Calculate orbital angular momentum

AI Thread Summary
To calculate orbital angular momentum, it's essential to understand the relationship between distance, mass, and velocity in the context of Kepler's Second Law. The problem involves a satellite at a distance D from Earth's center, moving at V km/s, and seeks to determine the angle θ. However, accurately finding θ requires knowing if the satellite is at an orbital extreme, such as apogee or perigee, which would provide the necessary information to calculate sin θ. Without this specific condition, the problem cannot be solved effectively. Understanding these orbital dynamics is crucial for accurate calculations of angular momentum.
ssarpal
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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?
 
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Perhaps trying to find ##\theta## isn't the way to go. Any other ideas?
 
ssarpal said:
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##.
 
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