Elliptical Orbit Homework: Find Angular Momentum

In summary, the conversation discussed finding the angular momentum of a comet in an elliptical orbit around the sun, with a given mass and linear velocity at the perihelion. The equation for angular momentum was mentioned, and the participants agreed that it involves multiplying three values together.
  • #1
missnuss
8
0

Homework Statement


A comet of mass 5x10^16 kg moves in an elliptical orbit around the sun, with the sun at one focus. At the perihelion, 10^6 m, the comet has a linear velocity of 1.5x10^7 m/s. Find the angular momentum of the comet with respect to a focus at the sun.


Homework Equations





The Attempt at a Solution

Ya, I have nothing except 0<e<1, Vmin<E<0
 
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  • #2
How about: What's the definition of angular momentum?
 
  • #3
Ok. So basically you multiply the three together? Sorry if I am slow.
 
  • #4
missnuss said:
Ok. So basically you multiply the three together? Sorry if I am slow.
Yes. -- I mean yes to multiplying them together.

I have no idea about you're being slow or not.
 
  • #5
.

The angular momentum of an object in orbit is given by L = mvr, where m is the mass of the object, v is its linear velocity, and r is the distance from the center of rotation. In this case, the center of rotation is the sun and the distance from the sun to the comet at perihelion is 10^6 m. Thus, the angular momentum of the comet is:

L = (5x10^16 kg)(1.5x10^7 m/s)(10^6 m) = 7.5x10^29 kg m^2/s

This is a very large angular momentum, indicating that the comet has a significant amount of rotational energy as it moves in its elliptical orbit around the sun.
 

1. What is angular momentum?

Angular momentum is a measure of the rotational motion of an object around a fixed point. It is equal to the mass of the object multiplied by its velocity and the distance from the fixed point.

2. How do you calculate angular momentum?

To calculate angular momentum, you need to know the mass of the object, its velocity, and the distance from the fixed point. The formula for angular momentum is L = mvr, where L is angular momentum, m is mass, v is velocity, and r is the distance from the fixed point.

3. What is an elliptical orbit?

An elliptical orbit is a type of orbit in which an object travels around another object in an oval-shaped path. This path is characterized by two focal points, with the larger object at one of the focal points.

4. How does angular momentum relate to an elliptical orbit?

In an elliptical orbit, the angular momentum of an object remains constant. As the object moves closer to the larger object, its velocity increases to maintain a constant angular momentum. As the object moves away from the larger object, its velocity decreases to maintain the same angular momentum.

5. How does angular momentum affect the stability of an elliptical orbit?

Angular momentum plays a crucial role in maintaining the stability of an elliptical orbit. If the angular momentum of an object is too low, it may fall into the larger object. If the angular momentum is too high, the object may escape the orbit. The right balance of angular momentum is necessary for a stable elliptical orbit.

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