Final answer:
The correct statements about a planet in an elliptical orbit around the sun are that its angular momentum is constant, and its areal velocity is constant. Option B and C are correct. These reflect conservation of angular momentum and Kepler's laws of planetary motion, specifically the second law.
Step-by-step explanation:
When considering a planet revolving around the sun in an elliptical orbit, we must refer to the laws established by Johannes Kepler, which are foundational to orbital mechanics. Based on these laws, two correct option statements about the properties of a planet in such an orbit are:
B) Its angular momentum is constant. This is supported by the conversation of angular momentum in systems with only radial forces, which indicates that a planet will speed up when closer to the sun and slow down when farther to conserve angular momentum.
C) Its areal velocity is constant. Kepler's second law, also known as the Law of Equal Areas, states that a line connecting the sun and the planet will sweep out equal areas during equal intervals of time, reflecting the conservation of angular momentum.
However, the following options are incorrect:
A) Its kinetic energy is not constant because the planet's speed varies along its orbit.
D) Its time period is not strictly proportional to r³, which is the distance from the sun, but rather to the semi-major axis of the ellipse according to Kepler's third law, which states that the square of the period is proportional to the cube of the semi-major axis of the orbit.
In the final answer, the correct options are B and C.