1 Astronomy 1 Fall 2016 Comet Halley Edmund Halley, a friend of Newton s used Newton s math to predict the return of a comet seen at intervals of 76 years. Lecture 3; September 29, 2016
2 Previously on Astro-1 Earth s Rotation Diurnal motion of stars Earth s Orbit Seasonal motion of stars The moon s orbit Lunar eclipses Solar eclipses UCSB Astro 1 - Martin 2
3 Today on Astro-1 The motion of planets Geocentric Models Evidence for a heliocentric solar system Newton s laws of dynamics Newtonian gravity The motion of planets explained by Newton s gravity Tides
4 The ancient Greek (wrong) notion of planetary motion
5 But sometimes the motion of planets is retrograde Can t explain this with simple perfect circular motion of the planets
6 The Geocentric explanation of retrograde motion: circles within circles epicycles.
9 Copernican Revolution
10 Nicolaus Copernicus ( ): revolutionized our understanding of our place in the universe by introducing the heliocentric (suncentered) model of the solar system. De Revolutionibus was published in 1543, but he had been circulating the ideas for 30 years. Aristarchus suggested a heliocentric model in the 3 rd century BC, but it didn t catch on.
11 Heliocentric explanation of retrograde motion
12 Maximum greatest elongation for Venus is 45, and for Mercury 28, so they can never be farther than that from the sun.
13 iclicker Question You see a very bright planet at midnight. Is it Venus? Assume Venus is 45 o from the Sun at greatest eastern elongation. A. Venus will set 45 minutes after sunset. It cannot be seen at midnight. B. Venus will rise 45 minutes before sunrise. It cannot be seen at midnight. C. Venus will set 3 hours after sunset. It cannot be seen at midnight. D. Yes, Venus is visible all night at greatest eastern elongation. E. Venus will set 3 hours before sunrise. It cannot be seen at midnight. Note: You know the bright object is a planet because the object does not twinkle like stars do. UCSB Astro 1 - Martin 13
14 Iclicker Answer You see a very bright planet at midnight. Is it Venus? Assume Venus is 45 o from the Sun at greatest eastern elongation. A. Venus will set 45 minutes after sunset. It cannot be seen at midnight. B. Venus will rise 45 minutes before sunrise. It cannot be seen at midnight. C. Venus will set 3 hours after sunset. It cannot be seen at midnight. D. Yes, Venus is visible all night at greatest eastern elongation. E. Venus will set 3 hours before sunrise. It cannot be seen at midnight. Note: You know the bright object is a planet because the object does not twinkle like stars do. UCSB Astro 1 - Martin 14
15 iclicker Question Copernicus used the fact that Mars can sometimes be seen high in our sky at midnight to conclude that A. Earth can come between Mars and the Sun B. Mars and the Sun can never be on the same side of Earth at the same time C. Mars can come between Earth and the Sun D. The Sun can come between Earth and Mars UCSB Astro 1 - Martin 15
16 Iclicker Answer Copernicus used the fact that Mars can sometimes be seen high in our sky at midnight to conclude that A. Earth can come between Mars and the Sun B. Mars and the Sun can never be on the same side of Earth at the same time C. Mars can come between Earth and the Sun D. The Sun can come between Earth and Mars UCSB Astro 1 - Martin 16
17 Tycho Brahe ( ) Here shown at Uraniborg, one of the two observatories that he built under the patronage of Frederik II of Denmark (though the telescope had not yet been invented). Kepler later used Tycho s exquisite measurements.
18 From Tycho s Stella Nova
19 Parallax: Tycho Brahe argued that if an object is near the Earth, an observer would have to look in different directions to see that object over the course of a night and its position relative to the background stars would change. Tycho failed to measure such changes for a supernova in 1572 and a comet in 1577, and concluded that these objects were far from the Earth.
20 Kepler s Laws
21 Johannes Kepler ( ) By analyzing Tycho Brahe s detailed records of planetary positions, Kepler developed three general principles, called Kepler s laws, that describe how the planets move about the Sun. Kepler was the first to realize that the orbits of the planets are ellipses and not circles.
