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May
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May
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Apr
(Source: dastardlypsychoticprankster)
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Apr
Laws of Planetary Motion a little history
In astronomy, Kepler’s laws give a description of the motion of planets around the Sun. Kepler’s laws are:
• The orbit of every planet is an ellipse with the Sun at one of the two foci.
• A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
• The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
Johannes Kepler published his first two laws in 1609, having found them by analyzing the astronomical observations of Tycho Brahe. Kepler discovered his third law many years later, and it was published in 1619. At the time, Kepler’s laws were radical claims; the prevailing belief, particularly in epicycle-based theories, was that orbits should be based on perfect circles. Most of the planetary orbits can be rather closely approximated as circles, so it is not immediately evident that the orbits are ellipses. Detailed calculations for the orbit of the planet Mars first indicated to Kepler its elliptical shape, and he inferred that other heavenly bodies, including those farther away from the Sun, have elliptical orbits too. Kepler’s laws and his analysis of the observations on which they were based, the assertion that the Earth orbited the Sun, proof that the planets’ speeds varied, and use of elliptical orbits rather than circular orbits with epicycles — challenged the long-accepted geocentric models of Aristotle and Ptolemy, and generally supported the heliocentric theory of Nicolaus Copernicus, although Kepler’s ellipses likewise did away with Copernicus’s circular orbits and epicycles.
Some eight decades later, Isaac Newton proved that relationships like Kepler’s would apply exactly under certain ideal conditions that are to a good approximation fulfilled in the solar system, as consequences of Newton’s own laws of motion and law of universal gravitation. Because of the nonzero planetary masses and resulting perturbations, Kepler’s laws apply only approximately and not exactly to the motions in the solar system. Voltaire’s Eléments de la philosophie de Newton — Elements of Newton’s Philosophy was in 1738 the first publication to call Kepler’s Laws “laws”. Together with Newton’s mathematical theories, they are part of the foundation of modern astronomy and physics.http://goo.gl/hl48D
Image animated gif of Kepler’s second law: Antonio González Fernández
Glen Van Brummelen’s site gives a set of computer animations for the Almagest geometric models of planetary motion. On this site there is a very brief introduction to the models and an equally brief user’s guide. He’s also added a section for a more detailed and background :Six Easy Lectures on Ancient Mathematical Astronomy.
Ancient Planetary Model Animations:http://people.sc.fsu.edu/~dduke/models
One of the last interactive models is of Isaac Newton’s approach to Kepler’s area law, also linked to a short explanation.
04
Feb
i made the same bet with my dad, his dad my grandpa died from cancer of the lung when i was really little i never really got to meet him, i don’t want it to be like that with my kids please help.
02
Feb
(Source: fuckyeah1990s)
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