Where a = G*M metres, and e = 0, the circular orbit velocity equation simplifies to:
v = sqrt[(G*M)/(G*M)] = 1 m/s.

Using this as the lower and upper bound values for the periapsis and apoapsis transverse velocities (respectively), where e = x, and v = y:


Periapsis(red): y = sqrt[1*(1 + x)/(1 - x)]
Apoapsis(blue): y = sqrt[1*(1 - x)/(1 + x)]

Periapsis parameter limits: c > v > 1, 1 > e > 0.
Apoapsis parameter limits: 1 > v > 0, 1 >= e > 0.

In the periapsis configuration, e = 1 is not attainable, because it would cause a divide by 0. An orbit v = c is not allowed either, since this velocity cannot be maintained by any body that follows a curved geodesic through space or time.

Technically, a velocity of 0 should not be considered due to the possibility of unknown quantum events.

An eccentricity of 0 refers to a perfect circle. Again, probably should not be considered due to the possibility of unknown quantum events.

For perspective: A semi-major axis of G*M metres is roughly 22.5 million times longer than the semi-major axis of Pluto.

[Edited by - taby on May 13, 2007 10:15:57 PM]

It looks like taby is out of control. Why don't you create another thread called analysis of motion on the ellipse?

Quote:e = 1 is not attainable, because it would cause a divide by 0

Actually it's not applicable because it will not be elliptic trajectory.

Good point. Not that I thought the solar system would unravel if my AMD did a divide by 0 though. :)