PHYS1002: Foundaons of

• [email protected] • Course Text: Astronomy: A Physical Perspecve, Marc Kutner • 9 Lectures + 2 Assessments + Final Exam • New course component • Exams will be similar to tutorial sheets. Lecture outline

1. Astronomical Coordinates: The Astronomical sky, Kepler’s Laws, the 2. Flux & Distance: Magnitudes, magnitudes, , and distance

3. Stellar nucleosynthesis: Fusion, the CNO cycle 4. Properes of : The Hertzsprung-Russell diagram, stellar lifecycle

5. : morphological types, number of stars, space density, distribuon 6. spectra: spectra, moon, inclinaon and peculiar velocies 7. Dark Maer: The virial theorem, galaxy rotaon curves, galaxy formaon

8. Expansion: Olber’s Paradox, Hubble’s Law and the expanding Universe 9. Cosmology: The Cosmological Principle, the Hot Big Bang, Dark Energy The Astronomical Sky • On a human lifeme the Celesal Sphere is frozen • As the Earth rotates the celesal sphere appears to move – We can photograph trails (24hrs for one 360 degree rotaon)

• As the Earth orbits the – The stars visible in the night sky change over the course of the year (different constellaons become visible) Equatorial Coordinates

• At a fixed me in the Earth’s orbit we project our latude and longitude system onto the sky and call these Right Ascension and Declinaon – Longitude = Right Ascension: 0 – 24 hours [or 0 degrees to 360 degrees.] – Latude = Declinaon: -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 ~ 21st March – Autumnal Equinox ~ 21st September

• Because the Earth’s orbit precesses (once every 26,000 years) the first point of Aries moves along the eclipc# (1 deg per 78 years). NB: Sun now in Pisces at Vernal Equinox

• Astronomers work to either the 1950 or 2000 projecon denoted B1950.0 or J2000.0

*Equinox: When the Earth’s axis of inclinaon neither points towards or away from the sun. #Eclipc: The plane of the Earth’s rotaon around the Sun.

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 projecon.

• The equator is projected to become the Celesal equator, i.e., 0o declinaon

• This grid is then frozen onto the Celesal Sphere and used to define posions of the fixed objects.

• E.g., M31: 00h44m37.99s, +41o16’9’’, J2000.0

E.g., What RA is overhead at 10pm tonight?

• On the Vernal Equinox: 0h RA is overhead at noon • Hence stars with coordinates ~12h will be overhead at midnight • The Earth completes one rotaon during the year • What is overhead moves on by: – 1h per hr • What is overhead at midnight moves on by: – 2h per month

• 29th July is (roughly) 4 months aer the Vernal Equinox, hence tonight we will have stars with coordinates at ~20h overhead at midnight

• 10pm is two hours before midnight so we will have stars with coordinates 18h overhead at 10pm tonight.

Exercise 1 • Calculate what coordinates were overhead at the date/me of your birth?

• Path: – Calculate how many days your birthday is aer 21st March = N

– Add 12h+24hxN/365.25 = Q Because the sky completes one rotaon 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 rotaon.

• 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/me as long as they can remember 12h overhead around midnight on the 21st March. (Classic viva Q). Exercise 2

• What is the approximate locaon of the Sun in Right Ascension at 5pm on the 23rd of July. – Sun is at 0h RA on 21st March at noon – Sun is at 0h+24*(124/365.25) on 23rd July = 8.15h or 8h 08m 52.24s

• Note in this case we do not factor in any offset for the Earth’s rotaon about its axis. – The Sun’s posion in the Celesal Sphere changes because of the Earth’s orbit not the Earth’s rotaon (which is irrelevant). – The chunk of sky overhead changes because of both the Earth’s rotaon an the Earth’s orbit Standard Times in Astronomy

Local Sidereal me (ST) = RA overhead now.

Most observatories have Sidereal clocks as well as local me clocks

Coordinated Universal me (UTC or UT1) = Time at Prime Meridian (GMT)

Standard Time = wristwatch me! (GMT+7 in Perth)

What’s the me is suddenly not such an easy queson!

