Basics of Space Flight: Orbital Mechanics

Re:Basics of Space Flight: Orbital Mechanics by antognini on Wednesday October 07, 2015 @11:44AM (#10346663)

We are actually very fortunate that the Earth is not very spherical, because without that satellites on the high inclination orbits like the polar orbits and the Molinya orbits would crash into the Earth.

Due to perturbations of the Moon, high inclination orbits have a tendency to be pushed from low eccentricity to very high eccentricity. (This is known as the Kozai-Lidov mechanism.) However, the fact that the Earth's gravitational potential is not exactly spherical (it has a quadrupole moment) makes these orbits precess, and this precession happens to be fast enough to suppress the eccentricity oscillations.

There is a very good and very readable article by Scott Tremaine on this subject here: http://arxiv.org/abs/1309.5244

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Re:Basics of Space Flight: Orbital Mechanics by Retric on Wednesday October 07, 2015 @04:06PM (#10348658)

It would be very unusual for a planet to be spherical as it would have to not be rotating.

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Re:Basics of Space Flight: Orbital Mechanics by nsxwolf on Wednesday October 07, 2015 @04:37PM (#10348902)

What about Venus? It rotates really slowly compared to Earth.

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Re:Basics of Space Flight: Orbital Mechanics by antognini on Wednesday October 07, 2015 @05:21PM (#10349201)

The quadrupole moment of Venus is much, much less than that of the Earth. For comparison, the relative difference between the radius at the equator and the radius at the pole of Earth is about 0.3%. For Venus it's less than one part in 100,000. However, Venus doesn't have a moon, so there's no third body to cause Kozai-Lidov oscillations [1].

[1]: Actually, this is not strictly true, since the Sun acts as a third body. However, it's so much further away that the Kozai-Lidov effect from the Sun is weak. That's why the Venus Express was able to maintain a polar orbit around Venus.

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