Question
Asked Oct 30, 2019

Why do we see comet Halley only every 76 years? Explain your reasoning.

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Step 1

Halley is a comet and its orbital period vary from 74 to 79 years.

Since its orbit is highly elliptical around the Sun and has an eccentricity(e) around 0.967 and its perihelion(r) and aphelion(R) are 0.6 AU and 35 AU respectively from the Sun.

Let a be the semi-major axis of its elliptical orbit, write the equation which relates aphelion with semi-major axis and plug necessary values to find a.

R (1+e)a
а
(1+e)
1.496 x 10
(35 AU
1 AU
а 3
(1+0.967)
a 2.66x1012
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R (1+e)a а (1+e) 1.496 x 10 (35 AU 1 AU а 3 (1+0.967) a 2.66x1012

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Step 2

Write the Kepler’s law to find the time period(T) of the comet Halley, take the mas...

47T2
4л'
т
GM
4(3.14)
(2.66x102 m)
Т-
(6.67x101 m'kgs2) (1.989 x 100 kg)
1 year
3.154x107 s
T 2.36x 10 s
T 75 years
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47T2 4л' т GM 4(3.14) (2.66x102 m) Т- (6.67x101 m'kgs2) (1.989 x 100 kg) 1 year 3.154x107 s T 2.36x 10 s T 75 years

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