Do all comets approach the Sun along the plane of the elliptic? Are there any that approach perpendicular to the elliptic? If they do approach along the plane of the planets why don't they come from all directions given that we are surrounded by the Ort cloud? Is the gravitional pull of the sun the same 93 million miles north of the sun from the elliptic as it is on earth? How do we know that?


The inclination of a comet's orbit with respect to the ecliptic (approximately, the plane spanned by the orbits of the major planets) depends on the origin of the comet. Long-period comets come from the Oort's cloud; since Oort's cloud is spherical, long-period comets approach the inner solar system at random angles as you correctly guessed (note that their orbit can be majorly perturbed as they pass near the giant planets). Short-period comets originate in Kuiper's belt and orbit roughly along the plane of the ecliptic.

We know that the gravitational field of a spherical object like the Sun does not depend on the orientation as an elementary consequence of Newton's theory of gravitation. This is experimentally true as verified by the trajectory of satellites around the Earth and the other planets of the solar system (having taken into account the oblateness of the bodies themselves); trajectories of space probes are very precise and are calculated on computers using the laws of gravity. If the gravitational field of spherical bodies was not the same independently of orientation, the trajectories calculated with the law of gravity would not have corresponded to the actual orbit of the probe. As for the Sun, an example is the Ulysses probe that orbited out of the plane of the ecliptic (http://en.wikipedia.org/wiki/Ulysses_probe).

Hope this answers your questions.

 
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