Hi all. 1st post here. I've got a math question. I hope this is the right sub-forum. This is not homework, just stuff I like to work on. This question deals with celestial mechanics. But don't worry if you know nothing about celestial mechanics. It's the math that's bothering me.
To compute the eccentric vector, ( http://en.wikipedia.org/wiki/Eccentricity_vector ) the following formula is used:
It looks pretty straightforward. If I know v, mu, and r, I should just be able to plug in and solve for e.
I do know mu. However, v and r are vectors. What I do know is the x, y, and z components of both v and r. And where r is in absolute value brackets, I believe can just do
But where the vectors are not in absolute value brackets, I don't know what to do. I can't punch
into my calculator.
Similarly, in the formula for Eccentric anomoly ( http://en.wikipedia.org/wiki/Eccentric_anomaly ):
r is a vector. It represents distance. Taking its absolute value will give me the same answer for 2 different points on an orbit. But every point on the orbit should have a unique Eccentric anomoly.
I've never had a math class that dealt with vectors in equations like this. Any idea how I should treat them?