PHYS1002: Founda0ons of Astronomy

Transcription

1 PHYS1002: Founda0ons of Astronomy Course Text: Astronomy: A Physical Perspec0ve, Marc Kutner 9 Lectures + 2 Assessments + Final Exam New course component Exams will be similar to tutorial sheets.

2 Lecture outline Astronomical Coordinates: The Astronomical sky, Kepler s Laws, the solar system Flux & Distance: Magnitudes, magnitudes, parallax, and distance Stellar nucleosynthesis: Fusion, the CNO cycle Proper0es of Stars: The Hertzsprung- Russell diagram, stellar lifecycle Expansion: Olber s Paradox, Hubble s Law and the expanding Universe Cosmology: The Cosmological Principle, the Hot Big Bang, Dark Energy Galaxies: morphological types, number of stars, space density, distribu0on Galaxy spectra: spectra, mo0on, inclina0on and peculiar veloci0es Dark Ma]er: The virial theorem, galaxy rota0on curves, galaxy forma0on

3 The Astronomical Sky On a human life0me the Celes0al Sphere is frozen As the Earth rotates the celes0al sphere appears to move We can photograph star trails (24hrs for one 360 degree rota0on) As the Earth orbits the Sun The stars visible in the night sky change over the course of the year (different constella0ons become visible)

4 Equatorial Coordinates At a fixed 0me in the Earth s orbit we project our la0tude and longitude system onto the sky and call these Right Ascension and Declina0on Longitude = Right Ascension: 0 24 hours [or 0 degrees to 360 degrees.] La0tude = Declina0on: - 90 degrees to + 90 degrees This point in the Earth s Orbit around the Sun is called The first point of Aries and is one of two Equinoxes*. Vernal/Spring Equinox ~ 21 st March Autumnal Equinox ~ 21 st September Because the Earth s orbit precesses (once every 26,000 years) the first point of Aries moves along the eclip0c # (1 deg per 78 years). NB: Sun now in Pisces at Vernal Equinox Astronomers work to either the 1950 or 2000 projec0on denoted B or J *Equinox: When the Earth s axis of inclina0on neither points towards or away from the sun. # Eclip0c: The plane of the Earth s rota0on around the Sun.

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6 First Point of Aries At the moment of the Vernal Equinox the Sun will be directly overhead some point on the Earth (noon/midday). At this moment one can project a line of longitude onto the sky and define this as 0 degrees right ascension. This projected line is known as the First Point of Aries Right Ascension defined to increase East of this projec0on. The equator is projected to become the Celes0al equator, i.e., 0 o declina0on This grid is then frozen onto the Celes0al Sphere and used to define posi0ons of the fixed objects. E.g., M31: 00 h 44 m s, +41 o 16 9, J2000.0

7 E.g., What RA is overhead at 10pm tonight? On the Vernal Equinox: 0 h RA is overhead at noon Hence stars with coordinates ~12 h will be overhead at midnight The Earth completes one rota0on during the year What is overhead moves on by: 1 h per hr What is overhead at midnight moves on by: 2 h per month 29 th July is (roughly) 4 months auer the Vernal Equinox, hence tonight we will have stars with coordinates at ~20 h overhead at midnight 10pm is two hours before midnight so we will have stars with coordinates 18 h overhead at 10pm tonight.

8 Exercise 1 Calculate what coordinates were overhead at the date/0me of your birth? Path: Calculate how many days your birthday is auer 21 st March = N Add 12 h +24 h xn/ = Q Because the sky completes one rota0on due to the Earth s orbit during the course of one year. Calculate how many hours before midnight you were born = M Subtract Q M = P Because the sky rotates once per day because of the Earth s rota0on. This rule of thumb is good enough to plan what to observe on any night and any astronomer should be able to work out what is roughly overhead on any date/0me as long as they can remember 12 h overhead around midnight on the 21 st March. (Classic viva Q).

9 Exercise 2 What is the approximate loca0on of the Sun in Right Ascension at 5pm on the 23 rd of July. Sun is at 0 h RA on 21 st March at noon Sun is at 0 h +24*(124/365.25) on 23 rd July = 8.15 h or 8 h 08 m s Note in this case we do not factor in any offset for the Earth s rota0on about its axis. The Sun s posi0on in the Celes0al Sphere changes because of the Earth s orbit not the Earth s rota0on (which is irrelevant). The chunk of sky overhead changes because of both the Earth s rota0on an the Earth s orbit

10 Standard Times in Astronomy Local Sidereal 0me (ST) = RA overhead now. Most observatories have Sidereal clocks as well as local 0me clocks Coordinated Universal 0me (UTC or UT1) = Time at Prime Meridian (GMT) Standard Time = wristwatch 0me! (GMT+7 in Perth) What s the 0me is suddenly not such an easy ques0on!

