The Eliptical Orbit of Planets in our Solar System

Quick, hopefully easy question. And, yes, I tried google, and I searched the past threads. Goose egg. So…the planets have a somewhat eliptical orbit, correct? And, elipses have two foci, correct? If the sun is one, then what is the other focal point causing the eliptical orbits? BUT WAIT, here’s the catch. If at all possible, I would like an answer that is not merely a mathmatical equation. Those are so friggin’ abstract! Thanks in advance for your help.

You are correct, the orbits of planets are ellipses, and they have two focii. But there’s nothing physically significant about the “other” focus. Nothing “causes” it. It’s just a consequence of the gravity and motion work. It’s an abstraction.

Also consider - if an object achieves escape velocity, it’s path will be a parabola. And faster, a hyperbola. These are also conic sections. They don’t have any “other” focus.

The sun (the point that is the sun’s center of mass)
is not one of the foci. We can tell that because that point
would be the one foci of a perfectly circular orbit, and a
circle is nothing but an ellipse whose two foci have collapsed
into one.

With the nearly circular orbits of some planets, like Earth,
both foci might be points within the sun - I don’t know.

That should be “…would be the one focus…”

Sorry.

It isn’t the sun that is at one focus, it is the center of gravity of the two objects, and both orbit in elliptical paths around the focus.

The sun’s radius is greater than the distance to the focus in all cases for the planets, so the sun is in fact “at the focus.” It isn’t centered on the focus, though. The sun’s does wobble a bit, in fact as it “orbits” around each of its planets. That wobble is how we are currently able to find planets around distant stars. The extreme cases of gas giant planets in Mercury sized orbits puts the sun’s orbit in the 10 meter range.

Tris

“It should be possible to explain the laws of physics to a barmaid.” ~ Albert Einstein ~
“Man, you should see the place Einstein used to go drink!” ~ Triskadecamus ~

Well done Triskadecamus you’ve bested me.

But at least I can provide a NASA link that concurs here’s it’s exact quote

P.S. that’s why we know all those stars have planets around them. The planets are really big and rock that stars world

You can’t do this stuff without (a little) math.

First, the Sun is not at the exact center of Earth’s orbit as stated, but ~4 x 10^2 km away at the center of mass of the two bodies.

Based on Earth’s eccentricity of 0.0068, the foci will be found ~1 x 10^6 km from the center of the ellipse (e = c/a). The radius of the Sun is ~7x10^5 km. So, the foci are ~3x10^5 km from the surface, above the chromospehere, but within the corona.

I hope that clears up a little bit of the confusion.

An hyperbola does in fact have a second focus. For an illustration, Go here and scroll down.

And there actually is some slight physical significance to the empty focus, too, in cases where you have a tidal lock. The Moon, for instance, doesn’t quite face the same side towards the Earth, but rather faces the same side towards the “empty” focus (which I’m pretty sure is still inside the Earth). This is because a body’s rotational speed is constant, but its orbital speed is not.

Douglips, you are right.

There’s an alternate definition of conic sections that uses only one focus and a directrix (straight line). That’s the idea I was thinking of. It works for ellipses too.

According to evilhanz’s calculations, that is not true even for earth, correct? But even more, the center of mass of the Sun/Jupiter system is outside the Sun, is it not?

Really? I’m aware of the “focus + directrix” (though I’d never heard that word before) method for defining a parabola, but not for an ellipse or hyperbola. I’m curious about it - can you demonstrate?

For example, the parabola can be defined as “the locus of points equidistant from a line and a point not on the line.” I’m aware of a definition for an ellipse of “the locus of points whose distances from the two points (the foci) add to a constant value.” But, I’m not aware of a definition of an ellipse that involves a line, and I’d love to learn one.

Thanks for the one focus chime Kelly I have never liked the two foci thing, anyway. To find the barycenter, as it’s called, look at it like a balncing beam act. The Sun weighs about 1000 times what Jupiter weighs. The Jupiter-Sun distance is about 500,000,000 miles. Dividing the two quantities gives you a distance of about 500,000 miles. With the Sun having a radius of about 400,000 mile that does put the barycenter outside the Sun.

Given a point F and a line l, a conic section is the set of all points P such that:
d(F,P) = *ed(l,P)**

e is the eccentricity of the conic section. If the eccentricity is less than 1, the conic is an ellipse. Parabolas have eccentricity equal to 1. Hyperbolas have eccentricities greater than 1.

…and how about givin’ props to Apos (Alexandria, oh, say 300 A.D.) for that whole thing! The only drawback is you can’t draw a circle with that formula. At least not as long as you don’t have an infinite distance handy, say the separation between NY and LA…

Well, I can’t take all the credit.

Unfortunately, it adds some confusion also. The center of the Sun isn’t ~400 km from the center of the Earth’s orbital ellipse, it’s ~400 km from one of the foci of the Earth’s orbit. This means that one of Earth’s orbit’s foci is 400 km from the Sun’s center, and the other is ~2 x 10^6 km from the Sun’s center. (Neglecting all the other planets, of course.)

Hey, Chronos, I’ve been trying to prove this and failing. Farging trancendental equations!!! Anyway, can you tell me where I can find a proof?

Or gimme a hint?

My Most Brilliant Insight was that at any point in the orbit, the angle through which the body has rotated since periapse equals the mean anamoly. Is that right?

The moon rotates at a constant rate. It’s motion through its elliptical path around earth requires that it moves more quickly at some times, slowly at others. If you consider two orbits, one circular, the other an exaggerated ellipse with earth at the center, and two possible moons it is easier to see.

This drawing shows the moons each having passed through one quarter of their orbit. The black arrows show which direction the “visible half” of the moon is pointing. In the circular orbit, it faces the Earth (green circle) in the ellipse, it faces the same direction, but the Earth is not in that direction. The angles drawn show the difference.

This drawing is crude, of course, and does not accurately depict the real case, which is only slightly out of circular.

Hope this helps.

Tris

“It should be possible to explain the laws of physics to a barmaid.” ~ Albert Einstein ~
“You should see the place where Einstein used to drink!” ~ Triskadecamus ~

Yes, that’s correct. A slight miswording on my part. I’m surprised no one else noticed. Thanks, ZenBeam!