S2: Astrophysics Short Option From planets to the cosmos

1. S2: Astrophysics Short Option From planets to the cosmos Roger L. Davies

2. Recommended books: Main texts: “Introductory Astronomy & Astrophysics”(fourth edition ISBN 0-03-006228-4) M. Zeilek & S.A. Gregory, publ. Harcourt Brace College Publishers. This is the basic text for this course. “Universe”, R.A. Freedman & W.J. Kauffmann III, publ. Freeman. Quite up-to-date, and easy to read. 9th edition is the most recent.Their website contains some interesting material based on the book. Additional reading: “An Introduction to Modern Astrophysics” Carroll & Ostlie 2nd edition, Pearson Education. Covers this course and wider topics. "The stars: their structure & evolution", R.J. Tayler, publ Wykeham. Old but very good on basic stellar physics. "Introduction to Stellar Astrophysics", E. Boehm-Vitense, publ, Cambridge University Press. "Introduction to Modern Cosmology", A. Liddle, 2nd ed,publ. Wiley. "In Search of Dark Matter", K. Freeman and G. McNamara, publ. Springer Praxis. "Astrophysics", R. Bowers & T. Deeming, publ Jones & Bartlett.

3. From planets to the cosmos: course synopsis Week 1: Limitations of astrophysics, scale of the Universe. Motions of the Solar System bodies, Keplers laws,the Astronomical Unit, the parsec.The magnitude system. Detection and properties of exo-planets. Week 2: physical properties of stars, the Sun as a star, binary stars, stellar masses, mass-luminosity relation. Energy generation, the Virial theorem, stellar lifetimes, star clusters, evolution of low & high mass stars. End points of stellar evolution, white dwarf stars, supernovae, neutron stars & black holes, origin of the chemical elements. Week 3: the Milky Way: constituents & structure, central black hole, formation models. Galaxies, the Hubble sequence, active galaxies. The expanding universe, galaxy clusters, dark matter. Galaxy assembly. Week 4: large scale structure, the distance scale, cosmic microwave background, probes of dark energy, the hot big bang, age of the Universe, concordance cosmology.

4. From planets to the cosmos: problems & exam I will set problems each week and review them on the Wednesday of weeks 2, 3 & 4. Exam questions will have similar content to the questions in the problem set. On the exam you will have a choice of 2 questions from 3. There will be no essay question, however discursive answers to parts of the questions may be required.

5. Unique aspects of astronomy • Experiments are not possible. We cannot re-arrange the stars and galaxies. • We are part of the system. The only universes that are allowed are ones we can inhabit. The Anthropic Principle. • The Universe is, by definition, singular. We cannot observe an ensemble of Universes and deduce their properties statistically. • Because of the finite speed of light, we see distant objects as they were in the past. The Universe as a time machine.

6. The Universe as a Time Machine Object Light travel time Context The Sun 8.3 minutes here! Pluto 3½ hours asleep? The nearest star 4.2 years at school The Orion Nebula 1500 years Fall of Roman Empire Galactic Centre 25,000 years Ice Ages

7. The Universe as a Time Machine Object Lookback Time Context The Andromeda Galaxy 2 million years Primitive man Cluster of galaxies 200 million years Dinosaurs Distant cluster 3 billion years First multi- cellular life Distant galaxies 5 billion years Earth formed The most distant 12 billion years Universe only known galaxies 15% present age

8. Unique aspects of astronomy • We assume the universality of the laws of physics. We can use astronomical measurements to test physical laws in extreme regimes - eg. the 1919 solar eclipse was used as a test of General Relativity.

9. Headline form the New York Times 10th Nov 1919

10. The motion of the planets in the Solar System ………an ancient puzzle.

11. Consider the motions of the planets observed in pre-telescopic times: • The planets move eastwards through the sky with respect to the `fixed stars’. • Five planets visible with the unaided eye: Mercury, Venus, Mars, Jupiter & Saturn • They vary in apparent brightness: M, J & S brightest when opposite the Sun in the sky. • The rate at which they move also varies: M, J & S move slowest when faintest. • Mercury & Venus remain close to the Sun. • When Mars, Jupiter and Saturn are brightest – opposite the Sun in the sky, they move westward: `retrograde motion’

12. Retrograde motion of Mars. This composite of images spaced about a week apart - from late July 2005 (bottom right) through February 2006 (top left) East West

13. Brief History: The Babylonians (about 16th century BC) tabulated the positions of the Moon & planets. They predicted solar eclipses based on the Saros cycle of 18 years 11 days on which the relative positions of the Earth, Moon & Sun repeat. The Greeks summized that the Earth was stationary (they could not detect stellar parallax) and spherical (by observing the Earth’s shadow on the Moon during a lunar eclipse). Aristotle (384-322 BC) devised a geocentric model of the SS with the planets moving on circular orbits. Hipparchos of Rhodes (c. 190-127 BC) added epicycles to explain the retrograde motions and explained the change in the rate of planetary motion by moving the Earth off-centre.

