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Solar System, Kepler & Universal Gravitation. Physics 12. Clip of the day: . Minutephysics http :// www.youtube.com/watch?v=uhS8K4gFu4s. A bit of history about the solar system and orbits……. Ptolemaic System:. tä-lə - ˈ mā-ik 2 nd century AD
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Solar System, Kepler & Universal Gravitation Physics 12
Clip of the day: • Minutephysics • http://www.youtube.com/watch?v=uhS8K4gFu4s
Ptolemaic System: • \tä-lə-ˈmā-ik\ • 2nd century AD • Earth is at the orbital center of all celestial bodies (geocentric) • Very complicated as sun and moon orbited Earth but other planets both orbited the Earth and completed a Epicycle in their orbital path
Copernican System: • koh-pur-ni-kuhn • 1543 • Nicholas Copernicus • Simplified the mathematics as the Sun became the centre of the Solar System • This was rejected by the clergy and is most famous as a result of the persecution of Galileo Galilei for supporting this system
TychonicSystem: • tahy-kon-ik • Late 16th century • Combined what he saw as the mathematical benefits of the Copernican system with the philosophical and "physical" benefits of the Ptolemaic system. • This system never gained widespread acceptance but Tycho Brahe was responsible for contributing a significant amount of detailed information regarding the Solar System
Astronomy as Science: • Before the advent of modern telescopes, Tycho Brahe was able to develop instruments that were precise to 1/30 of a degree without magnification! • As a result, he was able to accurately catalogue over 700 stars was well as detailed information about our Solar System • Astronomy continued to evolve as a science as the ability to machine high quality lenses was refined
Kepler: • Brahe invited Kepler to be one of his assistants in 1600 which gave Kepler access to Brahe’s detailed records • Kepler was able to develop three empirical relationships to describe heavenly bodies, know today as Kelper’s Laws!
1stLaw: Planets move in elliptical orbits with the Sun at one Focus
Vocab Alert: • Aphelion: the point in the orbit of a planet, asteroid, or comet at which it is furthest from the sun • Perihelion: the point in the orbit of a planet, asteroid, or comet at which it is closest to the sun • Apogee: the point in the orbit of the moon or a satellite at which it is furthest from the earth • Perigee: the point in the orbit of the moon or a satellite at which it is nearest to the earth.
2ndLaw: A Planet will sweep out an equal area in equal time intervals
3rdLaw: The ratio of the radius cubed to the period squared will be the same for any two objects orbiting the same object Period = time to complete one orbit
Kepler, Halley and Newton: • When Kepler published his equations, they were not based on an understanding of why the universe behaved in this manner, rather it simply described how it behaved • Sir Edmond Halley had described a relationship between gravity and the square of the distance between objects but couldn’t make it predict orbits • He approached Newton about how to apply this concept……..
Newton’s Law of Universal Gravitation: • Newton immediately answered Halley with the fact that orbits must be elliptical • Despite the fact that this answer was purely intuitive, it led to an article called De Motu(on motion) • Newton later expanded this into one of the most famous works in scientific literature, PhilosophiaeNaturalis Principia Mathematica
Newton’s Law of Universal Gravitation: • Fg is the gravitational force • G is the Universal Gravitational Constant • m1 and m2 are the masses of the objects • r is the distance between the objects • Note, Newton did not measure G but it is now known to be • 6.67x10-11Nm2/kg2
Try it: • Page 580 • Question 1-7 • Kelper’s Law Graphing Assignment
