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I am aware that planets orbit in an elliptical fashion and that the sun occupies one of two focal points.

Let us say that the left focal point is f1 and the right f2.

Is the sun at the same focal point for each planet?

If not which ones are different?

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  • $\begingroup$ Planets don't share the same orbits; they all have different ellipses. $\endgroup$ – Phiteros Aug 16 '17 at 2:12
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    $\begingroup$ As @StephenG notes, this question is a bit undefined. When you say "left" and "right", what exactly do you mean? Are you talking about a specific viewpoint and orientation? $\endgroup$ – barrycarter Aug 16 '17 at 4:54
  • $\begingroup$ Its unclear what "left" and "right" mean, since these are determined by the observer's orientation. If an ellipse has its axis vertically, which focus is "left"? Perhaps you mean to ask about the orientation of the ellipses relative to the Earth's orbit, or the "argument of perihelion" of the planets. You can edit your question to clarify $\endgroup$ – James K Aug 16 '17 at 8:47
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    $\begingroup$ This may be a translation problem, but: the sun does not occupy a focus. The focus is inside the sun, but not at its center. $\endgroup$ – Carl Witthoft Aug 16 '17 at 13:26
  • $\begingroup$ @CarlWitthoft Except for Jupiter, where I believe both foci are outside the sun. For a highly circular orbit and close orbit (I don't think any of the planets qualify), both foci could be inside the sun. Splitting hairs, I admit. (and foci is Latin, focuses is English, but I like the word foci better and Latin is often used in science). $\endgroup$ – userLTK Aug 16 '17 at 20:07
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In addition to the other answers, that are right, a different doubt seem to arise from the wording of the question:

Let us say that the left focal point is f1 and the right f2.

Is the sun at the same focal point for each planet?

If the question is if the Sun is in f1 or f2, the answer is that it doesn't matter. Ellipses are symmetrical, and therefore both foci are equivalent and any naming of them is just conventional. Just by saying that planets move in elliptical orbits and the Sun occupies one focus, Kepler's first law is unambiguously established.

If you need to mention a particular focus, one is just the Sun position and the other one is often referred as the empty focus.

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I am aware that planets orbit in an elliptical fashion

Yes, or at least to a good approximation. Because the planets affect each other's motion to a small extent (and also because of relativistic effects) the motion is not quite elliptical.

and that the sun occupies one of two focal points.

Again, because of the complexities of the gravitational interactions of all the bodies, the Sun does not occupy a single position, but has a complex motion.

You need to read about Barycenter and have a look at this explanation of the complex motions this results in.

And in reality this all happens in more than two dimensions - the orbits are inclined at different angles as well.

Let us say that the left focal point is f1 and the right f2.

An ellipse does indeed have two foci, but the orbits of planets and the motion of the Sun are not quite ellipses anyway.

But even if we ignore these small deviations from an ellipse, each planet's orbit is in a different orientation and has different foci.

Is the sun at the same focal point for each planet?

So "no".

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Ignoring inclination and by simplifying the orbits into Kepler's ellipses, you still couldn't determine left and right because the relation would be relative to a 360 degree plane, like hands on a clock.

Using this simplified approach, the Perihelion, the Sun, the center of the ellipse, the other Foci and the Aphelion are all in a straight line along the major axis. The Sun and the Perihelion point in the same direction relative to the "fixed" stars.

enter image description here

So, another way to ask your question is to ask where and at what angle do the planets perihelion happen and this is a little bit easier to look up because the perihelion is a real event, unlike the foci which a largely irrelevant mathematical representation. Each planet passes through it's perihelion once every orbit. It's not like clockwork, as there's variation from the other planets, but it's roughly in the same place, once every orbital year.

I would think a table of planet's perihelion would be fairly easy to look up in a table or chart, but surprisingly, I didn't see any, but individual planets can be found.

Earth is at Perihelion usually in the first week of January.

Mercury was at perihelion (according to this website) on March 23, 2017 and about every 88 days after that (about June 19 and Sept 15, 2017)

Using NASA-Eyes on the Solar System, a ballpark estimate puts Earth and Mercury's Perihelion are some 30-40 degrees apart, and Venus will be at Perihelion on Oct 3, 2017, and it's perihelion direction relative to the Sun is even closer, between Earth's and Mercuries, but that pattern ends with Mars. Mars' next Perihelion will be on September 16, 2018. it appears to be nearly 180 degrees opposite Mercury.

Jupiter is in a different direction as well. Directions can be anywhere on the 360 degree orbital plane (ignoring inclination).

It's worth noting that over long periods of time (or not that long for Mercury), The planet's perihelion moves. Earth's moves around a full circle in roughly 112,000 years. This is called Apsidal precession.

It's also worth noting that if you do apply Kepler ellipses, the location of the focal point relative to the center of the ellipse is a product of eccentricity and distance. The focal point and center of the ellipse are just mathematical points in empty space anyway. They have no real use, but if you calculated about where each planet's focal point is relative to the sun, they'd not only be in different directions relative to the sun, but they'd all be different distances from the sun too and with difference inclination. That would be a kind of fun, but entirely useless mathematical exercise if you wanted to do it.

I want to stress that none of this is astronomically useful. It's not relevant to observation or location of planets because Kepler's laws, while a brilliant leap forward at the time and accurate enough to overcome the geocentric model, they are incomplete and so, the foci are a product of a roughly accurate but incomplete model.

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