A comet's perihelion distance is 1 AU, and its aphelion distance is 15 AU. In the following, we

step 1 Calculate the orbital period of the comet. You need to find the average of our two distances, A.

A comet's perihelion distance is 1 AU, and its aphelion...

A comet's perihelion distance is $1 \mathrm{AU}$, and its aphelion distance is $15 \mathrm{AU}$. In the following, we make a very very crude calculation of the average rate of shrinkage of the comet. (b) Estimate how many meters of ice the comet will lose each time it orbits the Sun. (Hint: To simplify the calculations, you may assume that ice sublimates off the comet's surface during one-tenth of its orbital period, that the average cometary distance over that period is $1.5 \mathrm{AU}$ and that the density of the cometary ice is 600 $\mathrm{kg} \mathrm{m}^{-3}$.)

A comet's perihelion distance is $1 \mathrm{AU}$, and its aphelion distance is $15 \mathrm{AU}$. In the following, we make a very very crude calculation of the average rate of shrinkage of the comet.
(b) Estimate how many meters of ice the comet will lose each time it orbits the Sun. (Hint: To simplify the calculations, you may assume that ice sublimates off the comet's surface during one-tenth of its orbital period, that the average cometary distance over that period is $1.5 \mathrm{AU}$ and that the density of the cometary ice is 600 $\mathrm{kg} \mathrm{m}^{-3}$.)

Key Concepts

Orbital Dynamics and Active Period

A comet’s orbit, defined by its perihelion and aphelion distances, determines not only the variation in received solar energy but also the duration during which sublimation is significant. The assumption that ice sublimation occurs during a fraction of the orbital period introduces a simplified time window over which the energy input is integrated to estimate the overall mass loss.

Density and Mass Conversion

Density is used to convert the mass loss due to sublimation into a loss in volume, and subsequently into a thickness of ice eroded from the comet's surface. This involves relating the total mass of sublimated ice to the volume removed, which is then linked to the effective rate of shrinkage of the comet's nucleus.

Cometary Sublimation

This is the process by which solid ices on a comet turn directly into gas when heated, without first becoming liquid. In the context of comet behavior, sublimation is the primary mechanism for mass loss as a comet approaches the Sun, and understanding this process is essential for estimating how much material is lost per orbit.

Solar Radiation Flux and Energy Balance

The amount of energy a comet receives from the Sun depends strongly on its distance, according to an inverse-square law. This concept is crucial when modeling sublimation rates because the intensity of solar radiation determines the rate at which cometary ice sublimates, especially during the portion of the orbit where the comet is closest to the Sun.

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