kepler's law?

Question

my question:

consider a space probe was sent to saturn. To avoid collision with saturns rings, it is proposed that we place the probe on an elliptical path.

what is wrong about this proposal? and which of keplers laws does it violate and why?

Answer 1

Not so, skeptik. While all BOUND orbits are elliptical (because a circle is indeed a degenerate ellipse with the semi-major and semi-minor axes equal), an unbound orbit is either hyberbolic or parabolic; all conic sections, but not all ellipses!

The question is ill posed, or you have left out some information or detail. "An elliptical path" is very vague. Is that an elliptical path around the Sun? Around Saturn? The point may be about geometry; if the orbit has a large eccentricity (is elliptical) and has a semi-minor axis that keeps it completely outside of the rings, a circular orbit with a radius of that same semi-minor axis will do the same. But that does not illustrate a violation of Kepler's laws.

Answer 2

I guess the proposal violates the law of Kepler's which states, "you don't have to do anything special for an orbit to be an ellipse."

According to Kepler's first law, ALL two-body gravitational orbits are ellipses. You don't have to "propose" making it be one.

*****
Mr. Quark, while it's true that these trajectories are all non-elliptical conic sections, I would hesitate to call them "orbits." Whether it's part of the classical definition or not, I would limit "orbit" to the bound variety. Since those are the only ones that go "orbit around."

But I realize that's not the convention - it's just my preference. And it's less confusing to those just learning.