Orbit shapes - why circular? How to calculate the path?

[ummwut]

I've been meaning to ask, why are the orbit shapes a circle instead of an ellipse?

And then, how does one calculate the circular path based on a velocity vector and an acceleration vector?

[KvickFlygarn87]

Well, it can be elliptic if you don't have the exact velocity required for a certain orbit.

As for calculating orbits, you'll need some other parameters to calculate the speed of an orbit. See "Vis viva calculation" on Wikipedia for that.

[ummwut]

Well, escape trajectories are elliptic, but I was wondering why orbits that don't leave the SOI are always circular in KSP.

As for "vis viva calculation", I did not know such a thing existed, thanks.

[KvickFlygarn87]

Well, escape trajectories are elliptic, but I was wondering why orbits that don't leave the SOI are always circular in KSP.

As for "vis viva calculation", I did not know such a thing existed, thanks.

You've got your terminology wrong; a circle is perfectly round and an ellipse is also a closed line but not perfectly round. Escapes are parabolic/hyperbolic.

[ummwut]

I am not good with terminology. The math is nothing special, but I cannot words. Thanks, though. Now how can I indicate that this thread has been [Answered]?

[Kasuha]

All orbits are in fact elliptic, it's just that people tend to make them as little eccentric as possible for various reasons. But there's no problem using even highly elliptic orbits in the game if you can handle them.

You can mark the thread as answered if you edit your first post in advanced editor and change the prefix.

[Red Iron Crown]

A circle is an ellipse with zero eccentricity, by some definitions. All closed orbits are ellipses, escape orbits are parabolic or hyperbolic.

[Claw]

I am not good with terminology. The math is nothing special, but I cannot words. Thanks, though. Now how can I indicate that this thread has been [Answered]?

Edit your original post and click on "go advanced." There is a dropdown where you can change the status.

[WhiteWeasel]

Hope the picture helps:

Blue and green are hyperbolic while red and grey are ecliptic.

[Red Iron Crown]

Green is parabolic, blue is hyperbolic. Red is elliptical, grey is considered by most to be elliptical with 0 eccentricity.

[wmheric]

Hmm I'm not sure what kind of answer OP is expecting, but I kind of treat it as a physics question. Most have responded with explanations on ellipses / circles, yet why is a deeper question.

In KSP, gravity is based on Newton's Law of Universal Gravitation, and in this classical picture of gravitation, a closed orbit is a perfect, eternal ellipse. It is a good description (an approximation) except in some special cases such as the precession of the orbit of Mercury, which later led to Einstein's General Relativity, which is a better description of gravity. Newton's gravitation does predict precession (of elliptical orbits) but attributes it to the perturbation of other planets and the oblateness of the Sun, but this is not enough; General Relativity says that there will still be precession if there are only two bodies (say, the Sun and Moho only). Or to put it loosely, gravity is not just gee-em-em-over-ar-squared.

So, orbits are circular/elliptical because we (KSP) are adopting simplifications such as

• ignoring effects of other planets
  
• assuming perfectly spherically symmetric gravity wells
  
• using Newton's gravitation
  

and orbits are not really perfectly circular/elliptical because they just aren't.

Given a velocity vector and an acceleration vector, you can always work out the whole orbit in a uniform circular motion. In general for an ellipse, you can still work it out by realizing the vectors are just the vis-viva equation in disguise.

[Claw]

I think the OP was confusing terms, and already posted that he/she has figured it out.