Question

Given the radius vector and the velocity vector of an orbiting bodyidentify the trajectory as either circular, elliptical, hyperbolicor parabolic.

r = J + 2K
v = .9I + .123K

Alright, so I guess my question is if I'm doing thiscorrectly?

I am trying to find the eccentricity of the orbital path which willtell me what type of trajectory it is on.
So I start by finding the angular momentum which is h. h = r crossv which gives me .123I + .18J - .9K

Then I use the equation for eccentricity, mag(e) = (v cross h)/mu -r/magnitude(r).
I need to find mu which is a gravitational constant and since itsgeneric units of DU (distance units) and TU (time units) the muconstant has units of DU^3/TU^2. To get these units I usemag(r)*mag(v)^2.
I do not know if this is the correct way of getting mu, thegravitational constant usually equals G*M (gravitational constant *mass of central body) but all I am given is the r and vvectors.

Anyway continuing on with the problem I get the magnitude of e =.02655 which is between 0 and 1 so the orbit is an ellipse.

Again, I just am wondering if I am doing this right.

Thanks.