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From Aristotle to Newton The history of the Solar System (and the universe to some extent) from ancient Greek times through to the beginnings of modern physics. Kepler (1571-1630) Used Tycho Brahe's precise data on apparent planet motions and relative distances. Deduced three laws of planetary motion. Kepler's First Law The orbits of the planets are elliptical (not circular) with the Sun at one focus of the ellipse. Ellipses distance between foci eccentricity = major axis length (flatness of ellipse) Kepler's Second Law A line connecting the Sun and a planet sweeps out equal areas in equal times. slower Translation: planets move faster when closer to the Sun. faster Kepler's Third Law The square of a planet's orbital period is proportional to the cube of its semi-major axis. P2 is proportional to or P2 a3 (for circular orbits, a=b=radius). Translation: the larger a planet's orbit, the longer the period. a3 a b Solar System Orbits Kepler's Third Law The square of a planet's orbital period is proportional to the cube of its semi-major axis. If P measured in Earth years, and a in AU, P2 = a3 (for circular orbits, a=radius). Translation: the larger a planet's orbit, the longer the period. At this time, actual distances of planets from Sun were unknown, but were later measured. One technique is “parallax”. “Earth-baseline parallax” uses telescopes on either side of Earth to measure planet distances. Orbits of some planets (or dwarf planets): Planet a (AU) Venus Earth Pluto 0.723 1.0 39.53 P (Earth years) 0.615 1.0 248.6 Clicker Question: A flaw in Copernicus’s model for the solar system was: A: It didn’t explain retrograde motion. B: He used circular orbits. C: The Earth was still at the center. D: He used the same mass for all the planets. E: All of the above Copernican model was a triumph of the Scientific Method Scientific Method: a) b) c) d) e) Make high quality observations of some natural phenomenon Come up with a theory that explains the observations Use the theory to predict future behavior Make further observations to test the theory Refine the theory, or if it no longer works, make a new one - Occam’s Razor: Simpler Theories are better -You can prove a theory WRONG but not RIGHT Prediction Observation Theory Characteristics of Scientific Theories Scientific Theories: a) Must be testable b) Along with their consequences, must be continually tested c) Should be simple (Occam’s Razor) and no more complex than necessary d) Should be elegant - simple and able to explain what were thought to be different phenomenon - An unproven idea or theory is a hypothesis -You can prove a theory WRONG but not RIGHT Newton (1642-1727) Kepler's laws were basically playing with mathematical shapes and equations and seeing what worked. Newton's work based on experiments of how objects interact. His three laws of motion and law of gravity described how all objects interact with each other. Newton's Zeroeth Law of Motion Objects are dumb. They do not know the past and they are not good predictors of the future. They only know what forces act on them right now. Newton's Zeroeth Law of Motion DEMO - Pushing the cart on track Newton's First Law of Motion Every object continues in a state of rest or a state of motion with a constant speed in a straight line unless acted on by a force. Newton's First Law of Motion DEMO - Air Puck motion DEMO - Smash the HAND DEMO - Tablecloth Newton's Second Law of Motion When a force, F, acts on an object with a mass, m, it produces an acceleration, a, equal to the force divided by the mass. Fnet a= m acceleration is a change in speed or a change in direction of speed. Newton's Second Law of Motion Demo - Force and Acceleration with fan carts Newton's Third Law of Motion To every action there is an equal and opposite reaction. Or, when one object exerts a force on a second object, the second exerts an equal and opposite force on first. Newton's Third Law of Motion DEMO: CART Clicker Question: Why didn’t my hand get crushed by the hammer? A: My bones are actually stronger than steel. B: The plate has a lot of inertia C: The plate is very strong D: The force of gravity kept the plate from moving Gravitational Force on a Planet For an object of mass m at or near the surface of a planet the force of their gravitational attraction is given by: F = mg F is the gravitational force. g is the planetary "gravitational constant". Your "weight" is just the gravitational force between the Earth and you. Newton's Law of Gravity For two objects of mass m1 and m2, separated by a distance R, the force of their gravitational attraction is given by: F= G m1 m2 R2 F is the gravitational force. G is the universal "gravitational constant". An example of an "inverse-square law". Your "weight" is just the gravitational force between the Earth and you. Clicker Question: Suppose Matt weighs 120 lbs on his bathroom scale on Earth, how much will his scale read if he standing on a platform 6400 km high (1 Earth radius above sea-level)? A: 12 lbs B: 30 lbs C: 60 lbs D: 120 lbs E: 240 lbs Newton's Correction to Kepler's First Law The orbit of a planet around the Sun has the common center of mass (instead of the Sun) at one focus. Escape Velocity Velocity needed to completely escape the gravity of a planet. The stronger the gravity, the higher the escape velocity. Examples: Earth Jupiter Deimos (moon of Mars) 11.2 km/s 60 km/s 7 m/s = 15 miles/hour Timelines of the Big Names Galileo Copernicus 1473-1543 1564-1642 Brahe 1546-1601 Kepler 1571-1630 Newton 1642-1727 Electromagnetic Radiation (How we get most of our information about the cosmos) Examples of electromagnetic radiation: Light Infrared Ultraviolet Microwaves AM radio FM radio TV signals Cell phone signals X-rays Radiation travels as waves. Waves carry information and energy. Properties of a wave wavelength (l) crest amplitude (A) trough velocity (v) l is a distance, so its units are m, cm, or mm, etc. Also, v = l n Period (T): time between crest (or trough) passages Frequency (n): rate of passage of crests (or troughs), n = (units: Hertz or cycles/sec) 1 T = hn Waves Demo: making waves - wave table Demo: slinky waves Radiation travels as Electromagnetic waves. That is, waves of electric and magnetic fields traveling together. Examples of objects with magnetic fields: a magnet the Earth Clusters of galaxies Examples of objects with electric fields: Power lines, electric motors, … Protons (+) "charged" particles that make up atoms. Electrons (-) } Scottish physicist James Clerk Maxwell showed in 1865 that waves of electric and magnetic fields travel together => traveling “electromagnetic” waves. The speed of all electromagnetic waves is the speed of light. c = 3 x 10 8 m / s or c = 3 x 10 10 cm / s or c = 3 x 10 5 km / s light takes 8 minutes Earth Sun c= ln or, bigger l means smaller n The Electromagnetic Spectrum 1 nm = 10 -9 m , 1 Angstrom = 10 -10 m c= ln A Spectrum Demo: white light and a prism Refraction of light All waves bend when they pass through materials of different densities. When you bend light, bending angle depends on wavelength, or color. Clicker Question: Compared to ultraviolet radiation, infrared radiation has greater: A: energy B: amplitude C: frequency D: wavelength Clicker Question: The energy of a photon is proportional to its: A: period B: amplitude C: frequency D: wavelength Clicker Question: A star much colder than the sun would appear: A: red B: yellow C: blue D: smaller E: larger Rainbows rred orange yellow green blue violet What's happening in the cloud? raindrop 42o 40o Double Rainbows