Physics 125 Solar System Astronomy

Transcription

1 Physics 125 Solar System Astronomy James Buckley Lecture 5 The Planets: History Part II and Celestial Coordinates + Time

2 Reading Quiz 3 Answer one of the following two questions. -What is the term for the apparent reversal of direction of motion of planets with respect to the background stars? -Time determined with respect to the position of the sun in the sky is referred to as Solar time. Time determined by the position of the stars goes by another name. What is it?

3 Geocentric Universe Circular acceleration v a = t Figure from a 16th century Portugese Cartographer showing the Ptolemeic geocentric system But Hipparchus rejected the ideas of Aristarchus and others, and adopted a Heliocentric model (as introduced by Plato ( BC) and Aristotle ( ) in the 4th century BC), and formalized by Ptolemy ( BC) Physics Lecture 1 p. 25/27

4 Planets in the Night Sky Compared with stars, planets: - Are often quite bright Mars - Twinkle less than stars becaues they are extended - Move relative to stars over the course of nights, years Greeks called planets Wanderers Venus, Mars, Jupiter and Saturn all clear to the naked eye.

5 Retrograde motion of planets If one maps the position of planets in the night sky, they often follow complex paths. What is the explanation?

6 Epicycles Geocentric cosmologists invoked a complex system of epicycles.

7 Heliocentric System: Retrograde Motion Heliocentric Model does a better job explaining retrograde motion, and a number of other things. Let s return to the History of Astronomy and Physics, in Modern

8 but planets move in circular paths in epicycles Ptolemaic System Circular acceleration Lecture 1 p.17/27 Aristotle said If the stars affixed to the celestial sphere are not centered Physics on the earth, and the earth is rotating around the sun, we should see some displacement of the stars. We don t see this, so unless the stars are ridiculously far away, the earth is the center of the universe! v a = Aristotle also said The natural state of a body t is to be at rest, and only the presence of a force or impulse would move it. Therefore a heavy body should fall faster than a light one, because it would have a greater pull towards Earth. Aristotle and Ptolemy prevailed with their Geocentric model of the universe until the 16th century. Everything was OK except for those darned wanderers or planets. Physics Lecture 1 p. 25/27

9 Copernicus Circular acceleration Nicolaus Copernicus ( ) born in Torun (now Poland) raised by an uncle who became of Ermland. (Later Copernicus was actually encouraged by members of the Catholic Bishop church to write up his heliocentric model). v a = tthen in Italy he studied church law, Copernicus studied astronomy at the U. of Cracow, medicine, astronomy, philosophy, mathematics and Greek. Copernicus worked on translating ancient literary works from Greek to Latin. It appears that he read of the theory of Aristarchus, and tried to apply the heliocentric model to come up with a simpler system for retrograde motion. Physics Lecture 1 p. 25/27

10 Tycho acceleration Circular Mural Quadrant used by Tycho The Uraniborg Observatory on the Island of Hven Danish nobleman Tycho Brahe ( ) made many of the key measurements needed to make the next step in developing a modern theory of planetary motion. At age 20, Tycho foot a duel with another student over who was the best mathematician, loosing his nose. Tycho had a false nose fashioned of gold and silver. v a = new star (actually it was a supernova, the In 1572 Tycho observed what he called a nova or t explosion of a distant star). King Frederick II of Denmark sponsored Tyco s work, providing him with money to build a (naked-eye) observatory, much like a giant protractor. Tycho made a number of precise measurements - to 1 arcmin (1/60 deg) precision. Physics Lecture 1 p. 25/27

11 Kepleracceleration Circular In 1600 Tycho hired the German astronomer Johannes Kepler ( ) to be his assistant. Kepler and Tycho had a strained relationship, some even speculate v that Kepler poisoned Tycho (stories had Tycho dying of a ruptured bladder a = waiting for an audience with the king, then t forensic evidence first pointed to poisoning, then later seemed to contradict this). Kepler tried to fit Tycho s data to circular orbits, but found up to an 8 arcminute discrepancy, not that much more than the state of the art for measuring angles. Physics Lecture 1 p. 25/27

12 Kepler s Laws Kepler s First Law: The orbit of each planet around the Sun is an Ellipse with the Sun at one focus. Kepler s Second Law: As a planet moves around its orbit, it sweeps out equal areas in equal times. Kepler s Third law: More distant planets orbit the Sun at slower average speeds, and the orbital period p (in years) is related to the average distance from the sun a (in astronomical units) according to the law p 2 = a 3

