Describe in detail what is keplers 3 law of planetary motion?

Question

Answer

Kepler's laws of planetary motion was derived by Johannes Kepler (German) based off his study of another astronomer Tycho Brahe (Danish) in 1609 A.D.

The three laws are –

★ All planets move about the Sun in elliptical orbits, with Sun being one of the foci.

★ A radius vector joining any planet to the sun sweeps out equal areas in equal lengths of time.

★ The squares of the sidereal periods (of revolution) of the planets are directly proportional to the cubes of their mean distances from the Sun.

Answer

Kepler's Third law of planetary motion :It states that 'The square of the time period of revolution of a planet is proportional to the cube of the semi major axis of the ellipse traced out by the planet'.So, if the length of semi major axis traced out by the planet is 'R' then it's time period of revolution, T, is given as,T^2 = kR^3 where k is some constant.

Answer

Kepler's Third Law of Planetary Motion

Kepler's Third Law of Planetary Motion, also known as the Harmonic Law, is one of the three laws formulated by the renowned German astronomer and mathematician Johannes Kepler. This law provides a mathematical relationship between the orbital period and the average distance from the Sun for any planet in our solar system or any other planetary system.

Heading: Statement of Kepler's Third Law

Kepler's Third Law states that the square of the orbital period (T) of a planet is directly proportional to the cube of its average distance (r) from the Sun. Mathematically, it can be expressed as:

T^2 = k * r^3

In this equation, k represents a constant value that is the same for all planets orbiting the Sun.

Heading: Explanation of Kepler's Third Law

Kepler's Third Law can be understood by considering the motion of planets in elliptical orbits around the Sun. According to this law:

1. Orbital Period: The orbital period of a planet refers to the time it takes for the planet to complete one revolution around the Sun. Kepler's Third Law states that the square of this orbital period is proportional to the cube of the average distance of the planet from the Sun.

2. Average Distance: The average distance of a planet from the Sun is the average of its closest distance (perihelion) and farthest distance (aphelion) from the Sun. This average distance is represented by 'r' in the equation.

3. Proportional Relationship: The equation T^2 = k * r^3 shows that the squared orbital period and the cubed average distance are directly proportional to each other. This means that as the average distance of a planet from the Sun increases, its orbital period also increases, and vice versa.

4. Constant of Proportionality: The constant 'k' in the equation signifies the same value for all planets orbiting the Sun. It encapsulates the combined effects of the mass of the Sun and the gravitational constant, ensuring that the relationship holds true for all planets.

Heading: Implications and Significance

Kepler's Third Law is significant because it helps astronomers and scientists understand the behavior of planets within our solar system and beyond. Some key implications of this law include:

1. Planetary Comparisons: By comparing the orbital periods and average distances of different planets, we can determine their relative positions and characteristics. This information aids in studying the structure and dynamics of planetary systems.

2. Predicting Planetary Motion: Kepler's Third Law enables astronomers to predict the orbital periods of planets based on their average distances. This knowledge is crucial for space missions and astronomical observations.

3. Verification of Kepler's Laws: Kepler's Third Law, along with the other two laws, provides a comprehensive framework for understanding the motion of planets. Experimental verification of this law further validates the accuracy and applicability of Kepler's laws.

In conclusion, Kepler's Third Law of Planetary Motion establishes a mathematical relationship between the squared orbital period and the cubed average distance of a planet from the Sun. This law aids in the understanding, prediction, and comparison of planetary motion, contributing to our knowledge of the

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