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?
Kepler's third law, also known as the law of harmonies, states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the sun.
The law that states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the sun is Kepler's Third Law.
The law you are referring to is Kepler's third law, also known as the Law of Harmonies. It states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the sun.
To understand how Kepler derived this law, here are the steps:
1. Kepler collected and analyzed extensive observational data on the motion of planets, specifically focusing on the orbital period and the average distance from the sun for each planet.
2. Kepler noticed that there was a relationship between the orbital period and the average distance from the sun for each planet. He observed that as the average distance increased, the orbital period also increased.
3. Kepler then plotted the square of the orbital period versus the cube of the average distance for multiple planets and found that the data points closely followed a straight line.
4. Based on this observation, Kepler formulated his third law, which mathematically expresses the relationship between the square of the orbital period (T) and the cube of the average distance from the sun (r) as T^2 ∝ r^3.
5. It's important to highlight that Kepler's third law describes a proportional relationship, not an exact equality. The proportionality constant in the equation is different for each planet, meaning that the law applies to each planet individually.
In summary, Kepler's third law states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the sun. It was derived through careful observation and analysis of planetary motion data.