1 Phys Astronomy

2 “The danger to which the success of revolutions is most exposed, is that of attempting them before the principles on which they proceed, and the advantages to result from them, are sufficiently seen and understood.” Thomas Paine - American Revolutionary “Anyone in a free society where the laws are unjust has an obligation to break the law.” Henry David Thoreau - American Philosopher

3 “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 “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

4 (rěv΄ə-lōō’shən)) 1.n A drastic and far-reaching change in ways of thinking and behaving. 2.n Orbital motion about a point, the planetary revolution about the sun.

5 The Copernican Revolution

6 Problems with Ptolemy There are problems with the Ptolemaic Model The solar system according to the Ptolemaic Model from 100 A.D. to 1500

7 Features Features… Deferent Circles Epicycles on the Deferents Inferior planets are never more than 47º from the sun Retrograde motion of mars is explained

8 As the precision of astronomical measurements grew the need for adjustments to the model called for additional epicycles. In 1252 King Alfonso X of Castile funded a 10 year project by Arab and Jewish astronomers to calculate extensive tables. Calculations became horrendously complicated and even Alfonso suggested that the model should by simpler if it was to have any truth in it.

9 “Multiplicity ought not be posited without necessity.” William Occam – English Scholar “Keep it simple, stupid.” Anonymous 20 th Century Philosopher This principle is known as Occam’s Razor…

10 Copernican Theory… The motions of the planets would be more easily explained if the sun were at the center.

11 DeRevolutionibus, 1543… “Venus and Mercury revolve around the sun and cannot go nearer or further from it than the circles of their orbits permit…If, acting upon this supposition, we connect Saturn, Jupiter and Mars with the same center, keeping in mind the greater extent of their orbits…we cannot fail to see the explanation of the regular order of their motions. This proves sufficiently that their center belongs to the sun…”

12 Going Further… “The extent of the universe…is so great that…[the earth] disappears when compared to the sphere of the fixed stars.” “Although this may appear incomprehensible and contrary to the opinion of many, I shall, if God wills, make it clearer than the sun, at least to those who are not ignorant of mathematics.”

13 “…that fool who would reverse the entire art of astronomy…Joshua bade the SUN and not the earth to stand still.” Martin Luther Under very real threat of persecution, Copernicus changed the title of his book and its publication was finished only in the final days of his life.

14 Tycho Brahe Royal Astronomer of Denmark Uraniborg Observations with the naked eye Measured parallax of planets Observed a supernova (1572) Realized that Ptolemy was not right but denied Copernicus Proposed a model with the earth at the center and the sun revolving around it, but all of the other planets revolved around the sun Collected the best data available

15 KEPLER!

16 Kepler Johannes Kepler – Deeply religious believer in astrology Mathematics was evidence of God Subscriber to the Copernican theory Hired by Tycho to prove the earth centered model Convinced that a mathematical “harmony” existed for the planets Inherited Tycho’s fine data Analyzed data regarding mars

17 Kepler’s laws Kepler’s Laws 1.Each planet moves in an ellipse, with the sun at one focus. 2.The line between the sun and the planet sweeps out equal areas in equal times. 3.The ratio of the cube of the average radius of a planets orbit to the square of its orbital period of revolution is the same for each planet. (Harmonic Law)

18 Ellipses and Areas This orbit is in the shape of an ellipse…. The area A AB = The Area A CD

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20 Law of Conservation of Angular Momentum

21 Harmonic Law The Harmonic Law: a = Average radius of planet’s orbit P = The orbital period of the planet k = A constant for all objects orbiting the sun

22 Harmonic Constant Consider the earth… This is true for all planets no matter what the radius of their orbit.

23 Retrograde Motion Retrograde motion explained at long last…

24 How does Kepler know times? How does Kepler know the time periods of planets other than the earth? Consider… You can’t go to mars You can’t watch mars ‘go round’ Every so often, mars exhibits retrograde motion Retrograde motion is caused by the passing of mars by the earth at various points in their orbits.

25 Working late on this lecture, the clock strikes midnight… And the hands line up. A little while later… And they aren’t lined up at all. I notice that they line up again sometime around 1:05 am. Is there some sort of a math rule that can predict when the hands will align?

26 A little scratch work and some calculations… Big deal…

27 Time period of mars If I use the hands of the clock as an analogy for the motion of the planets…

28 Radius of mars’ orbit

29 Measurement

30 IMPORTANT Occam’s Razor Copernicus Law of Ellipses Law of Areas Harmonic Law

31 Review REVIEW: Kepler Develops Three Laws: Law of Ellipses Law of Areas Harmonic Law We now understand HOW the planets move… but not WHY they move.

32 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. * Hans Lippershey invented the telescope in 1608

33 If we assume (incorrectly) that the Tower of Pisa is 20m tall, the ball will take 2s to hit the ground.

34 Even if the ball is thrown horizontally from the tower, the acceleration toward the earth is still 10m/s 2. 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…

35 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

36 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!!!! Newton v.s. GalileoNewton v.s. Galileo

37 Law of Universal Gravitation Newton knows that the more mass an object has, the greater the force of Gravity on it. F G = m g Where “g” is the special name given to the acceleration that is caused by gravity. 10 m/s 2

38 Inverse square The inverse square law…

39 The Law

40 Example Example:

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42 Mass of baby Mass of doctor Distance between baby and doctor Assumptions

43 “Knowns” Mass of Mars Mars-Baby Distance Universal Gravitational Constant

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45 “Weighing” the Earth… A & B have equal masses and therefore equal weights. The rod is balanced.

46 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

47 Return to Pisa Return to Pisa…The earth is not flat…

48 Curved Earth After one second the projectile has fallen five meters… But the earth has curved away.

49 QuestionQuestion 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? 8000 m/s!!!

50 Summary Universal Gravitation used to determine the mass of the Earth Satellite motion possible Solar system travel made possible Newton invents calculus Newton Proves Kepler’s Laws Tides understood Moon “lock” understood WE NOW UNDERSTAND… WE ARE UNCLEAR ON…

51 Calculus and Planetary Motion…

52 R R v t h

53 WHICH IS NOT THE RIGHT ANSWER….

54 This does not represent the true motion…. The true motion is revealed when we Make the time very, very, very small…

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56 Newton Tells us that… An that, for gravity in particular… We have just discovered that… We may deduce then that…

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58 Determine the mass of the SUN…. R = x m T = x 10 7 s G = x Nm 2 /kg 2 M = 1.99 x kg

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60 Forces are Balanced on a Spherical Moon Forces in Competition on a Prolate Moon Forces are Balanced when Collinear on a Prolate Moon

61 Summary IISummary II

62 IMPORTANT Objects fall at the same rate. Newton’s Laws Inverse Square Law of Gravity Nature of Orbits Renaissance Astronomers Occam’s Razor Copernicus Law of Ellipses Law of Areas Harmonic Law

63 IMPORTANT Occam’s Razor Copernicus Law of Ellipses Law of Areas Harmonic Law

64 Electromagnetic Radiation NEXT TIME