### What point does Earth actually orbit?

• If we consider the two largest masses in our solar system - the Sun and Jupiter, by themselves, they will orbit a common barycenter which is somewhere offset from the Sun's center in the direction of Jupiter (just above the Sun's surface). If we add Saturn, things get more complicated, but there is still a barycenter, even if it follows a complex path with respect to the Sun's center (or the Sun has a complex wobble around the barycenter). Add Neptune and all the other masses in the solar system, and things get even more complicated. Neverthess, there is still a barycenter (often outside the limb of the Sun) about which the Sun does a complex dance.

Now, what is Earth actually orbiting? The Earth's orbit is described to be an ellipse; the "center" of an elliptical orbit occurs at one of the focal points of the ellipse. What is at the focal point of the elliptical path the Earth follows? Is it the solar system barycenter or is it the Sun's (wobbling) center of mass? In other words, is the Earth's orbit shifting as the Sun is tugged around, our distance from the Sun never varying by more than the eccentricity of the ellipse, or do we orbit the solar system barycenter, and our distance from the Sun varies by the sum of our orbital eccentricity plus the amount the Sun wobbles in its own orbit around the barycenter?

When there are more than 2 bodies involved generally none follow a elliptical or other conic section path and the idea of a centre is not well defined.

If you're insanely interested in this, contact me: I'm trying to find the "best fit ellipse" for the Earth at any given point in time based on its location and velocity, or for a given specific orbit. If you use the Sun as one focus, the other focus is more stable than if you use the barycenter as the first focus.

On how much Jupiter might perturb another planet's orbit, it's worth pointing out that Kepler used Mars' orbit to work out his 3 laws. If Mars' orbit was significantly wobbled, I don't think he'd have been able to do that.

It's fascinating that no one here addresses the fact that the location of barycenters is entirely dependent on one's preferred inertial reference frame. Personally, I prefer the one where I actually am.

6 years ago

As Conrad notes, since when you include the effects of Jupiter, the Earth orbit is non-keplerian, notions of centre are not really defined. But you can ask, in Newtonian gravity, where the Earth's acceleration vector points. Now the acceleration of the Earth is due mostly to the Sun, partly to the moon and slightly to the other planets.

Let's ignore the moon (ie consider the motion of the Earth Moon barycentre)

The acceleration due to the sun is 4 orders of magnitude greater than that due to Jupiter. So if Jupiter is at right angles to the Earth, the acceleration vector of the Earth is slightly pulled away from the centre of the sun. But not by much, in fact it points to a point about 4000km from the centre. The sun has a radius of 700000km, so the point the Earth is orbiting is well inside the sun, and isn't the Sun Jupiter barycentre.

To see why the Earth doesn't orbit the barycentre, consider the motion of the Sun in a three body system (Sun-Jupiter-Earth) The Earth doesn't orbit the Sun-Jupiter barycentre just as the Sun doesn't orbit the Earth-Jupiter barycenter.

Fun fact about our non-Keplerian orbit: If Kepler's data had been more accurate by a factor of 10, he would have been able to see all the non-keplerian perturbations on our orbit and likely never would have come up with this three laws.

The short answer might be the barycentre of the Earth+Moon+Sun (if you wish to ignore the influence of everything else), but it certainly isn't "the Sun".

It is the sun. The talk of barycentres confuses people. It makes people think that the barycentre is the attractive point. But it's not. You're well aware of that, but questions here suggest that it does cause confusion. The Earth orbits the sun, with pertubations from the moon and planets.

"The Earth doesn't orbit the Sun-Jupiter barycentre just as the Sun doesn't orbit the Earth-Jupiter barycenter." Nobody is claiming this. The argument is whether both the Earth and the Sun can be considered to orbit the Sun+Jupiter+Earth barycentre.

In a simple two body system both bodies execute Keplerian ellipses with the barycentre at one of the foci. Kepler's first law is an approximation for $m_{\rm planet} \ll M_{\odot}$. So, as I said, even if you ignore all the other planets, the answer is not "the Sun". If you are just arguing about the scale of the effect you should be clearer - at the moment your definiteness is the thing causing confusion.

People often seem to misunderstand barycentres. Obviously I don't need to explain them to you. But other people think that the barycentre is the bottom of the gravitational well (or their questions imply this). Now in the two body system, the centre of the ellipse is an undistingushed point in space. The centre of the Earth's ellipse isn't the sun or the barycentre or anything particular. So to answer the question "what does the Earth orbit" is not about what is at the centre or at the focus. I understand it to ask what causes the centripetal acceleration. And that is the Sun.