## Velocity of object with inverse square force?

Mechanics, discrete, statistics, ...
helstreak
Posts: 19
Joined: Mon Jan 26, 2009 5:00 am

### Velocity of object with inverse square force?

If object_1 is acted on by a force from object_2 that is inversely proportional to the square of the objects distance (think gravity), is there away to determine the velocity of object_1 at a given distance from object_2?

So the force between the two things is: F=-1/r^2 where r is the distance between said objects. Object_1 is being pulled to object_2. Now if we start with object_1 being R distance away from object_2, how would one find an equation for velocity after time t and velocity at distance r?

Thanks for any help you can give. I'm a little out of practice with differential equations.

rmillika
Posts: 39
Joined: Thu Apr 05, 2007 3:37 pm

### Re: Velocity of object with inverse square force?

helstreak wrote:If object_1 is acted on by a force from object_2 that is inversely proportional to the square of the objects distance (think gravity), is there away to determine the velocity of object_1 at a given distance from object_2?

So the force between the two things is: F=-1/r^2 where r is the distance between said objects. Object_1 is being pulled to object_2. Now if we start with object_1 being R distance away from object_2, how would one find an equation for velocity after time t and velocity at distance r?

Thanks for any help you can give. I'm a little out of practice with differential equations.
You don't need any differential equations, just energy and momentum conservation. The potential energy is -G*m1*m2/r. If the two objects start at rest, the momenta have to stay equal and opposite so m1*abs(v1)=m2*abs(v2). The kinetic energy of each is m*v^2/2. The total kinetic energy is the change in the potential energy. You have two equations in two unknowns.