14. Brief History: The Babylonians (about 16th century BC) tabulated the positions of the Moon & planets. They predicted solar eclipses based on the Saros cycle of 18 years 11 days on which the relative positions of the Earth, Moon & Sun repeat. The Greeks summized that the Earth was stationary (they could not detect stellar parallax) and spherical (by observing the Earth’s shadow on the Moon during an eclipse). Aristotle (384-322 BC) devised a geocentric model of the SS with the planets moving on circular orbits. Hipparchos of Rhodes (160-127 BC) added epicycles to explain the retrograde motions and explained the change in the rate of planetary motion by moving the Earth off-centre.

15. Copernicus (1473-1543) heliocentric model: 1543 `De revolutionibus orbium coelestium’ planets move on circular orbits around the Sun with the closer planets moving faster. The Sun became the center of the cosmos. Recognised that this hypothesis implies stellar parallax but concluded that the stars are too distant for parallax to be measured. By making one assumption the world model is simplified: (i) The daily motion of the heavens is caused by the Earth’s rotation this removes the need for numerous spheres & epicycles. (ii) The apparent motion of the Sun through the constellations of the zodiac is generated by the annual motion of the Earth around the Sun. (iii) Retrograde motion of arises because of the relative motion of the earth and outer planets.

16. This composite of images spaced about a week apart - from late July 2005 (bottom right) through February 2006 (top left) Retrograde motion of Mars. East West

17. Johannes Kepler 1571-1630Was able to account for Tycho’s observations of Mars by postulating three laws 1. The Law of Ellipses: the orbit of each planet is an ellipse with the Sun at one focus. e2 = 1 – (b/a)2 2. The Law of equal areas: a line joining the planet and the Sun sweeps out equal areas in equal times.

18. Kepler’s 2nd Law & conservation of angular momentum (1st law arises from any central force)

19. Distance measurements:Kepler’s laws 3.The Harmonic Law: the square of the orbital period of a planet (P) is proportional to the cube of its average distance from the Sun (a). P2 = 42a3 G(M1 +M2) This implies that if we know one length in the Solar System all the other dimensions are specified.

20. Derivation of Kepler III for face on circular orbits A star and planet orbit about their common centre of mass. m2 m1 a2 a1 Centre of mass

21. Derivation of Kepler III for face on circular orbits We now use (2) to eliminate v1 & v2 from (1): v1 = 2πa1/P & v2 = 2πa2/P a= a1 + a2 = a1(1+a2/a1 ) = a1(1+m1/m2) so eliminating a1 we have:

22. Kepler’s predictions of the positions of the planets based on these laws (in the Rudolphine Tables) were ten times more accurate than those of Copernicus. Kepler’s laws abandoned the need for uniform motions & recognised the controlling influence of the Sun. Derivation of Kepler’s 3rd Law (assuming circular motion) NB. Units : a3/P2 = G(M1 + M2)/42 if we use units of years, solar masses & Astronomical Units (Earth-Sun distance) this becomes: a3/P2 = (M1 + M2)

23. Galileo Galilei (1564-1642): 1610: `Starry messenger’ 1611: Kepler showed that Jupiter’s satellites obey his laws of planetary motion. 1613: Sunspots, phases of Venus • celestial bodies are imperfect, changing and conform to the heliocentric model. 1632 : `Dialogue on the two chief World Systems’ the text was banned by the Catholic church until 1835. The church acknowledged its error in …… 1992

24. Distance measurement: The Astronomical Unit One Astronomical Unit is the average distance between the Earth and the Sun . 1 Astronomical Unit = 1AU = 149.6 x 106 km = 8.3 light minutes Two methods for measuring the AU: • The geometrical method • The radar method

25. Geometrical method Problem 1: The orbital period of Mars is 1.881 yrs. When Mars is opposite the Sun in the sky its position with respect to the background of fixed stars is measured at sunset and again at sunrise. The effective baseline between these two positions is 11,700km and the change in the position of Mars on the sky is 30.8”. Calculate the length of the Astronomical Unit in metres. Radar method Problem 2: The orbital period of Venus is 0.6152 yrs. When Venus is between the Earth and Sun (at inferior conjunction) radar signals are launched from the Earth and the signal reflected off Venus arrives after 276.2s. Calculate the length of the Astronomical Unit in kilometres.