11 Sidereal Time Sidereal day = 23hrs 56m 4s Solar day = 24hrs

12 Kepler s Laws and our Solar System The Astronomical Unit, AU Kepler s Empirical Laws of Planetary mo0on The mass of the Sun, M O. A very brief tour of the solar system Major planets Dwarf planets (defini0on) Minor bodies Asteroid Belt, Trojans, Centaurs TNOs Kuiper Belt Oort cloud The mass distribu0on and abundance of the solar system

13 The Astronomical Unit (AU) Approximately: the mean Sun- Earth distance: x m (i.e., ~1.5x10 11 m or 150 million kilometers) Precisely: Radius of a par0cle in a circular orbit around the Sun moving with an angular frequency of radians per Solar Day (i.e., 2π radians per year) Measured via: Transit of Venus (trad.), Radar reflec0ons from the planets, or the 0me delay in sending radio signals to space missions in orbit around other planets and the applica0on of Kepler s Laws

14 Kepler s Empirical Laws of Planetary Mo0on REMINDER: Defini0on of an ellipse. The set points whose sum of the distances from 2 fixed points (the foci) is a constant. f b a a: semi- major axis b: semi- minor axis e: eccentricity e = f a b = a %1 e 2

15 Kepler s Empirical Laws of Planetary Mo0on REMINDER: Defini0on of an ellipse. The set points whose sum of the distances from 2 fixed points (the foci) is a constant. a f b 2a a a: semi- major axis b: semi- minor axis e: eccentricity e = f a!!!!!!!!

16 Kepler s First Law 1. Each planet moves about the Sun in an ellip0cal orbit, with the Sun at one focus of the ellipse. Perihelion (near Sun) distance: d perihelion = 1 2 (2a! 2 f ) d perihelion = a(1! e) Aphelion (away Sun) distance: d aphelion = d perihelion + 2 f d aphelion = a(1+ e) Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Eccentricity A comet has a perihelion distance of 3AU and an aphelion distance of 7AU. What is the semi- major axis of the ellipse? What is the eccentricity?

17 Kepler s Second Law 2. The straight line (radius vector) joining a planet and the Sun sweeps out equal areas of space in equal intervals of 0me. C B Planet Aphelion D Sun A Perihelion Area Sun- A- B = Area Sun- C- D if planet moves from C to D in same 0me as from A to B.

18 Kepler s Second Law Area = 0.5 r.v o.t = constant From considera0on of areas being swept at Perihelion and Aphelion: v aph v per = ( )*+ (,) h

19 Kepler s Second Law Forced via conserva0on of energy and angular momentum When an object is closer to the Sun the radial gravita0onal force felt is greater (inverse square law) which induces faster circular mo0ons along the orbit path. v perihelion = ( 1+ e)gm (1! e)a, v = ( 1! e)gm aphelion (1+ e)a

20 Keplerʼs Third Law# 3. The squares of the sidereal periods (P) of the planets are proportional to the cubes of the semi-major axes (a) of their orbits: # # ## P 2 = ka 3 ()*h, = 4.2 /0 If we choose the year as the unit of time and the AU as the unit of distance, then k=1.# #

21 Kepler s Third Law - - verifica0on. Planet a in AU P in yr Mercury Venus Earth 1 1 Mars Jupiter Saturn Uranus Neptune

22 Kepler s Third Law - - verifica0on. Planet a in AU P in yr a 3 P 2 Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune

23 Kepler & Newton Newton s Laws of Mo0on and Gravita0on give Kepler s Law: Consider the simple case of a circular orbit, Centrifugal=gravita0onal forces (in equilibrium) => mv 2 r = GMm r 2 P = 2! " = 2!r v => 4! 2 mr => P 2 P 2! r 3 = GMm r 2 Can be shown to hold for ellipses as well via conserva0on of energy and angular momentum where r becomes a the semi- major axis.

24 Mass of the Sun, M o. Kepler s third law allows us to derive the solar mass: 4! 2 P 2 = GM O. r 3 M O = 4! 2 r 3. GP 2 M O. = (4! 2 )(1.5!10 11 ) 3 (6.67!10 "11 )(365.24! 24! 60! 60) 2 M O. = 2.0!10 30 kg Using radar measurement of the AU The solar mass is the standard by which we measure all masses in astronomy, e.g., Milky Way central SMBH = 10 6 M o.

25 Inner planets Rocky

26 Outer planets Gassy

27 Planet sizes to scale (not distances)

28 Our backyard: Geophysics

29 Credit: Anima0on taken From the Minor Planet Centre h]p:// Permission to show granted: Gareth Williams 20/11/11

30 Inner Solar System

31 Major planet Def n: 1. Orbits the Sun 2. Enough gravity to be spherical 3. Master of orbit Dwarf planet Def n 1&2 above 3 Not cleared orbit 4 Not a satelli]e Dwarf planets ~9 known All else: Small solar System bodies. Ceres = planet ( ), then asteroid ( ), now dwarf planet (2006+)!

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33 Kuiper Belt

34 Kuiper Belt s around other stars

35 Oort Cloud: source of comets?

36 Sedna an Oort cloud object?

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38 Mass of solar system Sun: 99.85% Planets: 0.135% (Jupiter 0.09%) Comets: 0.01%? Satelli]es: %? Minor Planets: %? Meteoroids: %? Interplanetary Medium: %?