Chaos in the Solar System
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This is a talk I've give to various astronomical societies about chaos theory and how it affects the Universe
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Fisica
1) Early models of the universe included geocentric models where Earth was the center, and heliocentric models where the Sun was the center. Kepler deduced 3 laws of planetary motion based on observations of Mars's orbit. 2) Newton formulated the law of universal gravitation, explaining that gravity is what keeps the planets in orbit. He determined that the force of gravity follows an inverse square law based on mass and distance between objects. 3) Cavendish later calculated the gravitational constant by measuring the small torque caused by the gravitational attraction between lead balls, allowing calculations of masses like Earth's.
Lesson 1 history of astronomy3
- Ptolemy placed the Earth at the center of the universe, with the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn circling the Earth. This geocentric model held sway for 1400 years.
- Copernicus proposed that the Sun, not the Earth, was the center of the Solar System in his book On the Revolutions of the Heavenly Bodies. This heliocentric model made Copernicus the "father of modern astronomy."
- Kepler formulated his Three Laws of Planetary Motion using Brahe's precise observations. The first law states that the orbits of the planets are ellipses with the Sun at one focus.
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Ptolemy and the Geocentric Model
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- Galileo Galilei was the first to use the telescope astronomically in 1609, observing sunspots on the Sun and features on the Moon like seas. His observations of Jupiter's moons provided evidence that bodies can orbit something other than Earth. His observations of Venus' phases provided evidence that Venus orbits the Sun.
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Galileo Galilei's observations of Venus, Jupiter, and the Moon provided strong evidence supporting Copernicus' heliocentric model of the solar system. Galileo observed phases of Venus similar to Earth's Moon, proving that Venus orbits the Sun. He also discovered four moons orbiting Jupiter, showing that other celestial bodies can orbit something other than Earth.
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- Galileo Galilei was the first to use the telescope astronomically in 1609, observing sunspots on the Sun and features on the Moon like seas. His observations of Jupiter's moons provided evidence that bodies can orbit something other than Earth. His observations of Venus' phases provided evidence that Venus orbits the Sun.
- Kepler developed his three laws of planetary motion based on Brahe's astronomical measurements. His laws improved the Copernican model by showing planets orbit in ellipses rather than perfect circles.
Gravitazione
1) Early models of the universe ranged from geocentric to heliocentric, with Copernicus and Kepler improving on them by establishing orders of planets and describing elliptical orbits.
2) Kepler deduced three laws of planetary motion based on observations of Mars. Newton later explained these laws through his universal law of gravitation.
3) Cavendish calculated the gravitational constant by measuring the tiny torque caused by the gravitational attraction of lead spheres, allowing for calculations of planetary masses and properties.
WEEK 1 MODEL OF THE UNIVERSE.pptx
The document discusses the celestial sphere and coordinate system used in astronomy. It identifies key points on the celestial sphere including the north and south celestial poles, declination, right ascension, the ecliptic, and the vernal equinox. It then discusses the contributions of various ancient Greek astronomers such as Aristarchus, Hipparchus, Ptolemy, Copernicus, Brahe, and Kepler. Key contributions included Aristarchus proposing the heliocentric model of the universe, Hipparchus' astronomical observations and measurements, Ptolemy developing the geocentric Ptolemaic system, Copernicus also proposing the heliocentric model, Brahe's precise observations, and Kepler's formulation of the three laws of planetary
WEEK 1 MODEL OF THE UNIVERSE.pptx
The document discusses the celestial sphere and coordinate system used in astronomy. It identifies key points on the celestial sphere including the north and south celestial poles, declination, right ascension, the ecliptic, and the vernal equinox. It then discusses the contributions of various ancient Greek astronomers such as Aristarchus, Hipparchus, Ptolemy, Copernicus, Brahe, and Kepler. Key contributions included Aristarchus proposing the heliocentric model of the universe, Hipparchus' astronomical observations and measurements, Ptolemy developing the geocentric Ptolemaic system, Copernicus also proposing the heliocentric model, Brahe's precise observations, and Kepler's formulation of the three laws of planetary
Fisica clase universo
- Cosmology is the study of the origin, structure, and future of the universe. The Big Bang Theory proposes that the universe began in an extremely hot and dense state and has been expanding ever since.
- There are three main types of galaxies: spiral, elliptical, and irregular. Spiral galaxies have a disc shape with densely packed stars surrounding a central bulge, while elliptical galaxies have all stars formed at once in an elliptical shape. Irregular galaxies lack a defined shape and have new stars continuously forming from gas and dust.
- Key figures in the development of astronomy include Copernicus, who proposed the heliocentric model of the solar system; Galileo, who made early telescopic observations; Kepler
Astronamy in quran.ppt saleel@hira
1) According to NASA scientist Jim Kasting, there could be dozens of habitable planets surrounding us that we cannot yet see.
2) Seven Earth-sized planets were recently discovered orbiting the star Trappist-1 that may be capable of sustaining liquid water and life.
