Question About Elliptical Orbits

[zoobyshoe]

The orbits of celestial bodies are described as elliptical.

If we look at the well known means of drawing an ellipse with two tacks and a string, you can keep moving your pencil around and around and it will draw over and over the same line.

The same cannot be said of an orbit. The center of all orbits is constantly traveling. The orbiting body will never retrace a previous path.

My question is: are there some orbiting bodies that would end up describing circles if the centers of their orbits would just stay still, and others that would actually describe ellipses, or do all orbits always describe ellipses because of the fact all centers of orbit are continuously moving?

 

[wolram]

http://burtleburtle.net/bob/physics/orbit101.html

hi ZOOBY,
i have come across this website while looking for
information on orbits, I am not sure if it is all you
want, but it is worth a look.

 

[zoobyshoe]

Thanks Wolram,

I have this primitive system called "WebTv", not a computer, which does not allow me to use java, or pdf/adobe. I couldn't view the animation at the link.
If the text there had the answer to my question, I did not recognise it behind the concepts and formulas I don't grasp yet.

 

[Janus]

Originally posted by zoobyshoe
The orbits of celestial bodies are described as elliptical.



The same cannot be said of an orbit. The center of all orbits is constantly traveling. The orbiting body will never retrace a previous path.

Do you want to clarify this statement? In terms of the orbit, the focus remains fixed.

 

[zoobyshoe]

Originally posted by zoobyshoe The same cannot be said of an orbit. The center of all orbits is constantly traveling. The orbiting body will never retrace a previous path.

Here is what I mean using the earth, sun, and moon as examples.
The Earth orbits the sun. The Earth is, therefore, not standing still, but constantly traveling.
While it is doing this, the moon orbits the earth.

Each time the moon comes round the earth, the Earth has moved from where it was the last time the moon came round. The moon will never, therfore, retrace the exact path of a previous orbit.

 

[wolram]

http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

It fell to Kepler to provide the final piece of the puzzle: after a long struggle, in which he tried mightily to avoid his eventual conclusion, Kepler was forced finally to the realization that the orbits of the planets were not the circles demanded by Aristotle and assumed implicitly by Copernicus, but were instead the "flattened circles" that geometers call ellipses (See adjacent figure; the planetary orbits are only slightly elliptical and are not as flattened as in this example.)
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try this one zooby.
as long as a two body system is not perturbed the orbit remain
the same, over a reasonable period, "eliptical".

 

[chroot]

Originally posted by zoobyshoe
Each time the moon comes round the earth, the Earth has moved from where it was the last time the moon came round. The moon will never, therfore, retrace the exact path of a previous orbit.

In a simple two-body system, both bodies orbit in ellipses with the center of mass at once focus. Excepting for general relativistic precession, the two bodies will follow the same two ellipses together, forever, in a resonance.

- Warren

 

[russ_watters]

Originally posted by zoobyshoe
Here is what I mean using the earth, sun, and moon as examples.
The Earth orbits the sun. The Earth is, therefore, not standing still, but constantly traveling.
While it is doing this, the moon orbits the earth.

Each time the moon comes round the earth, the Earth has moved from where it was the last time the moon came round. The moon will never, therfore, retrace the exact path of a previous orbit.

I think you are mixing two separate principles. Precession of an orbit is not due to the motion of the body being orbited. It happens even without factoring in other sources of motion.

Pick a stationary frame of reference at the center of mass of two objects and both objects will orbit the center of mass in ellipses with precession.

To answer your first question though, YES, it is possible to have a circular orbit, as a circle is simply a special case of an ellipse with a distance of zero between the two foci. This type of perfection is however, unlikely to happen naturally.

 

[zoobyshoe]

OK. Each has contributed a piece of the puzzle and the question is answered:

My question is: are there some orbiting bodies that would end up describing circles if the centers of their orbits would just stay stillAffirmative: special case ellipse.

and others that would actually describe ellipses
Yes, all orbits are elliptical.

or do all orbits always describe ellipses because of the fact all centers of orbit are continuously moving?
Answer is No. I guess this one threw people off the most because I didn't know how to explain what I was wondering about explicitly enough.

Thanks everyone for your imput.

Wolram: That keppler/Brahe site looks very readable and easy to understand. Thanks for finding it.

-Zooby

 

[Ivan Seeking]

I think that by the laws of large numbers, assuming of course that planets are in fact common, we can safely assume that circular orbits do occur. However, due to the drag created by the molecules of hydrogen, dust, and any other debris floating around in space, no circular orbit could remain stable.

 

[Janus]

Originally posted by zoobyshoe


or do all orbits always describe ellipses because of the fact all centers of orbit are continuously moving?
Answer is No. I guess this one threw people off the most because I didn't know how to explain what I was wondering about explicitly enough.



-Zooby

Weather or not you consider the focus of the orbit as moving or not has no effect on the shape of the orbit around that focus.

 

[zoobyshoe]

Originally posted by Janus
Weather or not you consider the focus of the orbit as moving or not has no effect on the shape of the orbit around that focus.

This is one of the things I was, clumsily, trying to figure out: do astronomers say orbits are elliptical from the perspective of the focus or from some larger perspective; looking down on the solar system, for instance, and imagining each planet and moon left a trail. I figured out the latter option had to be impossible when I was able to imagine the trail left by the moon over one year: it would look over all like a circle, but made of 12 shallow scallops.