A planet revolving in elliptical orbit has:
A. a constant velocity of revolution.
B. has the least velocity when it is nearest to the sun.
C. its areal velocity is directly proportional to its velocity.
D. areal velocity is inversely proportional to its velocity.
E. to follow a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below:

Let us analyze each statement for a planet revolving in an elliptical orbit.

Statement A says the planet has a constant velocity of revolution. This is false because by Kepler's second law, a planet moves faster when closer to the Sun and slower when farther away.

Statement B says the planet has the least velocity when nearest to the Sun. This is also false; the planet has the greatest velocity at perihelion (nearest point) and the least velocity at aphelion (farthest point).

Statement C says areal velocity is directly proportional to velocity. Areal velocity is $$\frac{dA}{dt} = \frac{1}{2}rv\sin\theta$$, which depends on both $$r$$ and $$\theta$$ in addition to $$v$$. Since areal velocity is constant while the orbital speed varies, areal velocity is not directly proportional to velocity. This is false.

Statement D says areal velocity is inversely proportional to velocity. This is also false because areal velocity is constant, not inversely varying with speed.

Statement E says the planet must follow a trajectory such that the areal velocity is constant. This is exactly Kepler's second law, which states that a line joining the planet and the Sun sweeps out equal areas in equal intervals of time. This is true.

Hence the correct answer is Option 3: E only.