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We want to investigate whether the law of harmonies holds for a selection of planets (Mercury, Venus, Earth, and Mars), and for the Halley's comet that revolves around the Sun.

We want to investigate whether the law of harmonies holds for a selection of planets (Mercury, Venus, Earth, and Mars), and for the Halley's comet that revolves around the Sun.

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Kepler's laws of planetary motion published in 1609, are three scientific laws describing the motion of planets around the Sun. Actually the usefulness of Kepler's laws extends to the motions of all natural and artificial satellites, as well as to stellar systems and exoplanets. The third law summarizes the relation between the period of an orbiting body and its average distance to the body it orbits. The ratio of the square of an object's orbital period T with the cube of the average distance R is the same for all orbiting objects. Case 1: Kepler's Third Law relates the period T of a planet, which is the time spent for one revolution around the Sun, to the average distance R to the sun. The units for both quantities are taken from the earth's orbit: period is measured in years, which is the time taken for the earth to complete one of its orbits, and distance is taken in astronomical units (au), which is the average distance from the earth to the sun. So for the earth T=1 and R=1 by definition. Here is a table of periods and average distances for some planets, and other famous celestial bodies in the solar system such as Halley's comet: Planet Period (yr) Average Distance (au) 1 Mercury 0.241 0.39 Venus 0.615 0.72 3 Earth 1.00 1.00 4 Mars 1.88 1.52 Halley's comet 75.3 17.55 It is worth noticing that the distance from Earth to the sun is one a.u. equivalent to about 150 million km, and time taken for Earth to complete one of its orbits is 1 year, which is equivalent to 365 days. We want to investigate whether the law of harmonies holds for a selection of planets (Mercury, Venus, Earth, and Mars), and for the Halley's comet that revolves around the Sun.
Transcribed Image Text:Kepler's laws of planetary motion published in 1609, are three scientific laws describing the motion of planets around the Sun. Actually the usefulness of Kepler's laws extends to the motions of all natural and artificial satellites, as well as to stellar systems and exoplanets. The third law summarizes the relation between the period of an orbiting body and its average distance to the body it orbits. The ratio of the square of an object's orbital period T with the cube of the average distance R is the same for all orbiting objects. Case 1: Kepler's Third Law relates the period T of a planet, which is the time spent for one revolution around the Sun, to the average distance R to the sun. The units for both quantities are taken from the earth's orbit: period is measured in years, which is the time taken for the earth to complete one of its orbits, and distance is taken in astronomical units (au), which is the average distance from the earth to the sun. So for the earth T=1 and R=1 by definition. Here is a table of periods and average distances for some planets, and other famous celestial bodies in the solar system such as Halley's comet: Planet Period (yr) Average Distance (au) 1 Mercury 0.241 0.39 Venus 0.615 0.72 3 Earth 1.00 1.00 4 Mars 1.88 1.52 Halley's comet 75.3 17.55 It is worth noticing that the distance from Earth to the sun is one a.u. equivalent to about 150 million km, and time taken for Earth to complete one of its orbits is 1 year, which is equivalent to 365 days. We want to investigate whether the law of harmonies holds for a selection of planets (Mercury, Venus, Earth, and Mars), and for the Halley's comet that revolves around the Sun.
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