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# Lab 7 - Kepler’s Laws Laboratory 7 Objective In this...

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Unformatted text preview: Kepler’s Laws Laboratory 7 Objective: In this laboratory Johannes Kepler’s Laws of Planetary Motion will be studied with emphasis on his third law. The signiﬁcance of Kepler’s third law will be understood by graphing its relations. Background: Explaining the motion of the planets became a pursuit of many early scientists. Nicholas Copernicus, in 1543 proposed a theory that the solar system was heliocentric. ln other words, the planets orbit the central Sun in circular orbits. This was a profound statement during his time since the accepted theory of the solar system was that it was geocentric, everything revolved around the Earth, including the Sun. Later Johannes Kepler in 1609 proposed the three laws of planetary motion, using the detailed observations of Tycho Brahe. Kepler’s motivation was to find a simple explanation of how the planets orbited the Sun, as Copernicus thoaght, but soon discovered that the simplicity of circular orbits was not correct. Instead he found that the planets orbit the Sun in elliptical orbits. This was a small change that led to an abundance of information about how planets orbit the Sun. In 1687 Isaac Newton published the Principia in which he explained Kepler’s laws this time including using the force of gravity. The law of gravity states that the gravitational force between two celestial bodies is proportional to the product of the two masses and inversely proportional to the square of the distance between them. If the distance between two celestial bodies is doubled, the gravitational attraction between them is reduced by 1/4. If you triple the distance the force of gravity between the two celestial bodies drops to 1/9. Kepler’s Laws of Planetary Motion 1. Kepler’s 1St Law states that the orbit of a planet around the Sun is an ellipse, with the Sun’s center of mass at one feel. The eccentricity, e, of an ellipse can be determined by the following relationship: Where c is the distance between the two foci a is the Semi-Major Axis. The eccentricity is how ‘squashed’ the ellipse is compared to a circle. Notice that if c = 0, the two foci are at the same point and we have a circle. The Semi-Major Axis and the eccentricity is all that is needed to describe the size of a planet’s orbital path as well as its shape. 57 ...
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