Why are the orbits elliptical in shape?

[yalgaar]

I have been told most of the planets around the sun have orbots elliptical in shape.

I now understand that the orbits are formed due to 2 forces. i.e gravity of the parent body acting against the velocity of the orbitting body.

The above only tells me that all orbitting objects should orbit in circular orbit and not elliptical orbit.

What am I missing?

 

[Doc Al]

I now understand that the orbits are formed due to 2 forces. i.e gravity of the parent body acting against the velocity of the orbitting body.

There's only one force: The gravitational attraction of the parent body. Velocity is not a force.

The above only tells me that all orbitting objects should orbit in circular orbit and not elliptical orbit.

How does it tell you that?

 

[yalgaar]

There's only one force: The gravitational attraction of the parent body. Velocity is not a force.

How does it tell you that?

OK thanks for correcting me on Velocity not being a force. But I am sure you knew what I was talking about.

To me, orbits should be circular because the parent body are in shape of a globe. I know I am wrong. Just trying to understand why I am wrong.

 

[Nabeshin]

To me, orbits should be circular because the parent body are in shape of a globe. I know I am wrong. Just trying to understand why I am wrong.

You're correct, that's wrong. The "parent bodies" as you call them, are all treated essentially as points anyways in orbital determination so their shape (including size) has no effect on the orbit. The reason bound orbits are ellipses (of which, recall, a circle is just a special case) is because the gravitational force scales like 1/r^2. The mathematical proof of this is a little more involved than I care to go into right now, and there have been numerous other threads here on PF discussing it in detail.

What you actually get is that orbits are a conic section (circle, ellipse, parabola, hyperbola). The reason we see elliptical orbits is because they are the stable orbits (those in which the velocity is not great enough to expel the body from the gravitational system).

If you have specific questions I'd be glad to address them but look to other threads here if you want the proof of what I've said.

 

[DaveC426913]

The "parent bodies" as you call them, are all treated essentially as points anyways in orbital determination so their shape (including size) has no effect on the orbit.

This bears repeating.


To be slightly whimsical, the Moon has "no idea" what size or shape the Earth is. As far as the Moon's experience of Earth's gravity goes, the Earth could very well be a black hole one mile in diameter or even a giant cube* of aerofoam 50,000 miles on a side. As long the object masses 6 x10^24kg, that's all that matters.

(*Glossing over some details. Earth's shape does actually have a minor effect on the Moon. That's tidal locking - that's another discussion.)

 

[DaveC426913]

The above only tells me that all orbitting objects should orbit in circular orbit and not elliptical orbit.

What am I missing?

Read this post:
https://www.physicsforums.com/showpost.php?p=2172419&postcount=6
It shows the same effect on a very human scale. If you roll a coin in a funnel wishing well, it will follow an elliptical path. You would have to try very, very hard to get it to make a circle.

See, to get a circular path the velocity needs to be perfectly matched against the centripetal force. Even slightly too fast and you get an elliptical path, even slightly too slow and you get an elliptical path. Getting it right in the middle, is harder than ... well ... harder than balancing coin on its edge.

 

[gabrielh]

Gravity and intertia are, in a nutshell, the two things that make orbits elliptical. It does go deeper than that, but as a general explanation, the two suffice.

 

[yalgaar]

Gravity and intertia are, in a nutshell, the two things that make orbits elliptical. It does go deeper than that, but as a general explanation, the two suffice.

I have been in the impression that gravity and intertia keeps the orbit, but still don't get it why "elliptical"

 

[Nabeshin]

I have been in the impression that gravity and intertia keeps the orbit, but still don't get it why "elliptical"

http://radio.astro.gla.ac.uk/a1dynamics/ellproof.pdf

If you need any more convincing, I don't know what to tell you.

 

[DaveC426913]

http://radio.astro.gla.ac.uk/a1dynamics/ellproof.pdf

If you need any more convincing, I don't know what to tell you.

As with many posts on this forum, posters are usually looking ofr an intuitive answer, rather than a rigorous mathematical proof.

I'm sure the poster doesn't doubt that it is the case, he just wants to understand - in layperson's terms - why.

 

[DaveC426913]

I have been in the impression that gravity and intertia keeps the orbit, but still don't get it why "elliptical"

Yalgaar, have you ever played tetherball?

A ball is tethered by rope to the top of a pole. Players stand on either side and hit the ball in opposing directions to try to get the ball wrapped around the pole to win.

It is almost impossible to hit the ball with just the right amount of force to get it to go around the pole in a circle i.e. at the same height all the way around. Too light a hit and it will drop - even slightly toward the pole; too heavy a hit and it will fly way out and up.


