# Energy conservation problem (two star system)

Hi guys -

Here's the problem I am chewing on:

A binary star system consists of two stars, each equal to the sun in mass. The distance between the two stars is 1.0 X 10^12m. A comet which is essentially at rest, begins to make its journey toward the binary star system as a result of gravity acting upon the comet. If the comet begins a straight line approach that will result in it passing through the midpoint of the distance between the stars, what will the velocity of the comet be at the midpoint?

I believe this to be a problem in which we need to identify the gravitational PE between the two stars, and use the answer to calculate the gravitational force acting on the comet being pulled into the star system.

I can find Ug by using the PE formula for two bodies: Ug = -G(m1m2)/r

I am coming up with roughly 2.65 X 10^8 J, but I don't understand how I can turn this around to apply to the comet's approach to the system. Any suggestions as to where I can start?

Thanks

Jordan

Hi guys -

Here's the problem I am chewing on:

AI believe this to be a problem in which we need to identify the gravitational PE between the two stars, and use the answer to calculate the gravitational force acting on the comet being pulled into the star system.

I can find Ug by using the PE formula for two bodies: Ug = -G(m1m2)/r

I am coming up with roughly 2.65 X 10^8 J, but I don't understand how I can turn this around to apply to the comet's approach to the system. Any suggestions as to where I can start?

Thanks

Jordan

I'm not sure that you need to worry about the PE between the stars themselves.

It may be more fruitful to consider the PE difference between infinity and the comets closest approach to one of the stars, ie the 1/2 way point between the two. Realize that you have twice this quantity from symmetry, and convert to kinetic energy. The other approach I might consider would be to realize that the center of mass of the two stars is midway between them, make an adjustment in terms of distance or mass, as two masses separated by a huge distance will in unison exert less force than two side by side.

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