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The comet Churyumov-Gerasimenko has an unusual orbit for a comet. Instead of being far beyond Neptune like most comets, it is much closer to the Sun, and has a semi major axis of just 3.46 astronomical units (AU). Jupiter has a semi major axis of 5.20 AU. Based on Kepler’s 3rd law, does the comet orbit the Sun with a longer or shorter period than Jupiter?

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Answer:

comet has shorter period

Step-by-step explanation:

Given data:

comet semi major axis 3.46 AU

JUPITER major axis = 5.20 AU

We know that from kepler 3rd law, the square of orbital period is directly propotional to cube of semi-major axis of its orbit. i.e


P^2 ∝ A^3


P^2 = K A^3

where K is constant =1


P^2 =A^3

P - ORBITAL PERIOD (YR)

A - SEMI-MAJOR AXIS (AU)

For Jupiter


P =√(A^3)


P = √(5.20^3) = 11.85 Yr

for Churyumov - Gerasimenko


P = √(A^3)


P = √(3.46^3)

P = 6.43 Yr

Therefore comet has shorter period

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