Hyper- and para-bolas

[TechnicalK3rbal]

What's the difference when it comes to an orbit? trajectory/path?

Edited March 4, 2014 by TechnicalK3rbal

[capi3101]

Neither are orbits - both are escape trajectories. You have to fire retrograde at the apsis to establish an orbit.

[Starstrider42]

To get a parabolic trajectory, you have to be moving at exactly escape speed -- any faster, and it's a really narrow hyperbola, any slower, and it's a really eccentric ellipse. So while theoretically possible, parabolic trajectories don't exist IRL.

In KSP, there's the extra complication of spheres of influence, so it's possible to escape e.g. Kerbin while moving at just under escape speed. But that's still not a parabola, that's just an ellipse with one end cut off.

Hope that answers your question.

[Tank Buddy]

A parabola is a trajectory when your ship's velocity is AT escape velocity; it is in the shape of a parabola.

A hyperbola is a trajectory where your ship's velocity is ABOVE escape velocity; I assume it is in the shape of a hyperbola. Whatever it is, is isn't a circle, ellipse, or parabola.

[Kasuha]

Parabolic orbit/trajectory is just as elusive subject as circular orbit. They're extreme cases and you don't really need to care about them as hyperboles/ellipses right around them will do the trick for you just as well.

Parabolic orbit means your speed will technically reach zero as soon as you reach infinity.

Hyperbolic orbit means that when you reach infinity, you will still have some remaining speed.

[Claw]

To be pedantic, orbits can be hyperbolic and parabolic in addition to elliptical.A trajectory is usually associated with a limited path (but can be more).

Parabolic occurs when the orbital energy is just enough to cancel out with the angular momentum. So it's just barely outside of the max elliptical orbit, but still doesn't return. These are mostly mathmatical byproducts, as the range to get into a parabolic orbit is practically infinitely narrow.

Hyperbolic orbits have excess energy, so they are more eccentric ("flatter") than a parabolic.

Edit: Wow, ninjas.

[Red Iron Crown]

A parabolic trajectory intersects one of the foci. A hyperbolic trajectory passes between the foci. An elliptical orbit has both foci enclosed within its path.

[Kasuha]

A parabolic trajectory intersects one of the foci. A hyperbolic trajectory passes between the foci. An elliptical orbit has both foci enclosed within its path.

Um... no. Parabola is when the other focal point is at infinity, but it does not count as if it is running through it. When the point returns from the other side, you get hyperbola (both arms) as an ellipse stretched around the infinity with both focal points still safely inside.

[Red Iron Crown]

So, it's asymptotic as eccentricity approaches 1?

[Pecan]

What's the difference when it comes to an orbit?

[i think you've got your answers but this might help anyone else wondering the same thing...]

1. The direct answer: the difference is you'll never get a parabolic orbit in practice.

2. Conic sections (TL;DR - click '2 Features' on that page for the pretty pictures)

[Starstrider42]

So, it's asymptotic as eccentricity approaches 1?

That's one way of looking at it, yes (though I'm pretty sure a mathematician would disagree).