How To Find Angular Momentum of Elliptical Orbits

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In summary, in classical mechanics, the angular momentum of an orbiting object can be found using the definition involving vectors. This equation takes into account the velocity, mass, and distance from the object being orbited. At the apogee and perigee points, where the angle between the velocity and position vectors is 90 degrees, the magnitude of the cross product simplifies to the scalar expression mvr. This may be helpful in finding the angular momentum of an object in orbit.
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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:

[tex]\vec L = \vec r \times m \vec v[/tex]

Do you know about vectors and the vector cross product? Are you specifically looking for a relativistic version of this equation?
 
  • #3
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.
 

Related to How To Find Angular Momentum of Elliptical Orbits

1. How do I calculate the angular momentum of an elliptical orbit?

The angular momentum of an elliptical orbit can be calculated using the equation L = mvr, where L is the angular momentum, m is the mass of the orbiting object, v is its velocity, and r is the distance from the object to the center of the orbit.

2. What is the difference between angular momentum and linear momentum?

Angular momentum is a measure of the rotational motion of an object, while linear momentum is a measure of the straight-line motion of an object. Angular momentum takes into account both the mass and the distance from the center of rotation, while linear momentum only considers the mass and velocity of an object.

3. How does the eccentricity of an elliptical orbit affect its angular momentum?

The eccentricity of an elliptical orbit, which is a measure of how elongated the orbit is, does not directly affect the angular momentum. However, a more eccentric orbit may have a larger range of distances from the center of rotation, which can impact the value of r in the angular momentum equation.

4. Can the angular momentum of an elliptical orbit change over time?

Yes, the angular momentum of an elliptical orbit can change over time due to external forces or changes in the orbit itself. For example, if a planet experiences a gravitational pull from another object, its angular momentum may change.

5. How is the angular momentum of an elliptical orbit related to the conservation of angular momentum?

The conservation of angular momentum states that the total angular momentum of a system remains constant, unless acted upon by an external torque. In the case of an elliptical orbit, the angular momentum remains constant as long as there is no external torque acting on the orbiting object.

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