Two asteroids have elliptical orbits around the Sun with the same semimajor axes but different eccentricities.Which of the following statements is true?
A) The orbit with the smaller eccentricity comes closest to the Sun.
B) The orbit with the smaller eccentricity has a longer period.
C) The orbit with the larger eccentricity has a larger semiminor axis.
D) The orbit with the larger eccentricity has a larger change in speed.

Question

Quizplus · Accepted Answer

The eccentricity of an orbit determines its shape, with higher eccentricity indicating a more elongated ellipse. An orbit with a larger eccentricity will have a larger variation in distance from the Sun throughout its orbit, leading to a larger change in speed due to Kepler's second law, which states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means that the speed of the asteroid increases as it gets closer to the Sun and decreases as it moves away, with the change in speed being more pronounced for orbits with higher eccentricity.

Two Asteroids Have Elliptical Orbits Around the Sun with the Same