Calculate angular momentum of a planet only velocities and radii known

In summary, the question is how to calculate the mass of a planet orbiting a star, given the velocity and radius at a specific point. The attempted solutions involve using the equations L = rmv sintheta and E = 1/2 * mv^2 - mMG/r, but both require the mass as an unknown. However, applying the law of conservation of angular momentum, it is noticed that the mass cancels out and the angular momentum can be numerically calculated at point A.
  • #1
eb446
1
0

Homework Statement


a planet of mass m orbits a star. The Velocity at point A = 10^4 m/s the Radius at point A = 10^7, Vb = (10^4)/3, Rb = 3*10^7
Numerically calculate the angular momentum!

Homework Equations



The main question is how would you calculate the mass?

The Attempt at a Solution


L = rmv sintheta or L = IW but you need the mass.
E =1/2 *mv^2 - mMG/r but you need the mass for this as well. I also tried finding the value of mass by finding it in terms of one of the equations but you need more unknowns
 
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  • #2
eb446 said:

Homework Statement


a planet of mass m orbits a star. The Velocity at point A = 10^4 m/s the Radius at point A = 10^7, Vb = (10^4)/3, Rb = 3*10^7
Numerically calculate the angular momentum!

Homework Equations



The main question is how would you calculate the mass?

The Attempt at a Solution


L = rmv sintheta or L = IW but you need the mass.
E =1/2 *mv^2 - mMG/r but you need the mass for this as well. I also tried finding the value of mass by finding it in terms of one of the equations but you need more unknowns

Angular momentum at a, right? Apply law of conservation of angular momentum. You will notice that mass cancels out. :smile:

BTW, welcome to PF !
 

Related to Calculate angular momentum of a planet only velocities and radii known

1. How do I calculate the angular momentum of a planet?

To calculate the angular momentum of a planet, you will need to know its velocity and radius. The formula for angular momentum is L = mvr, where m is the mass of the planet, v is the velocity, and r is the radius. Simply plug in the values and solve for L.

2. Why is it important to calculate the angular momentum of a planet?

Calculating the angular momentum of a planet is important because it helps us understand the rotation and movement of the planet. It also plays a role in determining the stability of a planet's orbit and its interaction with other bodies in the solar system.

3. What units should be used when calculating angular momentum?

The units for angular momentum are typically kilogram meters squared per second (kgm2/s). However, if you are using different units for mass, velocity, and radius, make sure to convert them to the appropriate units before plugging them into the formula.

4. Can I calculate the angular momentum of a planet if I only know its velocity and radius?

Yes, you can calculate the angular momentum of a planet with just the velocity and radius. As mentioned earlier, the formula is L = mvr. If you do not know the mass of the planet, you can still calculate its angular momentum by using the mass of a reference object, such as the sun, and the ratio of the planet's mass to the reference object's mass.

5. How does the angular momentum of a planet change over time?

The angular momentum of a planet can change over time due to external forces acting on the planet, such as gravitational forces from other bodies in the solar system. However, the total angular momentum of a planet and its orbit will remain constant unless acted upon by an external torque.

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