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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?

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    $\begingroup$ 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. $\endgroup$ – Conrad Turner Sep 1 '16 at 5:02
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    $\begingroup$ 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. $\endgroup$ – barrycarter Sep 1 '16 at 17:12
  • $\begingroup$ 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. $\endgroup$ – userLTK Sep 2 '16 at 4:02
  • $\begingroup$ 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. $\endgroup$ – Bill Nov 20 '18 at 1:57
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Short answer is "The Sun".

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.

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    $\begingroup$ 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. $\endgroup$ – zephyr Sep 1 '16 at 14:13
  • $\begingroup$ 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". $\endgroup$ – Rob Jeffries Oct 17 '18 at 19:00
  • $\begingroup$ 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. $\endgroup$ – James K Oct 17 '18 at 19:37
  • $\begingroup$ "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. $\endgroup$ – Rob Jeffries Oct 17 '18 at 19:38
  • $\begingroup$ 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. $\endgroup$ – Rob Jeffries Oct 17 '18 at 19:48
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The only correct answer: no particular point, since Earth’s motion is complex.

First, the Earth orbits the Earth–Moon barycentre.
Surprisingly. But this points lies inside the planet, somewhere in the mantle.

Next, it would be a reasonable approximation to say that the Earth+Moon system orbits the system of Sun + inferior planets (Venus and Mercury). Of course, we shouldn’t exactly suppose their combined gravity emits from a single point. But, roughly and in average, it comes from the Sun+Mercury+Venus centre of mass (nearly the Sun’s geometric centre). At any time doesn’t any of these bodies pull Earth and Moon out of the Sun.

There are also influences from outer planets, such as Jupiter. But we shouldn’t, at any level of simplification, think of it as coming from inside the Solar System. Direction of the Jupiter’s gravity makes full turn around the ecliptic each time it completes the orbit (≈ 12 years). It would be reasonable to say that Sun+Mercury+Venus+Earth+Moon+Mars and Jupiter orbit about their common centre of mass (somewhere not far from the Sun’s surface), approximately. But not all bodies are, evidently, included here. Generally, “what point does … orbit” depends heavily on definition of our “stationary” reference frame, and arguing about this makes no sense, in principle.

An “Earth orbits the Sun” approximation would ignore not only influence of Venus (that has little significance over a human lifetime), but, first and foremost, gravity of the Moon.

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@Incnis Mrsi's answer is correct: The Earth orbits around the center of mass of the Solar System, which is dominated by the Sun with a small correction due to the Jupiter and smaller still by the other giant planets.

See NASA's Space Place for a nice short, simple explanation. See Zidbits for a description with a very nice graphic WMU has a nice article showing the effects of the different planets

You can easily see that this must be true in several ways.

First of all, let's consider just the Sun-Earth-Jupiter triplet. If each planet orbited around its barycenter with the Sun as if the other planets didn't exist, you'd have the sub moving in a small circle with the Earth and a much larger and 12x slower circle with Jupiter at the same time without one affecting the other.

Because the Earth's mass is so small, to a pretty good approximation, you can look at the Earth as orbiting once a year around a Sun which is itself orbiting around the Sun-Jupiter barycenter in twelve years.

A second experimental point in support of this comes from extra solar planet discovery through Doppler measurements. When a star has multiple planets big enough to cause stellar motions big enough to be detected by our instruments, we see the star's light-of-sight velocity changing in a way consistent with it rotating around the center of mass of the star and several planets. Otherwise, we could not detect the other planets.

A third way is a gedanken experiment. Consider Tatooine, and early-like planet orbiting a double star. Does Tatooine orbit just one of them, ignoring the other? How could that be? (How does it pick which one to ignore?) It must orbit their common center of mass.

Bottom line: The Sun and all the planets orbit around the Solar System's center of mass.

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What point does Earth actually orbit?

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 ...

Everything is relative, and relative to what.

See NASA's article "What is a barycenter?", the section "Barycenters in our solar system":

Where is the barycenter between Earth and the sun? Well, the sun has lots of mass. In comparison, Earth's mass is very small. That means the sun is like the head of the sledgehammer. So, the barycenter between Earth and the sun is very close to the center of the sun. [It orbits 449 km from the sun's center.]

Jupiter is a lot larger than Earth. It has 318 times more mass. As a result, the barycenter of Jupiter and the sun isn’t in the center of the sun. It’s actually just outside the sun's surface!

Sun - Jupiter Barycenter

The barycenter of our solar system is the combination of all it's masses, this is how much the sun wobbles:

Solar System Barycenter

Last but not least, user "fizixfan" at the PhysicsForum has provided this interesting graphic:

Orbit of the Solar System Through Space, Around the Supergalactic Plane.

Our orbit around the supergalactic plane.

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