Question

The line that joins any planet to the sun sweeps out equal areas in equal intervals of time. This statement is

• A. Kepler's first law
• B. law of periods
• C. law of gravitation
• D. Kepler's second law
• E. Newtons third law

Hint:

Kepler's second law is a consequence of the conservation of angular momentum.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question asks to identify a fundamental law of planetary motion based on its statement. The statement describes the relationship between the area swept by a planet's position vector and time.
Step 2: Detailed Explanation:
Let's review Kepler's three laws of planetary motion:
Kepler's First Law (Law of Orbits): Every planet moves in an elliptical orbit with the Sun situated at one of the two foci of the ellipse. This describes the shape of the orbit.
Kepler's Second Law (Law of Areas): The radius vector drawn from the Sun to a planet sweeps out equal areas in equal intervals of time. This means the areal velocity (\(\frac{dA}{dt}\)) of a planet is constant. This law is a consequence of the conservation of angular momentum. It implies that a planet moves faster when it is closer to the Sun (perihelion) and slower when it is farther away (aphelion).
Kepler's Third Law (Law of Periods): The square of the orbital period (\(T\)) of a planet is directly proportional to the cube of the semi-major axis (\(a\)) of its orbit. Mathematically, \(T^2 \propto a^3\).
The statement given in the question, "The line that joins any planet to the sun sweeps out equal areas in equal intervals of time," is the exact definition of Kepler's second law.
Step 3: Final Answer:
The statement is Kepler's second law. This corresponds to option (D).