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Deadstar

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Hey folks I'm trying to find some info on this scenario I'm working on.

Consider a particle orbiting a star with eccentricity e, basically standard two body problem. I have an approximation for the particles distance from the sun at some time t. I would now like to introduce another force,

I would like to calculate the distance shown below

[PLAIN]http://img842.imageshack.us/img842/6876/unledkdq.jpg

with the particle beginning at pericentre and completing one half of a full orbit. The black line is the standard 2-body orbit with no force and the red line is the (exaggerated) new path the particle will follow.

I thought this would be quite easy to do but because of the eccentricity it has become far too complicated. The distance from star to particle is always changing and so the acceleration is always changing too. Do I have to start right back at the equations of motion and throw in this extra force or can I modify what I know given that the eccentricity and force is small? The force is proportional to 1/d^2 where d is distance from the star so any attempt to solve a differential equation and find d as a function of time proves impossible.

If I have to start back at the equations of motion, how would I do that given that I don't know

I think I may have to make some assumptions to make this easier (which could perhaps be justified given that the eccentricity and force are small)...

Assumption..?

Particle takes the same time to orbit the star (at least for small timescales) so only need to think about how far it travels from 'original' orbit.

Consider a particle orbiting a star with eccentricity e, basically standard two body problem. I have an approximation for the particles distance from the sun at some time t. I would now like to introduce another force,

**F**, that acts on the particle via the line joining the star and particle. I know the equation that determines this force and it is dependent on the distance between the star and particle.I would like to calculate the distance shown below

[PLAIN]http://img842.imageshack.us/img842/6876/unledkdq.jpg

with the particle beginning at pericentre and completing one half of a full orbit. The black line is the standard 2-body orbit with no force and the red line is the (exaggerated) new path the particle will follow.

I thought this would be quite easy to do but because of the eccentricity it has become far too complicated. The distance from star to particle is always changing and so the acceleration is always changing too. Do I have to start right back at the equations of motion and throw in this extra force or can I modify what I know given that the eccentricity and force is small? The force is proportional to 1/d^2 where d is distance from the star so any attempt to solve a differential equation and find d as a function of time proves impossible.

If I have to start back at the equations of motion, how would I do that given that I don't know

**F**as a function of time?I think I may have to make some assumptions to make this easier (which could perhaps be justified given that the eccentricity and force are small)...

Assumption..?

Particle takes the same time to orbit the star (at least for small timescales) so only need to think about how far it travels from 'original' orbit.

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