A certain comet orbits the sun in an elliptical orbit of eccentricity equal to 1/2. In this case, the semimajor axis, 'a', is exactly equal to twice 'c', the distance from the sun to the center of the ellipse, as shown below. The speed of the comet when it is closest to the sun (the perihelion) compared to the speed of the comet when it is farthest from the sun (the aphelion) is

Engineering

Physics

Keplers Law

Collision

Angular Momentum and Conservation of Angular Momentum

Question

A certain comet orbits the sun in an elliptical orbit of eccentricity equal to 1/2. In this case, the semimajor axis, 'a', is exactly equal to twice 'c', the distance from the sun to the center of the ellipse, as shown below. The speed of the comet when it is closest to the sun (the perihelion) compared to the speed of the comet when it is farthest from the sun (the aphelion) is

the same

three times as larger

twice as large

1/3 as large

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In elliptical orbits, angular momentum is conserved: m v_p r_p = m v_a r_a, so v_p / v_a = r_a / r_p. Given eccentricity e = c/a = 1/2, and c = a/2. Perihelion r_p = a - c = a - a/2 = a/2. Aphelion r_a = a + c = a + a/2 = 3a/2. Therefore, v_p / v_a = (3a/2) / (a/2) = 3. So the perihelion speed is three times the aphelion speed.

Final answer: three times as large