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# 14.17: Kepler's Third Law of Planetary Motion

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### 14.17: Kepler's Third Law of Planetary Motion

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. In 1909, he formulated his first two laws based on the observations of his forebears, Nikolaus Copernicus and Tycho Brahe. However, in 1918, he published his third law of planetary motion, which gives a precise mathematical relationship between a planet's average distance from the Sun and the amount of time it takes to revolve around the Sun. It states that

The proportionality constant for this law was derived much later, after Newton established the universal law of gravitation. However, Kepler formatted this third law of planetary motion based on the observation of Galilean moons orbiting Jupiter.

This law established the ratios of the average distances of each planet from the Sun, to the Earth's average distance from the Sun, as shown in Table 1.

Table 1: Ratio of Planetary Distances from the Sun Compared to the Earth-Sun Distance.

 Material Planetary Distance Ratio Mercury 0.387 Venus 0.723 Earth 1.000 Mars 1.520 Jupiter 5.200 Saturn 9.570 Uranus 19.170 Neptune 30.180

The actual value for the distance of the Earth from the Sun was calculated for the first time during a transit of Venus using the parallax method. Using this value of the astronomical unit, the actual distances to all other planets were obtained. This law is very useful to estimate the distances of all the satellites around the Jovian planets, just by observing their time periods.

This text is adapted from Openstax, University Physics Volume 1, Section 13.5 Kepler’s Laws of Motion.

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Kepler's Third Law Planetary Motion Johannes Kepler Solar System Mathematical Relationship Average Distance From The Sun Time To Revolve Proportionality Constant Universal Law Of Gravitation Galilean Moons Ratios Of Planetary Distances Table 1 Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Earth-Sun Distance Parallax Method Astronomical Unit Satellite Distances

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