Why are planetary orbits elleptical and not circular?

Question

Keplers Laws can be used to calculate the elleptical orbits but thats only calcualting, not the reason.

Gravitational Force is the only significant force acting on a Planetary object orbiting another body (example Earth - Sun). This Force is calculated using F = G*M1*M2/(r*r) where G is the gravitational constant, M1 and M2 the respective masses of the two bodies and r is the distance between them.

This force F would be acting from center of mass of one body to the center of mass of the the other body, which would be a straight line and thus this Gravitational Force along with the Centrifugal Force (acting perpendicular to the Gravitational Force) should result in a circular orbit (one center).

But this is not the case, all planetary orbits are Elleptical (two centers). Also in a elleptical orbit the distance between the two bodies keeps changing, shouldn't this cause a variance in the Gravitational Force? And therefore this should make the orbit unstable?

Answer 1

Elliptical orbits are a natural result of gravity. Left to itself, an elliptical orbit is also very stable. Planets travel at different speeds at different parts of their orbits. A planet moves more quickly when it is closer to the Sun.

The change in speed is due to angular momentum. This is just momentum that is associated with rotation. It is determined by how far the object in question is from the point it is rotating around, and by how quickly it is rotating. Like energy, angular momentum must be conserved. Conservation of angular momentum is why, for example, an ice skater spins more rapidly when she pulls her arms in. As her arms come closer to her body, she must spin more quickly in order to have the same angular momentum. The same is true for planets orbiting around the Sun.

Think of it as a competition. As a planet moves further from the Sun, it slows down in its orbit. Because it is orbiting more slowly, it begins to "fall" towards the Sun, because of the Sun's gravity. As the planet comes closer to the Sun, it speeds up in its orbit, in order to conserve angular momentum. As it speeds up, it can pull away from the Sun. As it moves further away, it begins to slow down, and the process repeats. The result of this constant back-and-forth is an elliptical orbit.

The elliptical orbits of the planets will change slowly. This is due the gravitational influences of the other planets. Because these are much weaker than the gravity we feel from the Sun, the changes in planetary orbits are very slow.

Answer 2

Essentially what most of these folks said are correct.
I will only paraphrase somewhat for the purpose of clarification and to provide a less technical answer.

When an object passes the sun, there are three possible outcomes. The object is moving too slow for its distance and gets drawn into the sun, the object is moving too fast for its distance and passes thorugh the solar system and leaves forever, or the object is moving within a range that is neither too slow nor too fast and gets caught and pulled into an orbit.

The range of orbital velocities is quite large, and depending on where in that range the object is moving will determine what shape its orbit will take.

Within this range is a very narrow zone of speed whereby if the object is travelling at that speed then it will get a circular orbit. Outside of that narrow zone, the orbits will all be elliptical. Some are very eccentric, others are almost circular.

So the odds are that any object in orbit will have an elliptical orbit. But on very rare occasion, if the conditions are just right, the orbit will be a circle, which is also a type of an ellipse, a very special type.

Answer 3

Mathematically, the circle is a special case of the ellipse - it's just an ellipse with eccentricity = 0.

In order for an object to go into a circular object, it must have precisely the right velocity. Any deviation from that and the orbit becomes an ellipse. Think of it as trying to be circular, but it keeps overshooting, going first too far and then too close. It's not unstable; it's self correcting; a dynamic balance. Isaac Newton was the first to work out the math, and he found that the natural shape of an orbit is an ellipse, just as Kepler had described.

Answer 4

Elliptical orbits are the result of the solution of the differential equations of motion. While Kepler observed and postulated Planetary Laws of Motion, it was Newton who showed that these laws can all be derived from his Theory of Gravitation by using The Calculus (which Newton discovered, or "invented").

Mathematically, a circle is a special case of an ellipse. What is actually quite surprising is how nearly circular the planetary orbits are.

Answer 5

I think you sort of answered your own question. I think of it as swirling a ball around in a circle with an elastic string. As the ball gets farther away, the tighter the elastic band gets. Same thing with the planets, they can only get so far away from one object before the gravitational forces acts upon it, bringing it back toward the larger massed object.

The only this that is keeping the planets from colliding is the magnetic fields around it. Now, I'm not saying that the possibility of collision cannot happen but due to the fact that all bodies are in constant motion in different directions, the possibility of a collision are slim.

Answer 6

Orbital revolution is the cyclical path taken by one object around another object (or point, line, etc.)

In astronomy, the term revolution is most often used to describe the movement of large masses around the center of mass of a system, for example the movement of a moon around a planet or a planet around a star. These orbital revolutions were first described using elliptical orbits by Kepler. Newton later was able to provide a physical model for this motion, now understood to be due to the force of gravity. Our current understanding of gravitation, and therefore of orbital revolution, also owes a great deal to the Theory of relativity developed by Albert Einstein.

so it is due to centre of mass and force of gravity.

Answer 7

One possibility to keep in mind. The focus of the orbit is not stationary. Not only do the planets move around the Sun in their orbits, the Sun is going along in space along with other stars in this arm of the Milky Way. Yes, Newton's euqations of gravity will work in not-too-specifically describing the motion of celestial bodies. But, for more precise deacriptions, one must bring into play the equations of Einstein's General Theory. In one technical description, and I am a smart *** so I LOVE being technical, the earth does NOT move in anything except a straight line. That striaght line path, however, is across the curved or warped surface of spacetime. The motion of any massive body, like our Sun, affects the ripples in the curvature of that spacetime. Ellipses are the most efficient path thinking in a 2D sense, like Kepler, for the planets to travel along.

Answer 8

Circular orbits are demanding things. They require that a captured object (such as an asteroid) to have the circular orbit speed v = sqrt(GM/r) with respect to the primary, in a direction perpendicular to the radius from the primary. That's a very ordered condition, and there are many more (elliptical) ways for the captured object to be moving immediately after capture. The circular orbit is a special case; the elliptical orbit is the general case. Basically, the answer to your question is entropy.

Answer 9

the one constant that retains the object in orbit is gravity. gravity is also the reason for the eliptical orbit. much like the vaunted sci fi program, the object picks up speed as it makes the orbit around the gravitational object.

as it does, so, the captured object will "attempt" to escape the orbit, but will be brought back into the orbit, as long as the gravitational attraction is stronger than the "escape" velocity of the captured object.

-eagle

Answer 10

Math didn't work for circular orbits.