State keplers law of planetary motion
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http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion
Kepler's laws of planetary motion are a set of three laws describing the motion of planets around the Sun. Here is the first law:
1. Kepler's First Law, also known as the law of orbits, states that the planets orbit the Sun in elliptical paths with the Sun at one of the two foci of the ellipse. In simpler terms, the orbit of a planet is an ellipse with the Sun at one of the two foci.
An ellipse is a closed curve with two points inside it called the foci (plural of focus). In the case of planetary orbits, one of the foci is occupied by the Sun. The path of the planet along the ellipse is such that the straight line connecting the planet to the Sun sweeps out equal areas in equal intervals of time.
It is important to note that the orbits are not perfect circles but have some degree of eccentricity, meaning they are slightly elongated. This law disproved the commonly believed notion at the time that the planets moved in perfectly circular orbits.
Johannes Kepler's laws of planetary motion are three fundamental principles that describe the motion of planets in our solar system.
Kepler's First Law, often referred to as the "Law of Ellipses," states that planets move in elliptical orbits around the Sun. An ellipse is an elongated circle with two foci (plural of focus). In this case, the Sun is located at one of the foci of the elliptical orbit.
Kepler's Second Law, known as the "Law of Equal Areas," states that a line segment that connects a planet to the Sun sweeps out equal areas in equal time intervals. This means that as a planet moves along its elliptical orbit, it travels faster when it is closer to the Sun and slower when it is farther away.
Kepler's Third Law, often referred to as the "Harmonic Law," relates the orbital period of a planet to its average distance from the Sun. It states that the square of the orbital period (the time it takes for a planet to complete one orbit around the Sun) is directly proportional to the cube of the average distance between the planet and the Sun.
To mathematically derive Kepler's laws, Johannes Kepler extensively analyzed astronomical data collected by his predecessor Tycho Brahe. Kepler used observations of the planets' positions over time to develop his laws. Nowadays, these laws can be derived using concepts from classical mechanics and calculus.
To specifically state Kepler's laws of planetary motion:
1. Planets move in elliptical orbits with the Sun at one of the foci.
2. A planet sweeps out equal areas in equal time intervals as it orbits the Sun.
3. The square of a planet's orbital period is directly proportional to the cube of its average distance from the Sun.