What is the Semimajor Axis of a Planet's Orbit in Different Reference Frames?

In summary: In the sun-centered frame, the semimajor axis is the same as in the original coordinate system. In the frame of reference that the planet is orbiting the star, the semimajor axis is the distance between the sun and the center of mass of the system, which is different than the original coordinate system. This means that the semimajor axis changes when you switch frames of reference, but the orbit still has the same size and shape.
  • #1
cellery
6
0

Homework Statement


There is a planet of mass m_1 orbiting a star of mass m_2. One question is "What is the semimajor axis of the planet's orbit in the coordinate system centered at the star's center", and another is "What is the semimajor axis of the planet's orbit centered at the center of mass of the system.


Homework Equations


t^2/A^3 = 4pi^2/G(m_1+m_2)
^Kepler's Third Law

The Attempt at a Solution


Basically, as far as I can visualize this problem, the semimajor axis does not change when you switch the center of the system. The planet still has to make the same orbit, so the center of said orbit should still be the same. I have an answer, but I can't tell if I'm somehow supposed to modify it for one of these scenarios.
 
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  • #2
Think about this again. The orbit will have the same size and shape in any inertial frame, but the sun-centered frame is not inertial. The sun is orbiting the center of mass as well. What is the distance between the planet and the sun at apofucus and perifocus?
 
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  • #3
Alright, thanks, I'll give it a try. The problem is I just can't visualize what orbits look like if I have to account for a moving frame of reference as well. Everything changes. I don't quite see how to encorporate it into any equation, either.

But I'll see what I can do. The amount of help I need may be beyond the scope of what helpers are supposed to do.
 
  • #4
Answering these questions might help:
  • What is the distance between the planet and system center of mass at apofocus and perifocus?
  • What is the relationship between the distance between the planet and system center of mass and the distance between the sun and system center of mass?
  • What is the distance between the planet and the sun at apofocus and perifocus?
  • What does this mean in terms of the semimajor axis?
 
  • #5
Thanks. Based on that, I was able to get an answer for each reference frame. They make sense, as far as I can tell.
 

1. What is an orbital reference frame?

An orbital reference frame is a coordinate system used to describe the motion and position of an object in space. It is typically centered around a larger object, such as a planet or star, and is used to track the movement of smaller objects orbiting around it.

2. How is an orbital reference frame different from a terrestrial reference frame?

An orbital reference frame takes into account the rotation and movement of the larger object, such as a planet, while a terrestrial reference frame is fixed on the surface of the Earth and does not account for its rotation or movement around the sun.

3. Why are orbital reference frames important in space exploration?

Orbital reference frames are crucial in space exploration because they allow scientists to accurately track and predict the movements of objects in space. This is essential for planning and executing space missions, as well as for studying the dynamics of celestial bodies.

4. How are orbital reference frames established?

Orbital reference frames are established by using a set of standard reference points, such as stars or other celestial objects, as well as mathematical models and equations based on the laws of physics. These reference frames are constantly refined and updated as new data and technology become available.

5. Can multiple orbital reference frames exist for the same object?

Yes, multiple orbital reference frames can exist for the same object, depending on the purpose and perspective of the observer. For example, an object may have a heliocentric reference frame, which is centered around the sun, as well as a geocentric reference frame, which is centered around the Earth.

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