Calculate orbital angular momentum

[ssarpal]

Homework Statement

A satellite of mass M kgs has an elliptical orbit of T hours around the Earth with $Rmax = N * Rmin$.
At one instant, the satellite is at a distance D meters from center of Earth and moving at V km/s.

Q) Find the orbital angular momentum.

Relevant Equations

L = r * m * v * sin θ

The section Kepler’s Second Law here describes the above equation.

In this problem,
$\text{r = D, m = M and v = V}$

What is the way to go about finding out $\theta$ as shown in Figure 13.21?

 

[PeroK]

Perhaps trying to find $\theta$ isn't the way to go. Any other ideas?

 

[jbriggs444]

At one instant, the satellite is at a distance D meters from center of Earth and moving at V km/s.

As you seem to have discovered, this cannot be be solved unless the "one instant" is known to be at one of the orbital extremes (apogee or perigee). Then you would naturally know $\sin \theta$.