Comet Halley has a sidereal period of 75.316 years and an eccentricity of e=9.67.

a. What is the length of its orbital semi-major axis in AU?

b. What is the closest it gets to the Sun in AU?

c. The farthest in AU ?

i. How fast (orbital speed) is it moving at perihelion in

1. AU/yr

2. Km/sec

ii. How fast is it moving at aphelion in

1. AU/yr

2. Km/sec

Solutions

Expert Solution

Kepler’s third law says that a³ ∝T² . If we measure a in AU and T in years, then the constant of proportionality is 1, and we can write that a³= T² . Since we are given that T = 75.316 years for Halley’s comet: a = = = = 17.83 AU

a). Hence length of orbital semi-major axis is a= 17.83 AU

b)The perihelion distance is given by: = a(1 − e) = 17.83*(1 − 0.967) = 0.588 AU

c)Similarly, the aphelion distance is given by: = a(1 + e) = 17.83*(1 + 0.967) = 35.07 AU

d) The orbital speed of the comet at Perihelion is 54km/s or 11.39 AU/yr

e) The orbital speed of the comet at the Aphelion is 0.879km/s or 0.185AU/yr

genius_generous answered 1 year ago

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