Calculate orbital angular momentum

In summary, the section Kepler’s Second Law discusses the equation r = D, m = M, and v = V and how to find the value of theta in Figure 13.21. However, it is not possible to find theta unless the satellite is at apogee or perigee.
  • #1
ssarpal
7
1
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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  • #2
Perhaps trying to find ##\theta## isn't the way to go. Any other ideas?
 
  • #3
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##.
 

FAQ: Calculate orbital angular momentum

1. What is orbital angular momentum?

Orbital angular momentum is a physical quantity that describes the rotational motion of a particle or system of particles around a fixed point, such as an atom orbiting a nucleus. It is a vector quantity, meaning it has both magnitude and direction.

2. How is orbital angular momentum calculated?

The orbital angular momentum of a particle can be calculated using the formula L = r x p, where r is the position vector of the particle and p is its linear momentum. For a system of particles, the total orbital angular momentum is the sum of the individual angular momenta of each particle.

3. What is the unit of measurement for orbital angular momentum?

The unit of measurement for orbital angular momentum is kilogram meters squared per second (kg·m^2/s). In some cases, it may also be expressed in terms of Joule seconds (J·s) or electron volts seconds (eV·s).

4. How does orbital angular momentum relate to the quantum mechanical model of the atom?

In the quantum mechanical model of the atom, electrons are described as having discrete energy levels and orbital shapes. The orbital angular momentum of an electron is related to its energy level and orbital shape, and is used to explain phenomena such as the stability of atoms and the periodic table of elements.

5. What are some real-world applications of orbital angular momentum?

Orbital angular momentum has various applications in physics and engineering, such as in the study of celestial mechanics, the design of satellites and spacecraft trajectories, and the development of quantum computing technologies. It is also used in medical imaging techniques, such as magnetic resonance imaging (MRI), to study the structure and function of molecules and tissues.

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