Astronomy. = k. Phys We now understand HOW the planets move but not WHY they move. Review. Galileo: The Death of the Earth Centered Universe
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1 Phys 8-70 Astronoy Galileo s Apparatus Deutches Museu, Munchen, Gerany To coand the professors of astronoy to confute their own obserations is to enjoin an ipossibility, for it is to coand the to not see what they do see, and not to understand what they do understand, and to find what they do not discoer. Galileo Galilei In Science EVIEW: Kepler Deelops Three Laws: Law of Ellipses Law of Areas Haronic Law P a = k = constant Nuero pondere et ensura Deus onia condidit. Sir Isaac Newton Principia Matheatica P = k =constant a If I hae been able to see further, it was only because I stood on the shoulders of giants. Newton, in a letter to obert Hooke We now understand HOW the planets oe but not WHY they oe. eiew Galileo: The Death of the Earth Centered Unierse 56-6 Conteporary of Kepler Deonstrated that all objects are accelerated by graity by the sae aount Moing objects reain in otion Built a telescope in 609 * and obsered the Sun, Moon, Milky Way, Moons of Jupiter and the phases of Venus. * Hans Lippershey inented the telescope in 608 If we assue (incorrectly) that the Tower of Pisa is 0 tall, the ball will take s to hit the ground. 5 6
2 Sir Isaac Newton 6-77 Newton s Laws: Een if the ball is thrown horizontally fro the tower, the acceleration toward the earth is still 0/s.. All objects at rest shall reain at rest and all objects in otion shall reain in otion in a straight line, unless copelled by a FOCE to do otherwise. As a result, the ball that is dropped and the ball that is thrown both hit the ground after seconds!!!. The ACCELEATION of any object is directly proportional to the FOCE applied to it and inersely proportional to its MASS. We will return to this essential idea in a few slides 7. For eery force applied to an object, there is an equal and opposite force applied by the object on the actor. 8 N e w t o n. s Newton s Laws elatie to Galileo s Experient:. When the ball is dropped it ceases to be at rest. Therefore there ust be a force, directed downward, to cause the acceleration.. The acceleration will be equal to the force that graity exerts on the ball diided by the ass of the ball, that is, the acceleration is equal to the force per unit ass.. If the Earth exerts a graitational force on the ball, the ball ust exert an equal and opposite force on the Earth!!!! 9 Law of Uniersal Graitation Newton knows that the ore ass an object has, the greater the force of Graity on it. F G = g Where g is the special nae gien to the acceleration that is caused by graity. 0 /s 0 The inerse square law Inerse square F The Law = G MM r G = kg s
3 Exaple: M = ass of professor = M = ass of earth = kg 6 r = radius of the earth = F = = 9 Newtons ( ) kg 6 9 Newtons = 90 lbs 6. Newtons = lb Exaple = B kg Assuptions Mass of baby Knowns = 6. x0kg M Mass of Mars D = 70kg Mass of doctor = 8. x0 BM Mars-Baby Distance = BD Distance between baby and doctor G = 667. x0 Uniersal Graitational Constant 5 6 F BD G B D = = 9. x0 BD 9 N Weighing the Earth F BM G B M = = BM 60 x N A & B hae equal asses and therefore equal weights. The rod is balanced. 7 8
4 eturn to Pisa The earth is not flat eturn to Pisa The ery sall ass is needed to balance the graitational force of the ery large ass. G can be calculated! Knowing G and Kepler s Law s allows us to calculate the ass of the Earth, Sun and all of the planets oons and asteroids in the solar syste 9 0 Cured Earth Question If the earth is cured such that it cures away 5 eters for eery 8000 eters traeled, how fast would the projectile need to be going so that, after falling 5 eters, it was still 5 eters aboe the earth? After one second the projectile has fallen fie eters But the earth has cured away. Q u e s t i a = k P 8000 /s!!! WE NOW UNDESTAND Suary Calculus and Planetary Motion Uniersal Graitation used to deterine the ass of the Earth Satellite otion possible Solar syste trael ade possible WE AE UNCLEA ON Newton inents calculus Newton Proes Kepler s Laws Tides understood Moon lock understood
5 t h h= at ( ) ( ) + t = + h + ( t) = ( + h) + t = + h+ h t = at + at = a+ a t WHICH IS NOT THE IGHT ANSWE. 5 6 This does not represent the true otion. The true otion is reealed when we Make the tie ery, ery, ery sall 7 = a+ a t = a a = 8 Newton Tells us that F = a An that, for graity in particular F = G M We hae just discoered that We ay deduce then that a = = G M = G M G M π = but = T T π = GM 9 0 5
6 Deterine the ass of the SUN. M = π G T =.96 x 0 T =.56 x 0 7 s G = 6.67 x 0 - N /kg M =.99 x 0 0 kg Forces are Balanced on a Spherical Moon Forces in Copetition on a Prolate Moon Forces are Balanced when Collinear on a Prolate Moon S u a IMPOTANT Objects fall at the sae rate. Newton s Laws Inerse Square Law of Graity Nature of Orbits enaissance Astronoers Electroagnetic adiation NEXT TIME 5 6 6
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