posted by Stefanie .
Suppose there's a collison way out in the Oort cloud, say 30,000 AU away from the Sun. This collison causes one of the comets to alter its orbit and head almost directly at the Sun, such that the comet just skims the surface of the Sun and heads back out to its starting point. Assuming it can survive the intense heat that close to the Sun, how long will it take the comet to complete one orbit?
This calls for an easy application of Kepler's third law. With the semimajor axis (a) in a.u. and the period (P) in years,
P^2 = a^3
In this case, a = 15,000 au is the average distance from the sun, so
P = 1.84*10^6 years