One of the brightest cornets of the 20th century was Cornet Hyakutake, which pas

Question

One of the brightest cornets of the 20th century was Cornet Hyakutake, which passed close to the sun in early 1996. The orbital period of this cornet is estimated to be about 30000 years. Find the semi-major axis of this cornets orbit. Express your answer using two significant figures. Compare it to the average sun-Pluto distance. Express your answer using two significant figures. Compare it to the distance to Alpha Centauri, the nearest star to the sun, which is 4.3 light-years distant. Express your answer using two significant figures.

Explanation / Answer

The simplest form of Kepler's Law, for objects orbiting the sun, is

r3 = T2

Where, R in AU =1.496 x 10^11(Astronomical unit),T in light years

So r = [(30000)2]1/3 = 965.48 AU

=1.444 x10^14 m.

r_pluto = 40 AU

that's why,

r/r_pluto= 965.48/40

=24.137

r_alpha = 4.3 light years

= 4.3 x 365x 24x 3600 x 3 x 10^8

= 4.068 x 10^18 m

So that,

r/r_alpha = (965.48x 1.496 x 10^11)/4.068 x 10^18

=3.55x 10-5

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