- #1

- 143

- 0

Find the orbital angular momentum.

Know

[tex]v = \sqrt{\frac{GM}{r}}[/tex]

Orbital angular momentum of a system is defined as the angular momentum of the center of mass of the system.

Let the origin be at mass M.

[tex]r_{cm} = \frac{m}{M + m} r[/tex]

[tex]v_{cm} = \frac{v}{r} \frac{m}{M + m} r = \frac{vm}{M+m}[/tex]

[tex]l = r_{cm} \times p_{cm} = (M + m) r_{cm} v_{cm} = \frac{m^2 rv}{M+m} = \frac{m^2}{m+M} \sqrt{GMr}[/tex]

Correct answer in text is [tex]m \sqrt{GMr}[/tex]