General Conservation of Momentum Question

[putongren]

Hey All,

I was looking at several conservation of momentum question, and one question caused me to thinking about something. In those planet versus satellite questions, a satellite passes through a moving planet and the gravitational pull of the planet alters the final satellite's velocity and vice versa. I was wondering why do we use the conservation of momentum principle to solve for the final velocity of the satellite and the planet.

 

[Andy Resnick]

Because that's the most simple way to solve the problem. One could try and solve the problem using dynamics or conservation of energy, but it's more complicated.

 

[putongren]

Hey Andy,

Thanks for the reply, but I think what I'm really trying to ask is why does the conservation of momentum principle work in solving this type of problem. It's not enough for me to just memorize the fact that you use conservation of momentum to solve the planet versus satellite problem, I have to know why you choose it to work. Also, you mentioned other ways to solve this type of problem by using dynamics or conservation of energy. Can you give me an example of how one would go about using those principles?

 

[Andy Resnick]

how would you try and solve the problem?

 

[ojs]

Allthough I havn't gone through the calculations then I think that solving problems like that with anything other then conservation laws you would have to find the path of the trajectory (which involves solving some differential equations) and then get the final velocity from the trajectory path by differentiation.

This of course is a lot more complicated then with simple algebra using conservation laws.

Hope this explains it a bit (again, I havn't gone through the calculations so take this with a grain of salt).