23 Kepler s first law: The orbit of a planet about the Sun is an ellipse with the sun at one focus.
24 Kepler s second law: A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.
26 Iclicker Question Which of the following statements is true according to Kepler s third law? A. The smaller the orbit, the longer it takes for the planet to complete one revolution B. The smaller the radius of a planet the more rapidly it rotates on its axis C. The larger the orbit the longer it takes for the planet to complete one revolution D. The time to complete one revolution of its orbit depends on the size or radius of the planet
27 Iclicker Answer Which of the following statements is true according to Kepler s third law? A. The smaller the orbit, the longer it takes for the planet to complete one revolution B. The smaller the radius of a planet the more rapidly it rotates on its axis C. The larger the orbit the longer it takes for the planet to complete one revolution D. The time to complete one revolution of its orbit depends on the size or radius of the planet
28 Significance of Kepler s Laws Could describe the motions of the planets more accurately than any scheme before. Simpler than epicycles (so satisfies Occam s Razor). Occam s razor: simpler explanations of phenomena are more likely to be correct. ( Razor refers to shaving extraneous details from an argument) Helped justify the heliocentric model. Turned out to be a direct consequence of more fundamental physical laws of nature.
29 But What Observations Proved that the Earth Orbits the Sun?
30 Galileo Galilei ( ) Galileo was one of the first people to use a telescope to observe the heavens. He discovered craters on the Moon, sunspots on the Sun, the phases of Venus, and four moons orbiting Jupiter. His observations strongly suggested that the Earth orbits the Sun, not vice versa.
31 Numbers are angular size of Venus in arcsec, but mistakenly labeled as degrees in figure.
33 Galilean Satellites with a Small Telescope In 1610 Galileo discovered four stars that move back and forth across Jupiter from one night to the next. He concluded that these are four moons that orbit Jupiter, much as our Moon orbits the Earth.
34 Question 4.5 (iclickers!) The most significant observation Galileo made through his home-built telescope that convinced him that the planets revolved around the Sun was A. The appearance of the Milky Way as a mass of individual stars B. The discovery of rings around the planet Saturn C. The appearance of mountains and craters on the Moon D. That the appearance of Venus followed a cycle of phases, from crescent through quarter and gibbous phases to full phase
35 Question 4.5 (iclickers!) The most significant observation Galileo made through his home-built telescope that convinced him that the planets revolved around the Sun was A. The appearance of the Milky Way as a mass of individual stars B. The discovery of rings around the planet Saturn C. The appearance of mountains and craters on the Moon D. That the appearance of Venus followed a cycle of phases, from crescent through quarter and gibbous phases to full phase
36 Arguments favoring Heliocentrism over Geocentrism Observations: Phases of Venus Stellar Parallax Against specific feature of Ptolemy s model Moons of Jupiter Sun spots Moon spots
37 Newtonian Gravity
38 Isaac Newton ( ) Explained Kepler s Laws as direct consequence of fundamental physical laws. Established that the laws of physics on earth extend up into the heavens, Epitaph by Alexander Pope: Nature and nature's laws lay hid in night; God said "Let Newton be" and all was light. Newton in a letter to Robert Hooke: If I have seen further it is by standing on the shoulders of giants
39 Newton s First Law (Inertia) 1. An object remains at rest or moves in a straight line at a constant speed unless acted upon by a net outside force. Example: Voyager 1 -- launched in 1977, it is now on its way out of the solar system, forever traveling in a straight line (unless it encounters something).
40 Level Air Track Experiment iclicker Question What will happen to the cart when the professor turns the air off? A. Car will stop suddenly. B. Car will slowly come to a stop. C. Car will slowly speed up. D. Car will rapidly speed up. E. Car will continue to move at a constant speed along the track.
41 Newton s Second Law (acceleration) F = ma F = net outside force on a object m = mass of object a = acceleration of object It requires more force to accelerate more massive objects. OR If you push two objects of different masses with the same force, the less massive object will accelerate more
42 Skateboard Experiment iclicker Question When the skateboarders push off, who will accelerate more? A. Their accelerations are equal B. The more massive person C. The less massive person. D. Neither person will move E. It is impossible to predict with certainty.
