21. Which of Kepler's laws states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the sun?
A) Kepler's First Law
B) Kepler's Second Law
C) Kepler's Third Law
D) None of the above
C) Kepler's Third Law
The correct answer is C) Kepler's Third Law.
The answer is C) Kepler's Third Law.
To understand why, let's break down the key components of Kepler's Third Law. This law is also known as the law of harmonies.
1. Orbital period: The time it takes for a planet to complete one full orbit around the sun.
2. Average distance from the sun: The average distance between the planet and the sun, also known as the planet's semi-major axis.
Kepler's Third Law states that the square of the planet's orbital period is directly proportional to the cube of its average distance from the sun. Mathematically, it can be expressed as:
(T1^2) / (T2^2) = (r1^3) / (r2^3)
Where T1 and T2 are the orbital periods of two planets, and r1 and r2 are their average distances from the sun.
To find the answer to this question, we need to identify which of Kepler's laws states the relationship mentioned above. Let's review the other options:
A) Kepler's First Law: Also known as the law of orbits or the law of ellipses, this law states that the path of each planet around the sun is an ellipse, with the sun at one of the foci of the ellipse.
B) Kepler's Second Law: Also known as the law of equal areas, this law states that the line that connects a planet to the sun will sweep out equal areas in equal times.
Given that neither of these laws directly addresses the relationship between the orbital period and the average distance from the sun, we can eliminate options A and B.
Therefore, the correct answer is C) Kepler's Third Law, as it precisely describes the relationship mentioned in the question.