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Phys 181-701 Astronomy Galileo’s Apparatus – Deutches Museum, Munchen, Germany “To command the professors of astronomy to confute their own observations is to enjoin an impossibility, for it is to command them to not see what they do see, and not to understand what they do understand, and to find what they do not discover.” Galileo Galilei – In Science “Numero pondere et mensura Deus omnia condidit.” Sir Isaac Newton – Principia Mathematica “If I have been able to see further, it was only because I stood on the shoulders of giants.” Newton, in a letter to Robert Hooke REVIEW: Kepler Develops Three Laws: •Law of Ellipses •Law of Areas •Harmonic Law P2 k constant a3 We now understand HOW the planets move… but not WHY they move. Review Galileo: The Death of the Earth Centered Universe •Contemporary of Kepler •Demonstrated that all objects are accelerated by gravity by the same amount •Moving objects remain in motion •Built a telescope in 1609* and observed the Sun, Moon, Milky Way, Moons of Jupiter and the phases of Venus. 1564-1642 *Hans Lippershey invented the telescope in 1608 If we assume (incorrectly) that the Tower of Pisa is 20m tall, the ball will take 2s to hit the ground. Even if the ball is thrown horizontally from the tower, the acceleration toward the earth is still 10m/s2. As a result, the ball that is dropped and the ball that is thrown both hit the ground after 2 seconds!!! We will return to this essential idea in a few slides… Sir Isaac Newton Newton’s Laws: 1. All objects at rest shall remain at rest and all objects in motion shall Remain in motion in a straight line, unless compelled by a FORCE to do otherwise. 2. The ACCELERATION of any object is directly proportional to the FORCE applied to it and inversely proportional to its MASS. 3. For every force applied to an object, there is an equal and opposite force applied by the object on the actor. 1642-1727 N e w t o n v . s Newton’s Laws Relative to Galileo’s Experiment: 1. When the ball is dropped it ceases to be at rest. Therefore there must be a force, directed downward, to cause the acceleration. 2. The acceleration will be equal to the force that gravity exerts on the ball divided by the mass of the ball, that is, the acceleration is equal to the force per unit mass. 3. If the Earth exerts a gravitational force on the ball, the ball must exert an equal and opposite force on the Earth!!!! Law of Universal Gravitation Newton knows that the more mass an object has, the greater the force of Gravity on it. FG= m g Where “g” is the special name given to the acceleration that is caused by gravity. 10 m/s2 The inverse square law… Inverse square The Law Example: Example “Weighing” the Earth… A & B have equal masses and therefore equal weights. The rod is balanced. The very small mass is needed to balance the gravitational force of the very large mass. “G” can be calculated! Knowing G and Kepler’s Law’s allows us to calculate the mass of the Earth, Sun and all of the planets moons and asteroids in the solar system Return to Pisa…The earth is not flat… Return to Pisa Curved Earth After one second the projectile has fallen five meters… But the earth has curved away. Question… If the earth is curved such that it “curves away” 5 meters for every 8000 meters traveled, how fast would the projectile need to be going so that, after falling 5 meters, it was still 5 meters above the earth? Q u e s t a3 k P2 8000 m/s!!! •Newton invents calculus Summary •Newton Proves Kepler’s Laws •Universal Gravitation used to determine the mass of the earth •Tides understood •Moon “lock” understood •Satellite motion possible •Solar system travel made possible S u m m Electromagnetic Radiation Chapter 3 (3.3, 3.4, 3.5) Chapter 4 (4.2, 4.4) The frequency is measured in Hertz (Hz) and is the number of waves which pass a given point in one second. Time period of mars NEXT TIME: Two Laws of RADIATION E Phys 181-701 Astronomy Garment of Brightness May the warp be the white light of morning, May the weft be the red light of evening, May the fringes be the falling of the rain, May the border be the standing rainbow. Thus weave for us a garment of brightness. Song of the Sky Loom (Native American Traditional) •Light is a form of Electromagnetic Radiation •Radiation may be described as waves Review •Waves are described by their frequency, wavelength, amplitude and speed. The Interaction of Matter and IntroRadiation Electromagnetic (Light) Understanding This is an Important Tool of Astronomy Light Interacts with matter in several ways… •Reflection •Refraction •Diffraction •Absorption •Emission •Gravitation! Reflection Reflection Light simply scatters off the dust and gas… Reflection Nebulae Refraction Refraction Light bends when moving from one substance to another… r a c t i o n Light bends around obstacles… Diffraction Absorption and Emission Absorption&Emission O b s e r v a Thermal (Blackbody) Radiation Spectra T h e r m a l R 273 Kelvin = 0 ºC Two Laws of Thermal Radiation: Two Law s 1. Stefan-Boltzmann Law: Hotter objects emit more power per unit area. 2. Wien’s Law: Hotter objects emit light that has a higher average energy. Change in Brightness Practical Example Change in Color C a l c u l a t i o Example: Consider a perfect thermal emitter with a temperature of 15000 K. How much power does it emit per unit area? What is the wavelength of maximum intensity? Putting it Together… Putti ng it A n a l y D o p p l e S h i f t e d S Doppler Effect Formula: r F o r m u l a Next Time…… STARS, A Mass of Incandescent Gas E N