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Halley's Comet Calculations

Haley's comet orbits the sun every 76 years, and was first observed in 240bce. Its orbit is highly elliptical, so that its closest approach to the sun (perihelion) is only 0.587 AU, while at its greatest distance (aphelion), the comet is 34.39 AU from the sun. (An AU, or astronomical unit, is the distance from earth to the sun, 1.5 x 10^8 kilometers)

A.Calculate the distance from the sun to Haley's comet in meters at perihelion and aphelion.
B.Haley's comet has a volume of 700 cubic kilometers, and its density is about 0.1 gram per cubic centimeter. Calculate the mass of the comet in kilograms.
C.The gravitational force (in Newtons) exerted by the sun on its satellites is inversely proportional to the square of the distance to the satellite in meters. The constant of variation is Gm1m2, where m1 = 1.99 x 10^30 kilograms is the mass of the sun, m2 is the mass of the satellite, and G=6.67 x 10^-11 is the gravitational constant. Write a formula for the force, F, exerted by the sun on Haley's comet at a distance of d meters.
D.Calculate the force exerted by the sun on Haley's comet at perihelion and at aphelion.

Solution Preview

A. At perihelion, the distance is 0.587 x 1.5 x 10^8 x 10^3 = 8.805 x 10^10 m.

At aphelion, the distance is 34.39 x ...

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