Q251 · Practice questionSimple familiar1 mark
QUESTION 251
Two planets orbit the same star on elliptical paths with the same semi-major axis but different eccentricities. Neglect their masses relative to the star. Which statement follows from Kepler's laws?
(A)
Their speeds are equal at every point.
(B)
Their orbital periods are equal.
(C)
The star is located at the geometric centre of each ellipse.
(D)
Each planet sweeps out equal arc lengths in equal times.
WORKED SOLUTION
1 markAnswer B
ANSWER
B. Their orbital periods are equal.
Worked solution
Kepler's third law gives for elliptical orbits about the same star. Equal gives equal . The second law concerns equal areas, not equal arc lengths.
Equivalent physically justified methods, alternative valid sketches and consistent units accepted.
Accept sensible significant figures and consistent rounding from stated constants.
Select B.
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