# Why are orbits elliptical? [duplicate]

Almost all of the orbits of planets and other celestial bodies are elliptical, not circular.

Is this due to gravitational pull by other nearby massive bodies? If this was the case a two body system should always have a circular orbit.

Is that true?

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## marked as duplicate by ACuriousMind, Kyle Kanos, 0celo7, Floris, John RennieJun 4 '15 at 5:52

No, any ellipse is a stable orbit, as shown by Johannes Kepler.

A circle happens to be one kind of ellipse, and it's not any more likely or preferable than any other ellipse. And since there are so many more non-circular ellipses (infinitely many), it's simply highly unlikely for two bodies to orbit each other in a perfect circle.

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However, tidal and frictional forces will tend to dissipate energy while maintaining angular momentum, eventually resulting in an ellipse getting more and more rounded out into a circle. All of the planets are on very nearly circular elliptical orbits. – Andrew Aug 25 '11 at 18:58
@Andrew Except for many extrasolar planets, that's not true. – Mark Eichenlaub May 5 '12 at 6:11
Kepler lived before Newton, so did not know about gravitational attraction, let alone did he know about the inverse-square force law for it. He was therefore not in a position to compute that orbit should be elliptical (and indeed he tried other ideas for a long time), and certainly not to show that such a solution is stable. What he did do is by long calculations show that the orbit of Mars is observed to be elliptical with the Sun in one focal point, and to postulate (without verification) that the same is true for all planets. His "equal area" law also describes the speed variations. – Marc van Leeuwen Sep 8 '14 at 5:18
@Andrew: That's a complete misconception. What energy tidal forces dissipate is rotational energy of the body about its own axis, not orbital energy. So tidal dissipation makes the Earth slow down slightly and days become longer. This also requires angular momentum to be transferred to the Moon, which gets push forward in its orbital direction (since the Earth rotates faster than it), and so another part of the Earth's rotational energy is not dissipated but transferred to orbital energy of the Moon. Which thereby gets an ever wider orbit. It being fairly circular has other reasons. – Marc van Leeuwen Sep 8 '14 at 8:28

Every circle is elliptical since no answer for PI has been or can fully be achieved. The elliptical model fits as well as any. When taking into consideration Higgs Boson and Dark matter and there possible inflection on string theory in the fabric of space with multiple universes, it is very possible that the distortion of space-time make it impossible to achieve the theoretical circle. Once these distortions have been fully understood, we may find that all elliptic's are in actuality the eternal, just perceived now as a different form. The problem exists within our capability to measure what requires eternal rules or current rule have built in ambiguities. We have not achieved the eternal, therefore perfection is out of reach. You can always say; "For all practical purposes" but, that does not lead to the perfect or sacred knowledge in the quest for certainty.

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This really doesn't make much sense, could you elaborate? – Manishearth Dec 10 '12 at 23:05

Many objects presently in orbit around larger objects were originally 'captured' by the gravity of the larger one as the smaller one happened to pass by closely enough. Of all the possible combinations of speed and direction of the two objects relative to each other at the time of gravitational capture, only a very special subset will result in a circular orbit; all others are elliptical with varying degrees of eccentricity.

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Could you explain why "all others are elliptical"? – Manishearth Nov 22 '12 at 7:00

A circle is a very difficult shape to maintain. Even the slightest deviation, and a circle is bypassed.

Orbits are elliptical when any of the following things happen:

• Another object strikes the planet in such a way to change its orbit. It would have to be massive compared to the primary object, at least a sizable fraction.
• Gravitational interaction with other nearby objects, especially if resonance occurs. This is why Pluto has such an elliptical orbit.
• Differing albedo can cause differences to occur over a long period of time.

I'm sure I could come up with other reasons as well.

In order to have a perfectly circular orbit, one must achieve the perfect speed for one's distance from the body around which they are orbiting. The lecture Astronomy 106, Orbital Velocity gives the formula, which is:

# $$V_c = \sqrt {GM \over r}$$

Any deviation from this results in an elliptical orbit.

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If this was the case a two body system should always have a circular orbit.

There are a number of highly-eccentric orbits that aren't anywhere close to circular, but they're more difficult to maintain over time, as they're more likely to be biased by other objects.

For some spacecraft (eg, STEREO; watch the first movie), they actually use this behaviour so that the spacecraft orbit the earth such that the moon will effectively 'throw' the spacecraft where they're trying to get it.

The Voyager spacecraft used this multi-planet Gravitational Assist known as Planetary Grand Tour to achieve solar escape velocity with very modest fuel requirements.

It is not uncommon to use such assists as it can radically reduce the fuel costs of a mission (to the point of making it even possible), in exchange for increased mission durations.

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A circle is only a special case of an ellipse and obeys all the same mathematical rules. So even circular orbits are elliptical. Origin chance and third+ body perturbations will have random effects on the ellipticity, so no surprise purely circular orbits are rare to non-existent being only one of an infinite number of possible outcomes.

What I find much more interesting is how close to circular our planetary orbits actually are. Excluding Pluto as being not-a-planet any more, that is.

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Perhaps the elliptic orbits arise because of an expanding universe. If the universe were stationary, the orbits might have been circular.

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The derivation of elliptical orbits by Kepler was carried out well before any modern notion of an expanding universe was held. – Nic Jan 13 '12 at 12:25
It would be better if the answer was based on facts with some evidence rather than a supposition. – Stuart Woodward Jan 22 '12 at 11:56

In addition to the other answers I want to remark that the calculations from the conversation and force laws give you conic sections for the two body systems, parabolas, hyperbolas and ellipses (including circles).

Ellipses are the only paths for orbits because the other paths never come near the starting point again.

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Extending this idea, can almost-orbits be modelled with hyperbolas or parabolas? That is, the path of 2 celestial bodies that near each other but don't act on each other enough to create an orbit? – Eric Hu Feb 28 '13 at 1:47
Hyperbolas, yes. For a given orbital situation, relative speeds below a critical value give closed elliptical orbits; speeds above that value give a hyperbolic flyby. Hitting the critical speed exactly would give a parabolic orbit, but that would be an unstable solution. – Russell Borogove Jan 3 '14 at 5:46

On the most fundamental level, ellipticity comes from the conservation of energy, angular momentum, and the $1/r^2$ gravitational force law. Any freshman taking classical mechanics should be able to take these three constraints and get ellipses. The impressive thing is how Newton took Keplers laws and worked backwards to get the laws of gravity and conservation.

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Um, no, freshmen can't do it. It requires a tricky change of variables the way it is usually done. If you think it's easy--- try it. The problem is usually presented to 3rd year students, but you can do it with freshmen techiques if you don't want deep understanding. Newton did it with deep understanding. It was Hooke who derived the inverse square law from Kepler, and this was easier. Hooke didn't get the ellipse. – Ron Maimon May 5 '12 at 1:54
I'm going to back Ron here as a current 3rd year physics student. To get it you really need more development in math and physics than most first year students have. – Skyler Dec 18 '14 at 8:29

## protected by Qmechanic♦Jan 3 '13 at 18:21

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