Sidereal Time

Sidereal day = 23hrs 56m 4s

Solar day = 24hrs

Kepler’s Laws and our Solar System

• The , AU • Kepler’s Empirical Laws of Planetary moon

• The of the Sun, MO. • A very brief tour of the solar system • Major planets • Dwarf planets (definion) • Minor bodies • Belt, Trojans, Centaurs • TNOs • Kuiper Belt • Oort cloud • The mass distribuon and abundance of the solar system The Astronomical Unit (AU)

• Approximately: the mean Sun-Earth distance: – 1.495978707003 x 1011m (i.e., ~1.5x1011m or 150 million kilometers)

• Precisely: Radius of a parcle in a circular orbit around the Sun moving with an angular frequency of 0.01720209895 radians per Solar Day (i.e., 2π radians per year)

• Measured via: Transit of Venus (trad.), Radar reflecons from the planets, or the me delay in sending radio signals to space missions in orbit around other planets and the applicaon of Kepler’s Laws Kepler’s Empirical Laws of Planetary Moon • REMINDER: Definion of an ellipse. The set points whose sum of the distances from 2 fixed points (the foci) is a constant.

b f a a: semi-major axis b: semi-minor axis e: eccentricity f 2 e = b = a ⋅ 1 − e a Kepler’s Empirical Laws of Planetary Moon • REMINDER: Definion of an ellipse. The set points whose sum of the distances from 2 fixed points (the foci) is a constant.

a b f a a: semi-major axis 2a b: semi-minor axis e: eccentricity f ! e = ! ! ! ! ! ! ! a Kepler’s First Law 1. Each planet moves about the Sun in an ellipcal orbit, with the Sun at one focus of the ellipse.

Perihelion (near Sun) distance: Eccentricity 1 Mercury 0.205 d = (2a ! 2 f ) perihelion 2 Venus 0.007 Earth 0.017 dperihelion = a(1! e) Mars 0.094 Aphelion (away Sun) distance: 0.049 0.057 daphelion = dperihelion + 2 f Uranus 0.046 daphelion = a(1+ e) Neptune 0.011 A 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? 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 me.

B Planet C

D A Aphelion Perihelion Sun

Area Sun-A-B = Area Sun-C-D if planet moves from C to D in same me as from A to B. Kepler’s Second Law

• Area = 0.5 r.vo.t = constant • From consideraon of areas being swept at Perihelion and Aphelion: vaph = vper ℎ

Kepler’s Second Law

• Forced via conservaon of energy and angular momentum • When an object is closer to the Sun the radial gravitaonal force felt is greater (inverse square law) which induces faster circular moons along the orbit path.

1+ e GM 1! e GM v = ( ) , v = ( ) perihelion (1! e)a aphelion (1+ e)a 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:

2 2 3 4 P = ka ℎ = ⊙

If we choose the year as the unit of time and the AU as the unit of distance, then k=1. Kepler’s Third Law -- verificaon.

Planet a in AU P in yr Mercury 0.387 0.241 Venus 0.723 0.615 Earth 1 1 Mars 1.524 1.881 Jupiter 5.203 11.86 Saturn 9.539 29.46 Uranus 19.18 84.01 Neptune 30.06 164.8 Kepler’s Third Law -- verificaon.

Planet a in AU P in yr a3 P2 Mercury 0.387 0.241 0.058 0.058 Venus 0.723 0.615 0.378 0.378 Earth 1 1 1.000 1.000 Mars 1.524 1.881 3.540 3.538 Jupiter 5.203 11.86 140.9 140.7 Saturn 9.539 29.46 868.0 867.9 Uranus 19.18 84.01 7056 7056 Neptune 30.06 164.8 27162 27159 Kepler & Newton

• Newton’s Laws of Moon and Gravitaon give Kepler’s Law: • Consider the simple case of a circular orbit, Centrifugal=gravitaonal forces (in equilibrium) => m v2 GMm = Can be shown to hold for ellipses as well r r2 via conservaon of energy and angular 2! 2!r momentum where r becomes a the P = = semi-major axis. " v => 4! 2mr GMm = P2 r2 => P2 ! r3 Mass of the Sun, Mo.

• Kepler’s third law allows us to derive the solar mass:

2 4! GM . = O P2 r3 4! 2r3 MO. = GP2 (4! 2 )(1.5!1011)3 MO. = (6.67!10"11)(365.24 ! 24 ! 60 ! 60)2 30 MO. = 2.0 !10 kg

• Using radar measurement of the AU • The solar mass is the standard by which we measure all 6 in astronomy, e.g., central SMBH = 10 Mo. Inner planets • Rocky Outer planets • Gassy Planet sizes to scale (not distances) Our backyard: Geophysics Credit: Animaon taken From the Minor Planet Centre hp://www.minrplanetcentre.net

Permission to show granted: Gareth Williams 20/11/11 Inner Solar System 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 satellie

Dwarf planets ~9 known

All else: Small solar System bodies.

Ceres = planet (1801-1846), then asteroid (1847-2006), now dwarf planet (2006+)!

Kuiper Belt Kuiper Belt’s around other stars Oort Cloud: source of ? Sedna an Oort cloud object?

Mass of solar system

• Sun: 99.85% • Planets: 0.135% (Jupiter 0.09%) • Comets: 0.01%? • Satellies: 0.00005%? • Minor Planets: 0.0000002%? • Meteoroids: 0.0000001%? • Interplanetary Medium: 0.0000001%?