A plot of the probability of finding a comet peridocally appearing in any given region between the Sun and Saturn reveals a donut, with a distinct hole starting at the orbit of Mars.
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|Figure 1 plots all the known comets closer than 10 AU (about the orbit
of Saturn) and with periods less than 100 years (almost all the periodic
comets), as seen from above the ecliptic plane. (Nearly all solar system
objects orbit within 20 degrees of the ecliptic plane.) The larger diamonds
represent the positions on October 5, 1996. The dots are equal time-interval
points on the orbit of each comet. Each orbit is alloted 200 points, regardless
of the orbital period. The density of the ensemble of orbit dots is roughly
proportional to the probability of finding a comet in a given region, because
the periods of the comets are mostly within a factor of 3 of each other.
The plot was designed for instructional purposes only, because the mere existance of the comets and their relatively slow orbital velocities is not a well known fact in the scientific community. A startling donut (torus shape) with a distinct "hole" in the center appeared unexpectedly.
Objects move the fastest near periapsis (closest approach) and slowest at apoapsis (most distant point). Plotting the orbits as equal time dotted points far more accuirately depicts the orbital characteristics than plots of elliptic orbits.
The area is a radial disc with the Sun as center. At Mars (1.53 A.U.) the inner boundary of the disc is the semi-major axis value of Mars orbit. The outher boundary is 1.05 times the Mars orbit.
The plot of Figure 2 is generated by summing each orbit point dot, weighted by orbit frequency, into equal area bins. A dot weight is assigned a value proportional to the amount of time a comet would have its orbit project into the given area of the ecliptic plane. This frequency is proportional to the reciprocal of the orbit period. The reference bin is the area from the orbit of Mars to 1.05 times the orbit of Mars. This is about 0.1037 square A.U. Each orbit is calculated with 200 points. So a value of "50" in the figure means 50/200 of an orbit.
The integrated "density of dots" as a function of distance from the Sun drops by a factor of about 5 just at the boundary of the orbits of the inner planets Mars, Earth, Venus and Mercury.
The distribution abruptly increases at the orbit of Mars and abruptly decreases past the orbit of Jupiter. The abruptness of the distribution inside the orbit of Mars is unexpected. The comet orbits do indeed pass deep inside the orbit of Mars. However, the pronounced ellipticity of comet orbits results in their spending only a small fraction of their orbital period closer to the Sun.
That the distribution should taper off as one moves inward, toward the Sun, is completely expected, perhaps due to physical and elastic collisions with the inner planets. The tapering past Jupiter is also expected, perhaps due to our observational bias. However, the abruptness starting at the orbit of Mars suggests some effect peculiar to Mars changes the distribution of visible comets. And the abruptness just past the orbit of Jupiter suggests Jupiter may be herding the comets into an orbit with periapsis near JupiterÕs orbit.
The albedo of comets is believed to be the darkest matter in the solar System. Dehydrated comets herded within the orbit of Mars, Earth, Venus or Mercury would either become invisible or be classified as near Earth asteroids. This would suggest that the comet ÒholeÓ consists of the the remnants of comets.
The number of spent comets within the comet hole could be large compared to the number of periodic comets. A periodic comet evaporates in a time of order 1 Million years. The orbit of the comet is stable for periods of order 10 Million years. [reference George Wetherill]] If the planets herd comets then any comets coming within the orbit of any of the inner planets become herded into a region where they are too close to the sun to keep their volatiles. Once devoid of volatiles, the objects can remain for a time as long as their orbits are stable. We are not aware of a good estimate of the lifetime of near earth asteroid orbits within the influence of the inner planets.
The existence of this "hole" provides us with a puzzle.