13 Geometry of Elliptical Orbits perihelion major axis aphelion minor axis semimajor axis Sun is at one focus of the ellipse Closest approach is called the perihelion Most distant point is called the aphelion

14 Geometry of Elliptical Orbits perihelion distance a(1 e) c aphelion distance a(1 + e) a c is the distance from the center to a focus The eccentricity e is defined to be the ratio of c to the length of the semimajor axis e = c a perihelion distance = a(1 e) aphelion distance = a(1 + e)

15 Galileoacceleration Circular Galilei ( ) finally overturned the Aristotelian view of physics with Galileo some simple experiments, and a new instrument v called the telescope. a = t First. using experiments with rolling balls determined that a moving object remains in motion unless a force acts to stop it (providing the basis of Newton s first law). In 1608, the spyglass, a low power telescope invented by Hans Lippershey of Holland had become a popular invention. Galileo improved the design increasing the magnification to 8, then 10 and then 30 and provided a stable mount. Physics Lecture 1 p. 25/27

16 Phases of Venus Galileo s observation of Venus essentially ruled out the epicycles of the geocentric system. In science it is very hard to prove something, but a single ugly fact can disprove the most beautiful theory!

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19 Galileo s Observations Galileo saw sunspots on the sun (it wasn t a perfect sphere after all), and saw that the moon had valleys and mountains and was not a smooth sphere. When he pointed at the Milky Way, he resolved it into individual stars. Most significantly, he saw moons orbiting Jupiter. So the Earth was not special, and could not be the body about which all others revolve.

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21 Conflict with Catholic Church Circular acceleration Simplicio: God could construct the universe in any form, making it appear to us to have a different form. Thus observations can not be used to understand the observations Dialogo Dei Due Massimi Sistemi The Dialog Concerning Two World Systems (1632) - The pope thought the character Simplicio (simpleton) might represent him! v a = t Physics Lecture 1 p. 25/27

22 Galileo s Notebooks

23 Discussion question: You Have Observed a Star Over a Period of Several Years. The Star Orbits an Invisible Object, Probably a Black Hole. Where Is the Black Hole Located? 1/1/2000 1/1/2001 1/1/1998 1/1/1999 A B C 1/ (A) At Location (A) 1/1/1993 (B) At Location (B) 1/1/1994 (C) At Location (C) 1/1/1995 1/1/1996 (D) We Can Not Tell From the Orbital Data Alone. Discuss the answers, and using Socrative, check ALL correct answers (there could be more than one or zero!)

24 Diurnal Motion of Stars Polaris West North East As earth revolves about its axis, but to a terrestrial observer stars seem affixed to a celestial sphere that revolves around an axis pointing in the direction of Polaris

25 Precession Earth precesses due to torque from gravitational forces of the moon and sun on the equitorial bulge 26,000 year period over which pole star changes, it will not always be Polaris, or any star for that matter.

26 Equitorial Bulge Spin of the earth results in an equatorial bulge (Kind of like the middle age spread or love handles for planets)

27 Precession Angular Momentum L Gravitational Force F Gravitational force tries to twist the top, with a torque whose direction is perpendicular to both the axis and the force The angular momentum vector changes its direction in the direction of the torque

28 Precession 23.5 plane of the ecliptic F 1 = GMm r 2 F 2 = GMm (r + r) 2 Difference in gravitational force on near and far side bulge produces torque, trying to twist the planet. But like a gyroscope, the torque doens t twist the spinning planet the way we would expect, but instead changes the direction of the angular momentum in the direction of the torque (see demonstration)

29 Spookily Similar - Moon and Sun The fact that the angular size of the moon and sun means that the effect of these two objects on the Earth. Start with Newton s law of Gravity: The gravitational force between two masses is proportional to the product of the masses and inversely proportional to the square of the distances between the centers of the two masses M M 2 r F = GM 1 M 2 r 2

30 Tidal Forces math But the force of gravity on the near side of object M2 is larger than on the far side. The difference in these forces is called the Tidal force, and turns out to be proportional to the product of the two masses and the ratio of the length of mass M2 divided by the cube of the distance between the two objects r + r M M 2 r F near Stretching or tidal force = F near F far 1 1 = GM 1 M 2 r 2 (r + r) 2 if r is small compared with r, you can show that F tidal GM 1 M 2 r 3 r r F far

