Orbital Angular Momentum of the Sun-Jupiter System

In summary, the conversation discusses a question about a planet's orbit around the sun, and the equation that should be used to solve it. The question asks for the relation between the time period of revolution, the masses of the planet and sun, and the distance of the planet from the sun at apogee and perigee. The suggested answer is T2 = π2(Ra + Rp)3/2GM, which is obtained by averaging the radius. However, there is debate about whether this answer is correct, and what laws should be used to find the relation.
  • #1
jinksys
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Homework Statement


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In part A I know that I must use L = mu*Sqrt[GMa(1-e^2)], but for the variable 'a' do I use the semi-major axis of Jupiter or the semi-major axis of the reduced mass?

Homework Equations


The Attempt at a Solution

 
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  • #2
I don't know how you got that equation. This question does not require reduced mass concept. The Sun is stationary and Jupiter revolves around it.

Use L=mvr
substitute v from the equation T=2(pi)r/v
Now the r is actually the average of the radius at apogee and perigee.
i.e. r=(ra + rp)/2
Use properties of ellipse to find the unknown from the above equation.
If you have the mass of Jupiter you are done with the question.
 
  • #3
Abdul Quadeer said:
I don't know how you got that equation. This question does not require reduced mass concept. The Sun is stationary and Jupiter revolves around it.
This is wrong. The question is rather explicitly asking the student to consider the problem of a non-circular orbit of an object with enough mass that the simplistic Keplerian approach is no longer valid.


jinksys said:
In part A I know that I must use L = mu*Sqrt[GMa(1-e^2)], but for the variable 'a' do I use the semi-major axis of Jupiter or the semi-major axis of the reduced mass?
How do you know that that is the equation you need to use?

Hint: Depending on what you mean by the "semi major axis of Jupiter", this is also wrong.

The question is a bit sloppy in that it doesn't say what that 5.2 AU means. The usual meaning is in terms of Jupiter's orbit about the Sun rather than Jupiter's orbit about the barycenter.
 
  • #4
D H said:
This is wrong. The question is rather explicitly asking the student to consider the problem of a non-circular orbit of an object with enough mass that the simplistic Keplerian approach is no longer valid.

Can you explain me what is wrong?
Is there any problem with averaging the radius? Does the Sun + Jupiter revolve around their common centre of mass?
 
  • #5
Abdul Quadeer said:
Can you explain me what is wrong?
Is there any problem with averaging the radius?
Yes,there is. You can't average the the radius and then assume as you said that "T=2(pi)r/v".

Does the Sun + Jupiter revolve around their common centre of mass?
Yes, they do.
 
  • #6
I think I have misunderstood something.
This is a question in my book-
A planet is revolving around the sun. Its distance from the sun at apogee is Ra and that at perigee is Rp. The mass of the planet and sun is m and M resp, T is the time period of revolution of planet round the sun. What is the relation between T,M, Ra and Rp?

The answer given is T2 = π2(Ra + Rp)3/2GM, which is obtained by averaging the radius.

Is the answer given wrong? If yes then what laws should we use to find the relation?
 

1. What is the Orbital Angular Momentum of the Sun-Jupiter System?

The Orbital Angular Momentum of the Sun-Jupiter System is the measure of the rotational motion of the two celestial bodies around their shared center of mass. It takes into account the mass, velocity, and distance of both objects.

2. How is the Orbital Angular Momentum of the Sun-Jupiter System calculated?

The Orbital Angular Momentum of the Sun-Jupiter System is calculated by multiplying the mass of each object by its velocity, and then multiplying that value by the distance between the two objects. This calculation takes into account both the magnitude and direction of the objects' motion.

3. What is the significance of the Orbital Angular Momentum of the Sun-Jupiter System?

The Orbital Angular Momentum of the Sun-Jupiter System is significant because it helps to determine the stability and dynamics of the system. It also plays a role in the formation and evolution of the solar system.

4. How does the Orbital Angular Momentum of the Sun-Jupiter System affect other planets in the solar system?

The Orbital Angular Momentum of the Sun-Jupiter System can affect the orbits of other planets in the solar system through gravitational interactions. Jupiter's large mass and strong gravitational pull can influence the orbits of other planets, causing them to slightly deviate from their predicted paths.

5. Can the Orbital Angular Momentum of the Sun-Jupiter System change over time?

Yes, the Orbital Angular Momentum of the Sun-Jupiter System can change over time due to various factors such as the gravitational pull of other objects in the solar system, the tilt of Jupiter's axis, and other external forces. However, these changes are relatively small and do not significantly alter the overall stability of the system.

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