Can Friction Create Preferentially Circular Orbits?

[Simon Peach]

If we take 1 high gravity object and 1 smaller object at a distance from the first object, the first is stationary in relation to the smaller object, and it is in orbit around the first. Will the orbit be circular the center of mass of the two? Now if we put an other object in a different orbit, but in the same plane, around object 1, will that effect the orbits and move them into ellipses? If so is that why the planets orbits are ellipses?

 

[mfb]

The objects cannot be stationary relative to each other (zero tangential velocity) and in orbit around each other (non-zero tangential velocity) at the same time.

The ellipse is the general case, a circle is a special ellipse. In practice an orbit will never be an exact circle, but it can be a good approximation to it.

 

[lomidrevo]

by adding another object you'll will change the center of mass of the system, so that will definitively have impact on the previous trajectories, regardless those were circles or ellipses. But as mentioned by mfb, the circular orbit is very special case of elliptical orbit - not very likely to occur.

 

[Orodruin]

It should be pointed out that the general three-body problem does not have a closed form solution. In other words, when you introduce the third body you will generally end up with a system whose solution cannot be expressed on a closed form. However, the two-body approximation is often a sufficiently accurate description and the restricted three-body problem is an important example in orbital mechanics.

 

[Simon Peach]

" the circular orbit is very special case of elliptical orbit - not very likely to occur."
Why? This is very likely to be rubbish, when you swing a ball on a rope around your head the orbit is circular, replace the rope by gravity and it's still a circular orbit.

 

[Drakkith]

Why? This is very likely to be rubbish, when you swing a ball on a rope around your head the orbit is circular, replace the rope by gravity and it's still a circular orbit.

Any perturbation from another object, no matter how slight, will disrupt a circular orbit and make it elliptical. And since there are an innumerable number of objects out in the universe, all of which can interact gravitationally on a planet, it is impossible for an orbit to remain circular.

 

[mfb]

when you swing a ball on a rope around your head the orbit is circular

Only to a good approximation. You won't swing it in a perfect circle, the rope is elastic and so on. That is the point. Sometimes the approximations are better, sometimes they are worse.

Unlike a rope, gravity has nothing that would prefer a fixed distance.

 

[JMz]

" the circular orbit is very special case of elliptical orbit - not very likely to occur."
Why? This is very likely to be rubbish, when you swing a ball on a rope around your head the orbit is circular, replace the rope by gravity and it's still a circular orbit.

(1) If you want to use this metaphor, gravity is a stretchy rope. Stretchy ropes do not usually maintain circular orbits.
(2) I suggest that, with the benefit of 400 years of observational validation since Newton, "very likely to be rubbish" is ... not sensible. With modern equipment (meaning, telescopes of the last 200 or so years), it's easy to measure the non-circularity of even the most nearly circular planetary orbit (Venus's): It's about 2/3 of 1%. All the others are significantly less circular. Perfect circular orbits do not occur in nature.

 

[lomidrevo]

" the circular orbit is very special case of elliptical orbit - not very likely to occur."
Why? This is very likely to be rubbish, when you swing a ball on a rope around your head the orbit is circular, replace the rope by gravity and it's still a circular orbit.

Let's try to go back to two-body problem, where second body has a negligible mass compared to the first one. Let's imagine that this system is somehow miraculously isolated from rest of the universe. Now you can imagine that the trajectory of the second body around the first one will depend on some initial conditions, namely the initial position and velocity of the second body. Let's consider the first body at rest all the time. Now just considering kinematics of uniform circular motion, for each orbit (distance from the center of the first body) exists only single value of speed of the second body which allows its circular motion. And more over the direction of its initial movement must by exactly tangential, i.e exactly at right angle with radial direction (toward the center of the first body). Whatever else initial velocity will not lead to a circular motion (ellipse, parabola and hyperbola are possible depending on the total energy of the system).

As you can see, we made some approximations and considered unrealistic isolated system and even though the probability of second body orbiting the first one in an exact circle is very low. Now you can ask yourself, how probable is this to happen when planets are being formed in any real stellar system, where all bodies and dust interact with each other.

 

[russ_watters]

" the circular orbit is very special case of elliptical orbit - not very likely to occur."
Why? This is very likely to be rubbish, when you swing a ball on a rope around your head the orbit is circular, replace the rope by gravity and it's still a circular orbit.

First, we should just set aside the string; it doesn't behave at all like gravity. It has a preferred distance and the fore applied increases if you try to increase the distance and decreases if you try to decrease the distance. That's the even worse than opposite of how gravity works.

Second, note that "special" for circular orbits doesn't mean privileged, it just means unique. There is nothing special about a circular orbit; it's just a symmetrical ellipse. There is no force pulling an elliptical orbit to try to make it circular. Elliptical orbits are stable on their own.

Generalizing: Every closed path that an object takes around another (or their mutual center of gravity) due to gravity alone is an ellipse. If you throw a baseball, you've created an elliptical orbit...albeit short-lived. So you really don't even have to try hard to make an orbit. All you need to do is throw something hard enough that it misses the Earth on the way back down, but not hard enough to escape. Then the ellipse just happens. But only one of the infinite number of ellipses you can create that way is also a circle.

