Comet

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- Phase-mixed comet surface density Comet

Phase-mixed comet surface density ( $Σ_{c} (r)$ )

With uniformly distributed apsidal orientations, the phase-mixed radial probability of a Kepler orbit gives the surface probability per comet

Σ_{c} (r) = \frac{1}{π ^{2} ( Q + q ) ( r - q ) ( Q - r )} .

For

Q ≫ r > q

, this is

π^{- 2} Q^{- 3/2} r^{- 1/2} (1 - q / r)^{- 1/2}

. Multiply by the population size for a number surface density of a disk.

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Coplanar comet collision time
Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 316 / 1 / iii / Solution
Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 316 / 1 / ii / Solution
Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 316 / 1 / i / Solution
Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 316 / 1 / iv / Solution
Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 316 / 1 / v / Solution
Phase-mixed comet surface density
Planetary ejection of a comet

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