31 Compare the Sun and the Moon math Now, let s compare the effect of the Sun and the Moon on the tidal forces on the earth: Average density of the Sun is g/cm 3 and of the moon is 3.3 g/cm 3 - oddly similar! The sun and the moon have about the same angular size, 0.5 deg Tidal forces are proportional to 1/d 3, The mass of the moon or sun is proportional to the product of the density times the volume. The volume of a sphere is proportional to the radius cubed, and mass is radius times volume so: Since the angular size of an object is roughly the ratio of it s physical dimension (2 R) divided by the distance, and since the moon and the sun have the same angular size: So, comparing the tidal forces: M sun / 1.4 R 3 sun, M moon / 3.3 R 3 moon moon sun 0.5 =2R sun /d sun =2R moon /d moon F moon M earth (3.3 R 3 moon) d 3 moon F sun M earth (1.4 R 3 sun) d 3 sun so since R moon /d moon R sun /d sun we have : F moon (3.3/1.4)F sun

32 Annual Motion In addition to diurnal motion, sun appears to move through the constellations (the zodiac) making one trip each year Sagittarius (Dec 18 Jan 18) Capricornus (Jan 19 Feb 15) Aquarius (Feb 16 Mar 11) Pisces (Mar 12 Apr 18) Aries (Apr 19 May 13) Taurus (May 14 Jun 19) Gemini (Jun 20 Jul 20) Cancer (Jul 21 Aug 9) Leo (Aug 10 Sep 15) Virgo (Sep 16 Oct 30) Libra (Oct 31 Nov 22) Scorpius (Nov 23 Nov 29) Ophiuchus (Nov 30 Dec 17)

33 The Zodiac

34 Local Horizon Coordinates Horizon coordinates use the observers local horizon as the fundamental plane. Angles are measured as azimuth (the angle East or CW from north) and altitude (angle above the horizon along a great circle through the zenith)

35 The Ecliptic on the Celestial Sphere

36 Conservation of Circular acceleration Angular Momentum Angular momentum also stablizes - e.g. frisbee, gyroscopes objects want to keep spinning in the same direction unless acted Spinning va distance that produces a upon by an external torque (a force acting at a = t twisting moment) Conservation of angular momentum has a deep connection to the isotropy of space (there are no special directions in empty space) - Brilliant Mathematician Emmy Noether ( ) - while she was an unpaid, untenured professor with limited administrative rights and functions at the U. of Goettingen Physics Lecture 1 p. 25/27

37 Path of Sun Throughout Year The Sun rises in the East, Sets in the West, but during the course of the year, it appears to get higher in the sky (during summer) and cross the Horizon at different Points. If the sun spends longer above the Horizon, then it is warmer! Ancient structures marked times of year, by aligning objects with the position that the Sun crossed the Horizon in different seasons.

38 The Tilt of the Earth and Seasons

39 Why it is Warm in the Summer? Since the sun is more directly overhead in the Summer, the flux is more direct (and light travels through less of the atmosphere increasing the amount of harmful UV rays)

40 The Sun Never Sets in the Arctic Stay away from the far North if you have S.A.D! The sun never sets in the summer :) but the sun never rises in the winter :( (and the opposite in Antarctica)

41 Annual Motion Circular acceleration Equinoxes, Solstices v a = t A solstice is both a time (Dec 21, my son David s birthday. It was a very short day for everyone except my wife!) And a place (the point in the sky where you will find the sun on Dec 21) Physics Lecture 1 p. 25/27

42 Solstices and Equinoxes Equinoxes and Solstices are both positions in the sky and dates (when the sun appears in this position)

43 Summary Careful experiments (Tycho) and attention to detail (Kepler) led to an accurate description of the motion of planets around the sun. Other experiments by Galileo overturned the Aristotelian world view, and firmly established the Heliocentric model of the universe. Planets move on elliptical orbits with the sun at one focus. Later this will be seen to follow from Newton s laws. We can use our understanding of motions of the earth and the planets about the sun to accurately predict the appearance of the night sky. Reading assignment: Sections 3.3, 4.1, 4.2, 4.3 Looking ahead: we will follow chapters in order - 5, 6, 7, 8...