 

[Orodruin]

All you need to do is throw something hard enough that it misses the Earth on the way back down, but not hard enough to escape

Just nitpicking, but this is impossible if you are on the Earth. Since the ellipse intersects the Earth at its point of origin, it will intersect the Earth on the way down as well.

 

[russ_watters]

Just nitpicking, but this is impossible if you are on the Earth. Since the ellipse intersects the Earth at its point of origin, it will intersect the Earth on the way down as well.

I don't see that your description differs from mine except in the unstated implication that in order to call the path an "orbit", it has to complete a full orbit successfully. This is often, but not universally, used colloquially, but it actually gets in the way of the math/logic; it's logically inconsistent.

I consider the fact, as I stated it in the first sentence of that paragraph - that all such paths are elliptical - to be an important insight that changes how scenarios are viewed in an important way.

 

[lomidrevo]

Second, note that "special" for circular orbits doesn't mean privileged, it just means unique. There is nothing special about a circular orbit; it's just a symmetrical ellipse.

Yes, I agree, circle is just an ellipse with zero eccentricity - it is the same type of beast. The word "special" I used in the meaning that it is not probable to be found in nature.

 

[Orodruin]

I don't see that your description differs from mine except in the unstated implication that in order to call the path an "orbit", it has to complete a full orbit successfully. This is often, but not universally, used colloquially, but it actually gets in the way of the math/logic; it's logically inconsistent.

I consider the fact, as I stated it in the first sentence of that paragraph - that all such paths are elliptical - to be an important insight that changes how scenarios are viewed in an important way.

You seemed to be saying that it would be possible throw something fast enough to miss the Earth on the way down but yet not fast enough to escape. If it comes down, it hits the Earth, so it is not possible.

 

[russ_watters]

You seemed to be saying that it would be possible throw something fast enough to miss the Earth on the way down but yet not fast enough to escape.

Oh...ok...:

Since the ellipse intersects the Earth at its point of origin, it will intersect the Earth on the way down as well.

Since we are nitpicking; this path does not, in fact, intersect the surface of the Earth, but rather has a a perigee just above zero and up to about 5 feet (and then above that the origin point becomes the perigee).

 

[Orodruin]

Since we are nitpicking; this path does not, in fact, intersect the surface of the Earth, but rather has a a perigee just above zero and up to about 5 feet (and then above that the origin point becomes the perigee).

Depends on how you define "hit the Earth". Either way, you would need to throw it tangentially for this to happen and the entire thing is either way not possible to due to air resistance etc.

 

[stefan r]

...If you throw a baseball...

Just nitpicking, ...

Must include the magnus effect too. With a hook or slice it is not a circle or an ellipse because it is not in a plane. With backspin it could still be in a plane but not be a circle or ellipse. youtube

There is also a hyperbola. The set of all hyperbolic orbits passing through a point above a planet is larger than the set of elliptical orbits passing through that point.

 

[russ_watters]

Depends on how you define "hit the Earth". Either way, you would need to throw it tangentially for this to happen and the entire thing is either way not possible to due to air resistance etc.

Agreed! Nevertheless, it is a popular way to describe an orbit in the first pass. There's dozens of these online in k-12 course notes:

[Images not to scale]

 

[JMz]

In the spirit of the OP, I believe we can ignore air friction. (First we climb up a ladder that is 400 miles high, then we throw sideways really, really hard and ... we see that the path will escape the Earth or else be some kind of ellipse.)

 

[Chronos]

Tidal forces provide an easy way to see why orbits cannot remain circular. This alone is sufficient to explain why the moon is currently receding from Earth at an astounding ~4 meters per century.

 

[JMz]

Tidal forces provide an easy way to see why orbits cannot remain circular. This alone is sufficient to explain why the moon is currently receding from Earth at an astounding ~4 meters per century.

True, but this seems beyond the spirit of the OP: The tidal effect matters because the bodies are not perfectly rigid and each spans some measurable distance over which the other's gravity changes. But bodies can be perfectly rigid and arbitrarily small (relativistic effects aside) and still not have any special affinity for circular orbits.

 

[russ_watters]

But bodies can be perfectly rigid and arbitrarily small (relativistic effects aside) and still not have any special affinity for circular orbits.

I'll extend; the tidal effects will force a body not to have a circular orbit. Without them or other perturbations, a circular orbit could be passively stable...but never actively stable/preferred.

 

[JMz]

I'll extend; the tidal effects will force a body not to have a circular orbit. Without them or other perturbations, a circular orbit could be passively stable...but never actively stable/preferred.

Quite right.

One thing that can produce preferentially circular orbits is friction. In fact, the gas friction within the Solar nebula is presumably why the planetary orbits are as circular as they are. But that effect, too, seems outside the spirit of the OP. And once that dissipated, there wasn't anything left to continue circularizing the planetary orbits. (For Saturn, perhaps dynamical friction is having that effect on the tiny satellites. I'm not sure.)