3) Throughout history, various cultures made structures aligned with astronomical events like solstices, demonstrating early interest in the skies.
AStro20_C_ppt_ch01
This document discusses key concepts about the night sky and Earth's motions:
- It describes how astronomers organize the night sky into constellations to locate objects, and how Earth's rotation causes day/night and its orbit causes the seasons.
- It explains that the moon's orbit creates its phases and lunar/solar eclipses can occur when the sun, earth, and moon are aligned.
- It discusses how Earth's tilted axis and orbit around the sun cause the seasons, and how precession causes the north star to change over thousands of years.
Planetarymotionhistoricalpeopleinastronomy 131204162554-phpapp02
The universe contains billions of galaxies, each with billions of stars. A galaxy is a group of stars held together by gravity, and the main types are spiral, elliptical, and irregular. Stars are formed from the collapse of large clouds of dust and gas, releasing heat and light through nuclear fusion. Our solar system contains 8 planets that orbit the Sun, including Earth. Copernicus first proposed the heliocentric model that planets orbit the Sun, with Kepler developing the laws of planetary motion. Newton later explained that gravity and inertia cause planets to follow elliptical orbits around the Sun.
A. history of astronomy
1. The document discusses the history of astronomy from ancient Greek ideas of a geocentric universe to Copernicus' heliocentric model.
2. Key figures discussed include Ptolemy, who developed the geocentric model that dominated for over 1000 years, and Copernicus, who proposed placing the Sun at the center.
3. Kepler later determined that planets orbit in ellipses rather than circles, establishing his three laws of planetary motion.
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Chaos in the Solar System
- 1. Chaos in the Solar System Edward Gomez Las Cumbres Observatory - Cardiff University
- 2. Chaos in the Solar System Johannes Kepler Solar System runs like clockwork
- 3. Chaos in the Solar System Johannes Kepler Solar System runs like clockwork
- 4. Chaos in the Solar System Sir Isaac Newton Theory of gravity instantly has implications against a clockwork solar system
- 5. Chaos in the Solar System Sir William Herschel Discovers Uranus - 1781 Arguably starts the descent into ‘Chaos’
- 6. Chaos in the Solar System Edward Lorentz Meteorologist Realised that there was a sensitivity to initial conditions in weather simulations
- 7. To save paper he recorded his calculations to 3 dec. places 0.567234 0.567 Butterfly effect Periodic motion Developed ‘Strange Attractor’ model based on 3 variables (+ time)
- 12. Chaos in the Solar System Benoit Mandelbrot 1979 working at IBM invented term ‘fractal’
- 13. Found self similar structure on all scales while looking at cotton prices Divided up graph, always had structure Order matched Cantor set Found in many areas of nature Infinite area in finite space
- 14. Found self similar structure on all scales while looking at cotton prices Divided up graph, always had structure Order matched Cantor set Found in many areas of nature Infinite area in finite space
- 15. Found self similar structure on all scales while looking at cotton prices Divided up graph, always had structure Order matched Cantor set Found in many areas of nature Infinite area in finite space
- 16. Found self similar structure on all scales while looking at cotton prices Divided up graph, always had structure Order matched Cantor set Found in many areas of nature Infinite area in finite space
- 17. Found self similar structure on all scales while looking at cotton prices Divided up graph, always had structure Order matched Cantor set Found in many areas of nature Infinite area in finite space
- 18. Found self similar structure on all scales while looking at cotton prices Divided up graph, always had structure Order matched Cantor set Found in many areas of nature Infinite area in finite space
- 20. Zoom: 10
- 21. Zoom: 100
- 22. Zoom: 1000
- 23. Zoom: 10,000
- 24. Zoom: 100,000
- 25. Zoom: 1,000,000
- 28. Solar System Chaos Asteroid orbit Asteroid rotation Great Red spot Pluto is chaotic Fractal nature of 2df
- 29. 2-body Resonance Kirkwood gaps in distribution of semi-axis only where period is a rational fraction of Jupiter’s period Implies resonance Resonance = Stable orbits (Trojan asteroids 1:1, 3:2) Unstable 3:1, 2:1
- 31. Asteroid rotation Rotation of most Solar System bodies is stable because of tides Hyperion tumbles chaotically First seen to tumble by Voyager 4:3 Resonance Titan Irregular shape
- 32. Asteroid rotation Rotation of most Solar System bodies is stable because of tides Hyperion tumbles chaotically First seen to tumble by Voyager 4:3 Resonance Titan Irregular shape
- 33. Asteroid rotation Rotation of most Solar System bodies is stable because of tides Hyperion tumbles chaotically First seen to tumble by Voyager 4:3 Resonance Titan Irregular shape
- 34. Great Red spot
- 35. 3-body Resonance Chaotic motion in Pluto’s orbit 3:2 Resonance with Neptune Digital Orrery prediction Stable over Myr’s
- 36. Chaos in the Universe