# Halley's Comet Distance to Sun at Perihelion & Aphelion, and Speed of Closest Approach

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Halley's comet is in an elliptic orbit about the sun. The eccentricity of the orbit is 0.967 and the period is 76 years. The mass of the sun is 2 x 10^30 kg and G=6.67 x 10^-11 Nm^2/kg^2.

a) Using this data, determine the distance of Halley's Comet from the sun at perihelion and at aphelion.

b) What is the speed of Halley's Comet when it is closest to the sun?

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#### Solution Preview

a) T^2 = (4 pi ^2 / GM ) a ^3

T= 76 years= 76 x 365 x 24 x 3600 = 2.3967 x 10 ^ 9 seconds

GM = (6.67 x 10 ^-11 ) x (2 x 10^30)= 1.334 x 10 ^ 20

Therefore a ^3=( GM / 4 pi ^2 ) T ^2 = 1.9410 x 10 ^ 37

a=( 1.9410 x 10 ^ ...

#### Solution Summary

The solution determines the distance of Halley's Comet from the sun at perihelion and aphelion and its speed when closest to the sun.

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