# Creating an elliptical orbit with varying velocities

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What I'm looking for is an object to follow an elliptical curve, accelerating near the perigee and decelerating near the apogee. Theoretically I could wrestle with magnet forces and do a sim for this, but I feel that (1) that'd be unnecessarily complicated, and (2) that this is going to be a collider for another sim, and that might muck it up.

I've tried follow path and using primuv, but I have not been able to find a way to accelerate and decelerate them as they follow the curve.

I've tried something, attached, that is MOSTLY working. I get velocities from the tangent normals of the orbit curve, and a velocity multiplier based on the min and max x positions along the curve, so at the perigee the velocity multiplier is 1 (or whatever), and at the apogee it's 0.1. Using a solver SOP, each frame I transfer the curvevel attribute to the ball orbiting object at its current location, and then use @P += @curvevel. This actually works for the most part, except the orbiting object keeps going further and further out, creating a spiral orbit. Furthermore, even though I have a wrangle setting its initial position to be at point 0 of the path curve, starts farther away.(Also, I will need to figure out a way to orient it so it's always looking forward, but that will be easy enough, methinks.)

I assume I'm missing something obvious within the solver SOP. This might be easy and dumb, so thanks for any help. (Also, if there's just a way better way to do this, I'm open to suggestions!)

Edited by bentway23

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what's wrong with the good ol' sin and cos ?

adjust your shape with the magnitudes 10 and 6 in sin cos respectively

vu_Orbit.hiplc

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That gets the shape, but not the changes in velocity--what I'm looking for is the acceleration at the perigee and deceleration at the apogee. I tried basic trig early on, but couldn't translate that into varying velocities.

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Probably you want something like keplers second law.

The speed is something like the length of the cross product of the Direction from ellipse point to a focus point and the Derivative (of the ellipse function).

I've recently posted some examples using an inverted distribution function, which was defined by a density.

Here is a modification of it.

kepler.hipnc

Edited by Aizatulin

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This is fantastic--thanks for the pointers!

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