Lecture 6: Newton & Kepler. Tycho Brahe ( ) Johannes Kepler

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1 Lecture 6: Newton & Kepler Johannes Kepler (1600) was employed by Tycho to develop a mathematical theory to explain the observations made by Tycho Kepler was a pure theorist; Tycho a pure observer Issac Newton (1642) explained the natural origin of Kepler s laws in terms of a physical model that incorporated his laws of motion and of gravitation Tycho Brahe ( ) Tycho s observations were accurate to about 1 (one arc-minute) The observations were made without a telescope long sighting rods and protractors were used Johannes Kepler Kepler ( ) initially believed that the planetary orbits were related to the perfect geometry of nested solids 1

2 The nested solids idea did not agree very well with the data Later (1600) Kepler was employed by Tycho to develop a mathematical theory to explain the observations made by Tycho Kepler was a pure theorist; Tycho a pure observer In 1601 Tycho dies and Kepler replaced him as Imperial Mathematician At first, Kepler tried circular orbits, with the Sun at the center Johannes Kepler Johannes Kepler He used triangulation to determine the shapes of the orbits This required determination of Earth s orbit too! Later he realized that the orbits were elliptical, with the Sun at one focus of the ellipse: Kepler s Laws First Law (1609): The planetary orbits are elliptical, with the Sun at one focus 2

3 Kepler s Laws Second Law (1609): A imaginary line connecting the Sun to any planet sweeps out equal areas in equal times Kepler s Laws Animation Kepler s Laws Third Law (1619): The square of a planet s orbital period is proportional to the cube of its semi-major axis The orbital period is the time it takes to complete one orbit semi-major axis a 3

4 Kepler s Laws Third Law (1619): The square of a planet s orbital period is proportional to the cube of its semi-major axis 2 3 P a = years A.U. The orbital period P is the time it takes to complete one orbit The semi-major axis a is half the distance across the long dimension of the ellipse One A.U. (astronomical unit) is the distance form the Earth to the Sun = 1.5 x 10 8 km Example: Orbit of Venus Kepler s third law relates the semi-major axis a to the orbital period P 2 P years Solving for the period P yields 3 a = AU P a = years AU 3/ 2 Since a = 0.72 AU for Venus, we obtain P = Earth years or P = 225 Earth days Kepler s Laws Kepler was the first person to explain the planetary motions without any epicycles Kepler s laws are empirical why do they work?? This was the major question facing astronomy in the 17 th century Astronomers wanted a physical explanation 4

5 Isaac Newton ( ) Isaac Newton Isaac Newton ( ) was born in the year Galileo died He discovered the Law of Gravitation in 1665 He developed the Laws of Mechanics that govern all motions In order to solve the resulting mathematical problem to determine the motions of real objects, he invented calculus in 1665 Newton s laws explain the elliptical orbits deduced by Kepler! 5

6 Isaac Newton In 1670 he passed white light through a prism and observed the rainbow of colors, establishing that white light is not a single entity Isaac Newton Recognition of the problem of chromatic aberration in telescopes with lenses led Newton to design a reflecting telescope in 1672 Newton s Laws of Motion (1666) First Law: Every body continues in a state of rest or uniform motion unless acted on by an outside force 6

7 Newton s First Law of Motion Newton s Laws of Motion (1666) Second Law: When a force F is applied to a mass M, the resulting acceleration A is related to F by A = F M F = M A A is directly proportional to F (for fixed M ) A is inversely proportional to M (for fixed F ) Newton s Laws of Motion (1666) Third Law: To every action, there is an equal and opposite reaction 7

8 Newton s Law of Gravitation (1687) Universal Gravitation: Every particle in the universe attracts every other particle with a force that is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them Here, G is the universal gravitational constant, M 1 and M 2 are the two masses, and R is the distance between them Newton s Law of Gravitation 8

9 9

10 Newton s Laws Newton s three laws of motion combined with his law of universal gravitation form the basis for the study of mechanics These laws can be used together to derive all of Kepler s laws from basic physical principles! This yields a deeper, more satisfying explanation for the patterns of motion of the planets Questions remained: where does gravity come from? This was answered by Albert Einstein in 1915 Gravity is really due to the curvature of space-time Triumph of Scientific Method Science is a human endeavor, subject to the whims of culture, personality, religion, etc. The Scientific Method always guides us towards an objective description of our world Sometimes it takes hundreds of years to make progress!! Chapter 3: Radiation In order to understand the universe, we must be able to decode the information contained in the light we receive from celestial sources The light takes time to reach us: Moon: t=1 second Sun: t=8 minutes Jupiter: t=40 minutes Stars: t=years Galaxies: t=10 6 years Beginning of universe: t=10 10 years Hence telescopes are time machines 10

11 Radiation In one second, light travels a distance of 300,000 km or 186,000 miles One light-year is the distance light travels in one year, or 5.9 x miles (9.5 x km) The Andromeda Galaxy is about 2,000,000=2 x 10 6 light-years from Earth! Radiation The information contained in the light we receive is unaffected by distance The information remains intact so long as the light doesn t run into something along the way Since the Earth is not special (according to the Copernican hypothesis), we hypothesize that the physical laws we observe on Earth operate in the same way everywhere Radiation Even from such an enormous distance, the light from the Andromeda galaxy tells us about the stars there The color of the light is related to the temperature of the stars emitting it 11

12 Radiation As an object gets hotter, its color goes from red->yellow->blue->white As an object gets hotter, the radiation it emits becomes brighter Color and Temperature EM Spectrum Animation Wave Nature of Radiation Visible light is part of the electromagnetic radiation spectrum Why electromagnetic? Because the radiation contains oscillating electric and magnetic fields 12

13 Electromagnetic Radiation Radiation It s interesting to compare light waves with water waves If you drop a pebble in a pond, it produces rippling waves We can measure the height of the water at a fixed location as a function of time: 13

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