A particle is launched from the surface of a uniform, stationary spherical planet at an angle to the vertical. The particle travels in the absence of air resistance and eventually falls back onto the planet. Spaceman Fred describes the path of the particle as a parabola using the laws of projectile motion. Spacewoman Kate recalls from Kepler’s laws that every bound orbit around a point mass is an ellipse (or circle), and that the gravitation due to a uniform sphere is identical to that of a point mass. Which of the following best explains the discrepancy?
Answer Choices
A. Because the experiment takes place very close to the surface of the sphere, it is no longer valid to replace the sphere with a point mass.
B. Because the particle strikes the ground, it is not in orbit of the planet and therefore can follow a nonelliptical path.
C. Kate disregarded the fact that motions around a point mass may also be parabolas or hyperbolas.
D. Kepler’s laws only hold in the limit of large orbits.
E. The path is an ellipse, but is very close to a parabola due to the short length of the flight relative to the distance from the center of the planet.