The diagram shows an approximate orbit of a planet X around a star S.

Which of the following statements is false?

(a) The planet moves in an ellipse with the star at one focus.

(b) The planet moves at the same speed at points A and C.

(c) The planet moves fastest at point D.

(d) The potential energy of the planet changes during the orbit.

###### Solution.

(a) True. Kepler’s First Law. The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.

(b) True. According to the law of conservation of energy, if the points at the same distance from the star the potential energy is the same, then the kinetic energy of the planet at this points must be the same, thereby the speeds must be the same.

(c) False. Kepler’s Second Law. The radius vector from the Sun to a planet sweeps out equal areas in equal periods of time. The areas are equal, however the arcs that sweep out the areas are not, closer to the Sun the arcs are longer, the planet moves faster and further from the Sun the arcs are shorter, the planet moves slower.

Also, at D, potential energy is higher, so kinetic energy is lower, thus the planet speed is lower as well.

(d) True. The distance between the planet and the star changes during the orbit, so the potential energy of the planet changes.