Nicolas CopernicusIn the 16th century, a Polish astronomer called Nicolas Copernicus putforward the idea that the Earth and the planets rotate around the Sun asthis explained the apparently complex movement of planets in the night skyin a simple way. Previously, it was held that everything rotated around theEarth and that meant that planets sometimes moved backwards! Copernicusthought the orbits were circles and his ideas caused a lot of controversy.

Kepler and the Elliptical OrbitsIn the early-17th century, Johannes Kepler (1571 – 1630) produced asimple and precise description of planetary motion. He realized thatthe orbits of the planets were not the circles demanded by Aristotle( 384 – 322 BC) and assumed implicitly by Copernicus ( 1473 – 1543),but were instead the “flattened circles” that geometres call ellipse.

The Laws of Planetary MotionHe used the observational records of Danish astronomer Tycho Brahe(1546 – 1601) to produce a complete mathematical description of themotion of planet as it moves around the Sun. The description alsoapplies to a satellite as it moves around a planet. He created the ThreeLaws of Planetary Motion that govern the motion of each object.

Kepler’s First LawThe orbits of the planets are ellipses, with the Sun at one focus ofthe ellipse.The Sun is not at the center of the Sunellipse, but is instead at one focus. Theplanet then follows the ellipse in itsorbit, which means that the Earth-Sundistance is constantly changing as theplanet goes around its orbit.Focus 1 Focus 2 Orbiting Planet

EllipseAn ellipse is a special curve in which the sum of the distances from everypoint on the curve to two other points known as the foci is a constant. Thecloser together that these points are, the more closely that the ellipseresembles the shape of a circle. In fact, a circle is the special case of anellipse in which the two foci are at the same location. SunFocus 1 Focus 2 Orbiting Planet

Properties of an ellipseAn ellipse has two focuses (foci) F1 and F2. The semi-major axis isthe distance from the centre (halfway between the foci) and thewidest part of the ellipse. The semi-minor axis goes between thecentre and the narrowest part. Semi-minor Axis F1 F2 Semi-major Axis

The eccentricity of an ellipse is how long and narrow it is. Thefurther the foci are from each other, the more eccentric it is.

Kepler’s Second LawThe line joining the planet to the Sun sweeps out equal areas inequal times as the planet travels around the ellipse.The line joining Sun and Sun Areplanet sweeps out equal a2areas in equal times so the Orbiting Planetplanet moves faster when Areait is nearer the Sun. The 1point of nearest approachof the planet to the Sun iscalled perihelion; the pointof greatest separation iscalled aphelion. By Kepler’ssecond law, the planetmoves fastest when it isnear perihelion and slowestwhen it is near aphelion.

Kepler’s Third LawThe square of the orbital period of a planet is directly proportionalto the cube of the semi-major axis of its orbit. T2 = kR3where T is the orbital period of the planet, R is Semi-major Axis and kis a costant.Kepler’s laws also apply to any system of satellites, for example themoons of Jupiter as well as to comets and asteroids in orbit around theSun.For the special case of planets in orbit around our own Sun, a simplerversion of Kepler’s third law can be used. All the planetary orbits canbe scaled with respect to the Earth, which takes 1 year to travelaround the Sun in an orbit at a mean distance of 1 astronomical unit(AU).Using Kepler’s third law: 12 = k x 13So in this case k = 1If all the other planetary orbits are set out in years and astronomicalunits, then their orbits can be scaled with respect to the Earth, just bymeasuring how long it takes them to travel around the Sun.

Kepler’s Third Law implies that the period for a planet to orbit the Sunincreases rapidly with the radius of its orbit. Thus, we find thatMercury, the innermost planet, takes only 88 days to orbit the Sun butthe outermost planet (Pluto) requires 248 years to do the same.Sun Semi- major Axis R One complete orbit of the Sun in Time T

The planet move around the Sun. This motion is called revolution.

Each of the planets also spin around its own axis, which is calledrotation.

# Kepler's Law

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**Description: ** How planets move around the sun

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