Orbital Mechanics Angular Momentum

In summary, there are two definitions of angular momentum in orbital motion, one involving position, r, and radial velocity, r_dot, and the other involving position, r, and tangential velocity, rθ_dot. Both definitions can be correct depending on the specific context and source. However, the first definition provided in the conversation may not be accurate as it should involve velocity rather than radial velocity. The correct expression for angular momentum is h = r x m dot{r}.
  • #1
FQVBSina
39
8
Hello all,

I have a question regarding the precise definition of angular momentum in orbital motion.

I see one definition says angular momentum h, position, r, and radial velocity, r_dot, are related as follows:
h = r x r_dot.

However, I also see one definition that says h is related to r and tangential velocity as follows:
h = r2θ_dot = r* (r*θ_dot)
Where θ_dot is the angular velocity, which makes rθ_dot the tangential velocity.

How come both definitions can be correct at times?
 
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  • #2
tnich said:
I don't think your first definition makes sense. ##\vec r \times \vec {\dot r} = 0## since ##\vec r## and ##\vec {\dot r}## are in the same direction.
What would make sense is angular momentum ##\vec L =m \vec r \times \vec v##.
It is exactly as written in the book.
Actually, I just figured it out...
In an orbit, the r is defined from the center of the inertial frame. So r2 is rotated from r1 but the root of the vector is still at the inertial center. That means delta_r is a tangential vector that connects r1's vector head to r2's vector head. Making r_dot actually in the direction of the angular velocity.
 
  • #3
FQVBSina said:
I see one definition says angular momentum h, position, r, and radial velocity, r_dot, are related as follows:
h = r x r_dot.
You may want to check the source of this definition a little more carefully. Here ##r## should be position and ##\dot{r}## should be velocity (not radial velocity) and the expression should be ##r \times m \dot{r}##
 

1. What is orbital mechanics angular momentum?

Orbital mechanics angular momentum is a physical quantity that describes the rotational motion of an object around a fixed point. In the context of orbital mechanics, it refers to the rotational motion of a celestial body, such as a planet or satellite, around a central body, such as a star or planet.

2. How is orbital mechanics angular momentum calculated?

The formula for calculating orbital mechanics angular momentum is L = mvr, where L is the angular momentum, m is the mass of the object, v is the velocity of the object, and r is the distance between the object and the central body. This formula is derived from the principles of classical mechanics and is used to describe the rotational motion of objects in orbit.

3. What is the significance of orbital mechanics angular momentum?

Orbital mechanics angular momentum is a fundamental concept in understanding the motion of celestial bodies in space. It helps scientists and engineers predict and control the trajectories of satellites, spacecraft, and other objects in orbit. It also plays a crucial role in understanding the stability and dynamics of planetary systems.

4. How does angular momentum affect orbital stability?

Angular momentum is directly related to the stability of an orbit. In general, the greater the angular momentum, the more stable the orbit will be. This is because a higher angular momentum means that the object has a greater amount of rotational energy, which helps to counteract any destabilizing forces, such as gravity or atmospheric drag.

5. Can angular momentum be changed in orbit?

Yes, the angular momentum of an object in orbit can be changed through various means, such as thruster firings or gravitational assists from other celestial bodies. However, the total angular momentum of a closed system, such as a planet and its moon, remains constant. This is known as the law of conservation of angular momentum, which states that angular momentum cannot be created or destroyed, only transferred between objects.

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