Earth and moon barycenter question.

[Mr. Krang]

I was just reading about the barycenter of bodies in space. My question might not make sense but, if we sent hundreds of thousands (or millions) of spacecraft to the moon filled with dirt and rocks could we change the barycenter enough for the Earth to orbit the moon? I know this is a huge leap in logic but I just want to make sure I understand the way this works even if the example is absurd and unlikely.

 

[Drakkith]

Both the Earth and the Moon orbit their barycenter, not each other. What you're proposing would just shift the barycenter towards the Moon. In effect, yes, the Earth would orbit the Moon as it is commonly known.

 

[Mr. Krang]

That's what I meant to say. So increasing the moons mass while decreasing the Earth's would change the barycenter? I just needed it dumbed down since the article I was reading used a lot of technical terms and this is my way of simplifying it.

 

[Drakkith]

That's right. Shifting the mass around would change the position of the barycenter.

 

[Garth]

Interestingly, the orbital mechanics of two bodies (say Earth and Moon) rotating around the barycentre can be analysed either about the barycentre, the centre of mass of the system, in which case they both orbit in ellipses in which the barycentre is at one of the foci of each ellipse,
or around the greater mass (Earth), in which case the Moon orbits around the Earth on an ellipse with the Earth at one focus,
or around the lesser mass (Moon) in which case the Earth orbits around the Moon on an ellipse with the Moon at one focus.

You can take your pick as to the origin of your coordinates, whichever is the most convenient.

So both the Earth and Moon can be said to orbit around the barycentre, or the Moon can be said to orbit around the Earth, or the Earth can be said to orbit around the Moon! And all that without sending any "hundreds of thousands (or millions) of spacecraft to the moon filled with dirt and rocks"!

Garth

 

[dean barry]

Basic two body calculations, see the attached sheet.

 

[ChristianHaerle]

The answers above are correct, I would just add that for one body to be said to be orbiting the other, the barycenter has to be above the surface of the larger world. Christian

 

[Garth]

The answers above are correct, I would just add that for one body to be said to be orbiting the other, the barycenter has to be above the surface of the larger world. Christian

Why?

It is just a matter of where you choose to put the origin of your coordinate system: at the barycentre itself, or at the centres of mass of either body - it doesn't matter - Newton and Kepler do just fine, but to keep things simple choose the barycentre.

Garth

 

[D H]

The answers above are correct, I would just add that for one body to be said to be orbiting the other, the barycenter has to be above the surface of the larger world. Christian

That just isn't true. If the larger world has a spherical mass distribution, it acts just like a point mass. If the larger world doesn't have a spherical mass distribution, you don't get Keplerian orbits.

Why?

It is just a matter of where you choose to put the origin of your coordinate system: at the barycentre itself, or at the centres of mass of either body - it doesn't matter - Newton and Kepler do just fine, but to keep things simple choose the barycentre.

To keep things simple it's best to look at things from the perspective of a frame in which one of the orbiting bodies is stationary. This is the reduced mass formulation that is found in most upper level undergraduate and graduate level texts on classical mechanics. Proving that the other body's orbit about the fixed body is a conic section is non-trivial. Showing that this in turn results in both bodies orbiting in conic sections about the barycenter is even more non-trivial.