Johannes Kepler’s “Three Laws of Planetary Motion”

Johannes Kepler was a mathematician, astronomer and teacher, born in Germany in 1571. He studied under Tycho Brahe and expanded upon his knowledge to calculate planets orbits around the Sun. His works contributed to the heliocentric model that stated that the planets orbited around the Sun and not the Earth.

The difference between the Ptolemaic system (Earth as the center) and the heliocentric system can be seen here.

Kepler’s theories became proven fact and subsequently became physical laws, although there are now more precise laws that govern the actions of the planets’ orbit around the sun.

Kepler’s first law states that each planet moves in an elliptical orbit, with the sun located at the center.

Ke;[er's 1st Law

Kepler’s second law, known as the Law of Equal Areas states that the (triangular ) area between where the sun and the planets over a given time are always equal, despite the fact that the planets move faster when further away from the sun and travel slower when nearer to the sun. Consequently, the the triangular  area increases and decreases as the planets distances change.

For example, the image below depicts a planet revolving around the Sun. As the planet moves away from the sun, it picks up speed. If we draw a triangle where one point is time A and the other point is time B, then the area is equal to the same area for the triangle that represents time points C and D.

How can this be? It is because the lines that make up the area between A and B stretches out a longer distance, but the planet is moving slower over a shorter distance on the elipse. When the planet moves faster, such as the area between C and D, the distance is shorter, but the distance the planet moves along the elipse is longer. Thus we have a faster speed at a greater distance and a slower speed at a shorter distance, which equals the same amount of area.

The wider area is known as the Perihelion and the smaller area is known as the Aphelion.

Kepler’s  second law is illustrated in this animation.

Kelper's Second Law

Kepler’s third law states that the square of the orbital (time) period of any planet is equal to the cube of the distance (radios, called semimajor axis) from the planet from the sun.

Another way of stating this is that the square of the (time) period of a planet’s orbit is proportional to the cube of that planet’s semi-major axis, or t^2 X d^3.

T (planet) ^2 d (planet) ^3
_____________ = ___________

T (earth) ^2 d (earth) ^3

Kepler’s heliocentric calculations let to Isaac Newton’s theory of universal gravitation.

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