43 Newton s Third Law Whenever one object exerts a force on a second object, the second object exerts and equal and opposite force on the first object.
44 Skateboard Experiment icliker Question When the less massive person pulls on the rope what will happen? A. Both people move inwards toward the center of mass. B. The less massive person is pulled towards the more massive person. C. The more massive person is pulled towards the less massive person. D. The distance between the skateboarders increases due to Newton s third law.. E. Neither person will move
45 The Law of Universal Gravitation Two objects attract each other with a force that is directly proportional to the mass of each object and inversely proportional to the square of the distance between them. F=Gm 1 m 2 /r 2 F = gravitational force between two objects m 1 = mass of first object m 2 = mass of second object r = distance between objects G = universal constant of gravitation G = newton m 2 /kg 2
46 Difference between weight and mass Mass describes how much matter is in an object (measured in kg) Weight is a force (F=ma) that describes how gravity affects a mass (measured in Newtons: 1 N = 1 kg m /s 2 ) 100 kg on the surface of the Earth weighs 980 N Example: If the Earth were the same mass, but twice the radius, what would a 100 kg person weigh? F=Gm e m p /r 2 m e = kg and m p =100 kg r = 2 radius of Earth = m = m F = 245 Newtons = ¼ 980 Newtons
47 The fall of bodies in a gravitational field does not depend on their mass
48 Professor s Dinner iclicker Question Why doesn t her dinner fall on the ground?. A. Objects at rest stay at rest unless acted upon by a net outside force. B. The tablecloth was removed very quickly, so the force of friction did not last long. C. The acceleration occurred over such a brief period, that the table setting did not reach a velocity much larger than zero D. All of the above. E. None of the above. Gravity keeps the objects on the table regardless of the speed of the pull.
49 The orbits of planets
50 Ball Rolling Along Curved Track iclicker Question What trajectory will the ball take when it rolls out of the loop? A. It will continue around the circle back to where it first touched the loop. B. It will continue on a curved path for a brief period, but its path will eventually straighten out. C. It will go around the loop two more times. D. It will roll along a straight line. E. Really, I have no idea. Let s find out!
51 When a body moves in a circle, there must be a outside force acting on that body!
52 Newton s form of Kepler s Third Law # P 2 4" 2 = % $ G m + m 1 2 ( ) & ( a 3 ' P = period of orbit, in seconds m 1 = mass of first object, in kg m 2 = mass of second object, in kg a = semimajor axis of orbit, in meters G = universal constant of gravitation G = newton m 2 /kg 2 Note that Kepler s form is only valid for objects orbiting the sun. Newton s form can be applied to any two objects in the universe.
53 Energy of Orbits
54 Different Forms of Energy
55 Energy of Orbits
56 Energy is Conserved The first American in space, Alan Shepard, did not orbit the Earth, because his Redstone rocket (a ballistic missile) was not powerful enough. John Glenn would later orbit Earth after being launched from an Atlas rocket.
57 Discovery of Neptune Le Verrier 1846 noticed Uranus was not in the right place. Predicted the existence of Neptune. Neptune was found where predicted to within one degree!
62 Tides are a difference in gravitational forces over a body of finite size.
70 Summary In the modern Heliocentric model, the planets go around the sun (Copernican model) What pieces of evidence show that the Geocentric model is false? How did the Geocentric model explain retrograde motion of the planets? Kepler s Laws 1. The orbits of planets are ellipses 2. A planet s speed varies along the orbit 3. The period of the orbit is related to the size of the orbit Newton s Laws of Motion 1. Inertia 2. Relation between force and acceleration 3. Action/Reaction Newton s Law of gravity (orbits, tides, inertial vs. gravitational mass)
71 Homework #2 Due 10/06/16 On your own: answer all the review questions in chapters 3 & 4 To TAs: answer questions 3.31 diurnal motion of moon relative to stars 3.43 application of angular sizes to eclipses 4.46 gravitational force orbital periods
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