This is not a proper orbit - I'm not making a comparison - I'm merely trying to show how to opposing forces can trade off each other and work together to make a periodic behaviour.

 

[Phrak]

To be slightly whimsical, the Moon has "no idea" what size or shape the Earth is. As far as the Moon's experience of Earth's gravity goes, the Earth could very well be a black hole one mile in diameter or even a giant cube* of aerofoam 50,000 miles on a side. As long the object masses 6 x10^24kg, that's all that matters.

I don't believe a disk shaped mass, or a massive ring, say, acts like a point mass, does it? Correct me if I'm wrong.

Very nice tetherball example, by the way. I could do with more explanation such as that.

 

[DaveC426913]

I don't believe a disk shaped mass, or a massive ring, say, acts like a point mass, does it? Correct me if I'm wrong.

True. The theorem only holds if the bodies aren't too distorted.

One can see this easily enough in the fact that tides from the aspherical Earth and Moon have slowed each others' rotation over millenia. This would not happen with truly spherical bodies.

Very nice tetherball example, by the way. I could do with more explanation such as that.

Thank you. I have taken this as my PF mandate. There are so many here who have the rigorous math answers all down pat, I try fill the niche that bridges the gap between laypersons and the technical answers.

Indeed, flash forward ten years and I may be looking back to my PF addiction as the thing that finally got me to take up teaching.

 

[Nabeshin]

As with many posts on this forum, posters are usually looking ofr an intuitive answer, rather than a rigorous mathematical proof.

I'm sure the poster doesn't doubt that it is the case, he just wants to understand - in layperson's terms - why.

I was just getting the feeling that we had already given the intuitive answer of some kind of balance between centripetal force and inertia, and the OP remained unsatisfied.

Good thought with the tether ball example though, I'd never heard of that one.

 

[Phrak]

Thank you. I have taken this as my PF mandate. There are so many here who have the rigorous math answers all down pat, I try fill the niche that bridges the gap between laypersons and the technical answers.

Indeed, flash forward ten years and I may be looking back to my PF addiction as the thing that finally got me to take up teaching.

I think it makes for good counterpoint. One needs concepts, and analogies to hang the mathematics on, right? Or maybe that's may particular take. For me graphics is important. I want see visualize how physics works. There are a couple things I'd like to draw-up. But the current state of computer graphics doesn't lend itself to on the fly sketches. I suppose I could use a scanner.

 

[DaveC426913]

I think it makes for good counterpoint. One needs concepts, and analogies to hang the mathematics on, right? Or maybe that's may particular take. For me graphics is important. I want see visualize how physics works. There are a couple things I'd like to draw-up. But the current state of computer graphics doesn't lend itself to on the fly sketches. I suppose I could use a scanner.

Also part of what I want to do. Want to illustrate physics. Got anything I could illo? I try to whip up diagrams as needed.

I think your ideas are prolly more like complex 3D CG though.

 

[Phrak]

Also part of what I want to do. Want to illustrate physics. Got anything I could illo? I try to whip up diagrams as needed.

I think your ideas are prolly more like complex 3D CG though.

At the moment, the one thing I haven't seen anywhere on the internet is a kind of a 3d Ven diagram of the Bell inequality. To explain it better would take the drawing itself, it seems. I don't have anything simpler at the moment, though.

For electrical engineering, I've been accumulating a library of circuit elements in a drawing package.

 

[DaveC426913]

At the moment, the one thing I haven't seen anywhere on the internet is a kind of a 3d Ven diagram of the Bell inequality.

Uh. Ah. Well, my rendering might look more like a rubber duck, a socket wrench and a half-eaten Jos. Louis.

 

[Phrak]

Uh. Ah. Well, my rendering might look more like a rubber duck, a socket wrench and a half-eaten Jos. Louis.

I've spent the afternoon trying to learn 3d rendering, and all that. It's slooow going. Though most diagrams for homework help should be pretty simple, that could be done on the fly. Have you looked at Google sketchUp?

 

[DaveC426913]

Have you looked at Google sketchUp?

You're second person who's asked about that. I think I tried it a bit way back.

I've got Caligari Truspace on my system but it's too hard for me.

 

[Phrak]

You're second person who's asked about that. I think I tried it a bit way back.

I've got Caligari Truspace on my system but it's too hard for me.

I've got Google SketchUp downloaded, but I haven't tried it just yet, so I'm not endorsing it. I should give it a shot though. This 3D rendering is bananas. Hours later, I'm still making slow progress. But, I think most diagrams just need some nicely drawn lines and circles, and elipses and splined curves to approximate other shapes. I'll check out Caligari Truespace.