Gravitational force and tangential velocity of planets

[Cfem]

This isn't a HW question exactly, but I'm trying to model planetary motion and I've having trouble remembering something I learned a while ago when I took physics.

I remember that the tangential velocity for a something to orbit a planet is v = sqrt(-G * M/r), but I need to decompose this into an x velocity an a y velocity and I'm having issues with the Trig because I remember you have to draw the trig triangles properly or else the calculations don't come out properly. I need to break down the tangential velocity of each planet with respect to the sun into velocities in the x and y planes

My initial thought was to have it be something like

V_x = v_t * sin(angle between sun and planet)
V_y = v_t * cos(angle between sun and planet)

But it seems too simple and I don't know if that's correct.

There's a similar problem going on with calculating the acceleration of the planet. Once again, I need to break the acceleration cause by the gravitational force between the sun and the planet into x and y components.

F = ma set to the gravitational force, etc etc => a(towards the sun) = G * m_s / R

So to break it up I was going to do something similar to the above, but I can't get the trig triangles to look right.

If this is in the wrong section/is considered a HW problem, feel free to move it, but it's just a conceptual stumbling block I"m having because it's been a while since I've taken Physics and I need to get these right to try and construct a proper model.

Thanks.

 

[tiny-tim]

Hi Cfem!

I remember that the tangential velocity …

uhh? what other sort of velocity is there?

My initial thought was to have it be something like

V_x = v_t * sin(angle between sun and planet)
V_y = v_t * cos(angle between sun and planet)

If the orbit is circular, yes, v is constant, and its components are vcos and vsin of the angle.

 

[Uglybb]

If you want just a quick dirty answer look up "kepler's law" it will give you the solution.

However be aware the result is an approximation (Newtonian physics breaks down in space) you planet will not precess. You will need to invoke general relativity to solve that problem if you want correct modelling.

Wikipedia has a full explanation "Two-body_problem_in_general_relativity"