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Why are the orbits of the planets elliptical ? The circular orbit also satisfies all the conditions of gravitational force. Then why did nature choose the elliptical orbits ?

StephenG - Help Ukraine
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  • Just wondering - but how is asking why something is NOT circular a duplicate of asking why something is circular? – ProfRob Dec 05 '17 at 14:13
  • A circle is an ellipse with major and minor axes equal. equality is much rarer / harder to achieve than inequality (true both in algebraic systems and the universe) – Carl Witthoft Dec 05 '17 at 18:16
  • Can anyone source that a circular orbit actually does satisfy the conditions of gravitational force? Don't Kepler's laws guarantee two distinct foci? If the the primary body is much more massive, the foci are closer together, but can they ever converge? You might be able to show both the primary and the orbiting body have a circular orbit around some third point, but that's not the same thing. –  Dec 08 '17 at 01:28

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For a given amount of angular momentum, a circular orbit is the orbit with lowest energy.

Some orbits are elliptical (actually, all orbits approximate to ellipses) with a non-zero eccentricity, because they have yet to reach their lowest energy state, or because they have been excited from their minimum energy state circular orbit.

ProfRob
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  • This! What Rob is alluding to is the principle of minimum energy, which dictates that a closed system (a system that can exchange energy but not mass, linear momentum, or angular momentum with the external environment) will tend toward the system's minimum energy state if a path toward that minimum energy state exists. Tidal heating means that that pathway does exist. – David Hammen Dec 05 '17 at 11:26
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  1. Planets don't have elliptical or circular orbits. The elliptical orbit is the solution to the two body Newtonian gravity problem. As their are more than two particles in the solar system, the orbits aren't ellipses or circles.

  2. A circle is an ellipse with eccentricity = 0. It's special in some ways, but for orbits it's just another elliptical orbit. The universe doesn't care what the eccentricity of the planets orbits is (providing it's not too big) There is no special reason why the eccentricity should be exactly 0. The eccentricity is essentially a random value. If you choose a number at random between 0 and 0.1 the probability of choosing exactly zero is 0.

  3. The real question is Why are most planetary orbits nearly circular Since orbits of any eccentricty are possible it is (initially) surprising that all orbits are so close to circluar.

James K
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While a circular orbit is possible and consistent with equations of gravitation, elliptical orbits are almost a necessity due to the surroundings of any orbit. If you take our solar system as an example, the center of mass will change as not all planets orbit at the same speed. The center of mass is found with the equation: $$x_c=\frac{\sum\limits_{i=1}^{n}{m_{i}x_i}}{\sum\limits_{i=1}^{n}{m_{i}}}$$ As the planets mass distribution around the sun changes, the point which the planets orbit changes slightly, disrupting any circular orbits. All orbiting bodies will have some disruption, preventing orbits to always be perfectly circular. In addition, losing energy and angular momentum to other sources can cause bodies to lose their orbital shapes and degenerate into elliptical orbits.

In addition, please use this link also posted as a comment.

t.sand
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