differential equations, with two unknowns (their separation and their relative speed in 1D).

Once you solve this to find their relative speed you can find the kinetic energy of one (as seen by the other) using 0.5*m*v^2. Alternatively you can use energy conservation to say that their kinetic energy change must be equal to their loss in gravitational potential energy (which depends only on distance, not speed). This is probably a more accurate approach.

 

[sophiecentaur]

Do you really want to go into diff equations? Go for the second approach, above. If you just calculate the Gravitational Potential Energy when they're separated and the GPE when they are touching - at positions about their Centre of Mass. The difference will give their total Kinetic Energy and the ratio of their velocities can be found from Momentum conservation - hence, their shares in the total KE. Two simultaneous equations.
PS It's masses you want to work with as their 'weights' will be changing with separation distance.

 

[ZapperZ]

I was writing a script to help me calculate gravitation and various other things when i noticed i don't know how to calculate this
I need to calculate the kinetic energy of an object being pulled towards a second object until they meet knowing only the weight of the objects, the distance of the objects, and the distance at which they meet and thus stop accelerating towards each other
with a very large object like Earth accelerating a small object like a football you can assume gravity to be constant, but in this case the distance will change to a small fraction of what it was
I'd appreciate if you also knew if this equation translates to other forces

You might want to start by reading this first, and then figure out what level of complexity are you trying to consider in your calculation:

https://www.physicsforums.com/showthread.php?t=511172

For example, if this is a 2-body problem, and the bodies are of comparable size, then you simply have to describe MORE of the situation, i.e. are they bodies floating in space. This is because the center of mass of the system will remain fixed, but when you let the two bodies go, they will both move and meet at the center of mass location. So this can get more complicated than you are realizing.

Zz.

 

[pixelpuffin]

would it be wrong to say that for any two given bodies in space you could calculate the escape velocity of one of the objects from the other at it's current distance then calculate the escape velocity from the distance at which it collides with the other object from there calculate the energy required to get to escape velocity from both points and find the difference and that that would be the potential energy of the gravitation