Halley's Comet returns to the Sun's vicinity approximately every 76 years in an elliptical orbit.According to Kepler's third law,what is the semimajor axis of this orbit?
A) 0.59 AU
B) 17.9 AU
C) 50.000 AU
D) 1 AU

Question

Quizplus · Accepted Answer

Kepler's Third Law states that the square of the period of a planet (or comet) orbiting the Sun is proportional to the cube of the semimajor axis of its orbit. Halley's Comet has a period of approximately 76 years, so we can determine its semimajor axis as follows:

T^2 = a^3
76^2 = a^3
a = (76^2)^(1/3)
a = 17.904 AU (rounded to three significant figures)

Therefore, the semimajor axis of Halley's Comet's elliptical orbit is approximately 17.9 AU. Therefore, the correct choice is B.

Halley's Comet Returns to the Sun's Vicinity Approximately Every 76