The Orbit of Hale-Bopp Comet, Discovered in 1995, Is an Ellipse

question 18

Short Answer

The orbit of Hale-Bopp comet, discovered in 1995, is an ellipse with eccentricity $0.995$ and one focus at the Sun. The length of its major axis is $366.5 \mathrm { AU }$ . [An astronomical unit (AU) is the mean distance between Earth and the Sun, about 93 million miles.] Find the maximum distance from the comet to the Sun. (The perihelion distance from a planet to the Sun is $a ( 1 - e )$ and the aphelion distance is $a ( 1 + e )$ .) Find the answer in AU and round to the nearest hundredth.

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Definitions:

Prevail

To be widespread or dominant, or to win against opposing forces.

Concentration Ratio

A measure used in economics to assess the extent of market control held by the largest firms within an industry.

Profit-maximizing Output

The level of production at which a firm achieves the highest possible profit, where marginal cost equals marginal revenue.

Total Cost

The sum of all costs required to produce a certain amount of a good or service, including fixed and variable costs.