Universal gravitational, elliptical orbits

[carbon_mc]

Homework Statement

a spacecraft of mass 1000kg, in an elliptical orbit about the earth, at one point its distance from Earth is 1.2 x 10⁷ meters and its velocity is 7.1 x 10³ meters per sec, and the velocity vector is perpendicular to the line connecting the center of the Earth to the spacecraft . Mass of Earth is 6.0 x 10²⁴ kg and radius of Earth is 6.4 x 10⁶
Find the magnitude of the angular moemntum of the spacecraft about the center of the earth

Homework Equations

L = I $$\omega$$
L = r x p
$$\omega$$ = v/r

The Attempt at a Solution

ok so I know that energy and angular momentum is conserved. I know how to solve this but I just want to make sure. Do I just do this by finding the angular velocity by $$\omega$$ = v/r then multiplied by I which equals to mr² . it sounds really weird so I just want to make sure.

 

[Dick]

Just use L=rxp. What's the length of r, the length of p and the angle between them?

 

[carbon_mc]

I think it's mvr .. they didnt say anything about angle or anything. the velocity vector is perpendicular so it's sin 90 = 1 .

 

[lanedance]

so you shoul have all the info for L = r x p, which becomes |L| = r(mv).sin(theta) = r(mv) = mvr, when the velocity & position vector are perpindicular