Kepler’s Laws of Planetary Motion Johannes Kepler (1571-1630)

Kepler's firmly believed in the work of his predecessors. Aristotle & Copernicus – Orbits of the planets are round Tycho Brahe – mistrusted Kepler – was afraid of his intelligence Brahe gave Kepler the orbit of Mars to study and define. It was the most difficult one.

Kepler’s First Law (The Law of Ellipses) I. The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.

Kepler’s Second Law (The Law of Equal Areas) II. The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse.

Kepler’s Second Law (The Law of Equal Areas) Because a planet moves fastest when it is close to the sun, and slowest when far from the sun, equal areas are swept out in equal amounts of time.

Kepler’s Third Law (The Law of Harmonies) III. The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semi major axes: As a planet’s distance from the sun increases, the time it takes to make one complete revolution also increases

Newton’s Universal Law of Gravitation The gravitational force between two bodies is proportional to their masses and inversely proportional to the square of the distance between them.

Newton’s Universal Law of Gravitation The gravitational forces that exist between the sun and the planets are greatest for planets that are massive and are located near the sun.

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Nutation Small wobble in angle of Earth’s tilt Nutation Small wobble in angle of Earth’s tilt. The Earth’s tilt changes ½° over an 18 year period due to the moon’s gravitational pull.

Precession Slow wobble of the Earth’s axis caused mainly by the gravitational pull of the sun, moon and other planets (spinning top). Precession is a gradual drift relative to the equinoxes.

Barycenter The point between two objects where they balance each other Barycenter The point between two objects where they balance each other. The center of gravity of the Earth and Moon as they orbit each other. The Sun is not stationary. It moves as the planets tug on it, causing it to orbit the solar system’s barycenter.