Understanding Negative Inclination Orbits in Space Science

[Maher]

What does it mean for an orbit to have a negative inclination? is it equivalent to an orbit with the same positive inclination but a shift in the node \Omega by \pi ?

 

[Filip Larsen]

In what context have you seen this? How much negative is it?

Normally inclination is kept between 0 and 180 deg since, as you hint yourself, it is the angle of the orbital plane wrt the reference plane (e.g. equator) at the ascending node. Mathematically speaking and without knowing the context, I would think the same as you, that a negative inclination somehow is supposed to indicate the ascending node is really the descending node.

 

[stefan r]

You would need negative inclination in order to do average cumulative changes. Suppose, for example, an object has two encounters and each encounter causes a 5 degree inclination change. The objects inclination could be 10 degrees or 0 degrees.

 

[Filip Larsen]

You would need negative inclination in order to do average cumulative changes.

For the situation you describe (working with small inclination changes near zero inclination) I could see it would be nice if Omega (longitue of the ascending node) do not "flip around" 180 degree just because there is a small change, but that would still be an unconventional way to represent orbital elements. For instance, when giving orbital elements like the two-line elements for Earth satellites there are by definition never any negative inclinations, so if you were to see such a set with negative inclination you obviously have to question what that means.