26. Trigonometric parallax:the change in the apparent position of a nearby star, measured against the background of `fixed’ stars, as the earth moves through its orbit. The angle, p, the parallax is measured in arcseconds. The first stellar parallax was measured in 1844 by Fredrick Bessel. This page was copied from Nick Strobel's Astronomy Notes. Go to his site at www.astronomynotes.com for the updated and corrected version.

27. Distance measurements:The parsec 1 parsec = 1pc = the distance of a star at which 1AU subtends 1 arcsecond = 1´´= 1/60 of one arcminute par-sec : parallax of one arcsecond 1 parsec = (180/)x 60 x 60 AU = 206265 AU = 3.086 x 1016 m Distance, d, (in pc) =1/p, Where p is in arcseconds. d This page was copied from Nick Strobel's Astronomy Notes. Go to his site at www.astronomynotes.com for the updated and corrected version.

28. The magnitude system: definitions

29. The magnitude system: definitions ΔΕ Δt Luminosity= energy change per unit time: L = units Watts Flux= energy per unit frequency, per unit time passing through unit area: f= unitsW.m-2 .Hz-1 ΔΕ ΔΔΑΔt

30. Apparent magnitude and Absolute magnitude This logarithmic scale, originated by the ancient Greeks (Hipparchos 190-127 BC) designates the brightest stars as first magnitude and the faintest, about 100 times less bright, sixth magnitude. The modern definition of apparent magnitude is based on the flux received at frequency  from star at the Earth’s surface: f, Note : fainter stars have numerically larger (more positive) magnitudes Absolute magnitude is defined using the flux from a star 10pc distant, F and therefore is a measure of the star’s intrinsic brightness.

31. Apparent magnitude, m = - 2.5Log f + constant NB. Δm = ± 5  f or F  or / 100

32. Astronomical magnitudes Absolute Giant galaxies -24 Supernova 1987A -15.5 Brightest stars -9 Sun +4.8 Faintest stars +20 Apparent Sun -26.8 Full Moon -12.6 Venus -4.4 Sirius -1.5 Naked eye limit ~ 6 Brightest quasar 12.8 Pluto ~ 15 8m/HST limit ~ 28

33. Distance modulus Distance modulus, the difference between apparent and absolute magnitude, is a measure of the distance to a star. The inverse square law gives : F = f where d is the distance to the star in parsecs so 2.5Log F = 2.5 Log f + 5Log d - 5 -M = -m + 5Log d - 5 d2 102

34. Magnitude Systems In practice magnitudes are defined over a specific wavelength rangedefined by a combination of a set of filters and a detector. A commonly used system is the Johnson UBV system : Band U B V R I Wavelength 0.35 0.44 0.55 0.64 0.79 (in microns = 10-6m) mU mB mV mR mI

35. Magnitude Systems In the infrared the transmission of the atmosphere is restricted to specific wavebands: Band J H K L M N Q Wavelength 1.25 1.66 2.2 3.45 4.65 10.3 20 (in microns = 10-6m)

36. Bolometric magnitude Bolometric magnitude is the magnitude calculated from the flux integrated over all frequencies. It represents the total energy output of a star: fbol = ∫ fνdν Apparent bolometric magnitude, mbol= -2.5Log fbol + const Absolute bolometricmagnitude, Mbol= -2.5logFbol + const

37. Star clusters BRIGHT FAINT BLUE RED

38. The Solar System

39. The Solar System

40. The Solar System

41. The Solar System

42. Planets?

43. Pluto • Pluto is 1/6th the size of the Earth, smaller than the • Moon, Europa, Ganymede, Callisto, Titan and Triton. • Its orbit the most elongated & tilted at 17º to the • plane all the other planets move in. • Between 1979-1999 Pluto was NOT the planet furthest from the Sun as it passed inside Neptune’s orbit. Is Pluto really a planet?

44. What is a planet? A planet is (a) in orbit around the Sun, (b) nearly round & (c) has cleared a zone around its orbit → this gives us 8 planets.A dwarf planet is (a) & (b) but (c) has not cleared other material out of its orbit & (d) is not a satellite. The big Kuiper Belt Objects.All other objects orbiting the Sun are "Small Solar System Bodies". Pluto is a dwarf planet, the prototype of a new category called "plutonian objects."