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I do not claim to be an expert in the fields involved. Short-period comets Short period comets disinagrate rather quickly due to interaction with the sun while in the inner portion of the solar system.
Because of the forward motion of an object in orbit around the sun, the sun's radition strikes it at an angle and exerts a backwards force. In the case particles on the order of 1 mm or less in diameter, this force degrades the orbit, causing the particle to fall into the sun within thousands to a few million years.Also, the arguments I use here deal with the solar system, the earth, and man.They do not deal with the age of the universe as a whole.He also gives an average period for a class of short-period comets of 7 years, yielding an average lifetime of around 500 years.
With the average number of this class which are visible any one time, a 4.5 billion year old universe requires that at least several hundred million coments existing away from the sun have been diverted into the solar system.These methods don't assign an exact age; the rates and initial conditions are not exactly known.However, since the "young" and "old" age ranges differ by 5 1/2 orders of magnitude, it is easy to say which pieces of evidence favor which theory.The supporting details are based on study, briefer than I would like, done for this debate.