Halley's comet orbits the sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach. Estimate the greatest distance of the comet from the sun. Is it still in the Solar System? What planet's orbit is nearest when it is out there?

Question

Physics

Hodges

14 March, 19:00

Halley's comet orbits the sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach. Estimate the greatest distance of the comet from the sun. Is it still in the Solar System? What planet's orbit is nearest when it is out there?

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Cheese · Answer 1

r1 = 5*10^10 m, r2 = 6*10^12 m

v1 = 9*10^4 m/s

From conservation of energy

K1 + U1 = K2 + U2

0.5mv1^2 - GMm/r1 = 0.5mv2^2 - GMm/r2

0.5v1^2 - GM/r1 = 0.5v2^2 - GM/r2

M is mass of sun = 1.98*10^30 kg

G = 6.67*10^-11 N. m^2/kg^2

0.5 * (9*10^4) ^2 - (6.67*10^-11*1.98*10^30 / (5*10^10)) = 0.5v2^2 - (6.67*10^-11*1.98*10^30 / (6*10^12))

v2 = 5.35*10^4 m/s