Planetary Orbits - Elliptical or Wavelike?

[Devin-M]

I was running a simulation in Universe Sandbox where I placed a 10 million solar mass black hole about 10 light years from the Solar System, initially stationary relative to the Sun. I noticed once the Sun had reached about 70km/s relative to the black hole, all the orbits became wavelike rather than elliptical. Are orbits ever studied or described in a reference frame where they are linear or wavelike rather than elliptical?

Here's a video:

 

[Bandersnatch]

Are orbits every studied or described in a reference frame where they are linear or wavelike rather than elliptical?

I mean, you can? You are free to use any reference frame whatsoever.
I can't think of a reason to complicate the description like that, though. Normally you'd try to make things as simple as possible for yourself.

I noticed once the Sun had reached about 70km/s relative to the black hole, all the orbits became wavelike rather than elliptical.

They'll be spiral-like in any frame moving linearly w/r to the barycentre. If they look more wavy to you above certain speed is just due to exceeding the orbital speeds of even the innermost planets - the spirals get stretched enough that all the planets seem to always move more sideways in one direction, than up and down or backwards.

 

[Vanadium 50]

The parametric equations of a circle are x = cosine and y = sine. Toss substantial linear or near-linear motion on top of that, perhaps from choice of reference frame, and of course you get wiggly lines.

 

[Devin-M]

Mercury’s path looks very similar to a cycloid. I wonder if there are some reference frames where it’s exact.

 

[Bandersnatch]

In any frame moving parallel to the plane of the orbit, with velocity w/r to the barycentre equal to its orbital velocity.

(with the caveat that it can be perfect only for exactly circular orbits)

 

[Devin-M]

So from a certain frame you could see the Earth come to a rest once per year.

 

[Bandersnatch]

Well, from a certain frame you can see it at rest the entire year...

 

[Devin-M]

Here's Earth on a 1AU Cycloid Orbit:

 

[Devin-M]

Suppose I have 2 de-rotated cameras attached by a rigid rod, one mounted at the center of the Earth, the other in deep space where the sun’s gravitational influence is negligible. The rod passes through and is fixed to the geographical north pole. Next I detach the deep space camera from the rod. If I understand correctly, neither camera will detect any acceleration, but one camera sees the Earth at rest year round and the other camera sees the Earth move along a cycloid path and come to a rest once per year on the anniversary of being detached. The only problem is rigid rods don’t exist.

 

[DaveC426913]

Yes. At the risk of generalizing, it is universally and trivially possible to choose a point of view in 3D space wherein a given circularly- (or helically-)moving object is seen to come to rest at some point. Operative word: trivial. IOW, it doesn't imply any underlying principle, simply that which you choose to assign to your chosen POV.

An exercise for the reader: when we say "come to rest" do we mean actually come to rest in a 3-D coordinate system? Or simply appear to come to rest ... when viewed in the 2-D coordinate system of a screen render?

The only problem is rigid rods don’t exist.

Isn't this a thought experiment? You don't need a real rigid rod!

 

[collinsmark]

This was recently posted from PBS Space Time. 'Figured it's sort of relevant for this thread.