How To Find Angular Momentum of Elliptical Orbits

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SUMMARY

The discussion focuses on calculating the angular momentum of objects in elliptical orbits using classical mechanics principles. The angular momentum (L) is defined by the equation L = r × mv, where r is the distance from the center of the Earth, m is the mass of the orbiting object, and v is its velocity. At the apogee and perigee, where the angle between the velocity vector and the radius vector is 90 degrees, the calculation simplifies to L = mvr. Understanding vector cross products is essential for applying this formula.

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  • Understanding of classical mechanics principles
  • Knowledge of vector mathematics, specifically vector cross products
  • Familiarity with elliptical orbits and their characteristics
  • Basic grasp of angular momentum concepts
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  • Study the properties of elliptical orbits in celestial mechanics
  • Learn about vector cross products and their applications in physics
  • Explore the conservation laws of angular momentum and energy in orbital mechanics
  • Investigate the relativistic effects on angular momentum for high-velocity objects
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Students and professionals in physics, aerospace engineering, and astronomy who are interested in the dynamics of orbital mechanics and angular momentum calculations.

carbon_mc
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Hey there is one question I have that has been burning in my mind. I know that in elliptical orbits of satellites/ spacecraft s/planets around a planet, angular momentum and energy is conserved, but how do we find that angular momentum only knowing the velocity of the orbiting object, its mass and its distant from Earth's surface? thank you
 
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In classical (non-relativistic) mechanics, you find the angular momentum using the definition in terms of vectors:

\vec L = \vec r \times m \vec v

Do you know about vectors and the vector cross product? Are you specifically looking for a relativistic version of this equation?
 
There are two points, the apogee and the perigee, where the angle between v and r is 90 degrees, so if you know the magnitudes of v and r at either one of those two points, the magnitude of the cross product simplifies to the scalar expression mvr. I don't know if that will be helpful, but I happen to remember reading about it.
 

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