PHYS2220: Founda/ons of Astronomy

Transcription

1 PHYS2220: Founda/ons of Astronomy Course Text: Astronomy: A Physical Perspec/ve, Marc Kutner 13 Lectures + 1 Class Exercise + 4 Tutorial Sheets + Final Exam Final Exam = 50% Tutorial Sheets = 10% each Class Exercise = 10% each New course component, exams will be similar to tutorial sheets.

2 Lecture outline Astronomical Coordinates: The Astronomical sky Planetary Mo/on: The Solar System and Kepler s Laws Flux & Distance: magnitudes and parallax Stellar nucleosynthesis: Fusion, the CNO cycle Proper/es of Stars: The Hertzsprung- Russell diagram Stellar lifecycle: Stellar rota/on and the Galac/c Centre (SMBH) 7. The structure of our galaxy: Our Galaxy and its components Galaxies: morphological types, number of stars, space density, distribu/on Galaxy spectra: spectra, mo/on, inclina/on and peculiar veloci/es Dark Macer: The virial theorem, galaxy rota/on curves, galaxy forma/on Black Holes and AGN: Black holes, Quasars, AGN Unifica/on Expansion: Olber s Paradox, Hubble s Law and the expanding Universe Cosmology: The Cosmological Principle, the Hot Big Bang, Dark Energy

3 The Astronomical Sky On a human life/me the Celes/al Sphere is frozen As the Earth rotates the celes/al sphere appears to move We can photograph star trails (24hrs for one 360 degree rota/on) As the Earth orbits the Sun The stars visible in the night sky change over the course of the year (different constella/ons become visible)

4 Equatorial Coordinates At a fixed /me in the Earth s orbit we project our la/tude and longitude system onto the sky and call these Right Ascension and Declina/on Longitude = Right Ascension: 0 24 hours [or 0 degrees to 360 degrees.] La/tude = Declina/on: - 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 precesses (once every 26,000 years) the first point of Aries moves along the eclip/c # (1 deg per 78 years). NB: nowdays Sun in Pisces during Vernal Equinox Astronomers work to either the 1950 or 2000 projec/on denoted B or J *Equinox: When the Earth s axis of inclina/on neither points towards or away from the sun. # Eclip/c: The plane of the Earth s rota/on 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 la/tude 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 projec/on. This grid is then frozen onto the Celes/al Sphere and used to define posi/ons of the fixed objects. E.g., M31: 00 h 44 m s, +41 o 16 9, J2000.0

7 E.g., What 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 rota/on during the year Whats overhead moves on by: 1 h per hr Whats overhead at midnight moves on by: 2 h per month 15 th Sept is almost 6 months awer the Vernal Equinox, hence tonight we will have stars with coordinates at ~0 h overhead at midnight 10pm is two hours before midnight so we will have stars with coordinates 22 h overhead at 10pm tonight.

8 Exercise 1 Calculate what coordinates were overhead at the date//me of your birth? Path: Calculate how many days your birthday is awer 21 st March = N Add 12 h +24 h xn/ = Q Because the sky completes one rota/on 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 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 12 h overhead around 21 st March. (Classic viva Q).

9 Exercise 2 What is the approximate loca/on 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*(122/365.25) on 23 rd July = 8.02 h or 8 h 00 m s Note in this case we do not factor in any offset for the Earth s rota/on about its axis. The Sun s posi/on in the Celes/al Sphere changes because of the Earth s orbit not its rota/on. The chunk of sky overhead changes because of the Earth s rota/on.

10 Planning your observa/ons How long can I observe my target for? This depends on the target s declina/on rela/ve to your la/tude Seeing and transparency degrade rapidly at sec Z > 2. Wait /ll star has risen to Z = 60 degrees, i.e. al/tude 30 degrees. How much longer does it take to reach the meridian? It will take the same /me again from meridian crossing to se{ng below 30 degrees. Z=Zenith angle, angle from zenith to towards horizon, 0 0 =overhead

11 The Meridian A great circle divides the sky exactly into 2 hemispheres. The meridian is the great circle that runs overhead through the zenith Z and the celes1al pole P. Angle PZ = 90 - la/tude φ Z P

12 Right Ascension and Declina/on RA is the equivalent of longitude on the sky Line of constant RA is a great circle running through star S and pole P. Angle SP = 90 - declina/on, δ Z P S

13 Hour Angle The meridian intersects with a line of constant RA through the star, at the pole. The angle H = ZPS is the hour angle of the star. Nega/ve when star is east of the meridian Posi/ve when star is west of the meridian Increases with /me. Z H P S

14 Al/tude, Zenith distance & Airmass Draw a third great circle through zenith Z and star S. Angle ZS is the zenith distance z of the star. Al/tude = 90 - z Airmass Airmass = sec z [where sec z = 1/cos z] 1.00 = overhead 1.41 = 45 degrees Zenith angle 2.00 = 60 degrees Zenith angle 3.00 = 70.5 degrees Zenith angle P S z Z H

15 Spherical triangles: the essen/als All three sides are great circles. Sine rule: sin a sin A = sin b sin B = sin c sin C Cosine rule: cosc = cos a cosb + sin a sin bcosc B c C A

16 When is star at a given zenith distance? We know the angles ZP, PS and ZS need to know the hour angle H. cos z = cos(90 " #)cos(90 " $) + sin(90 " #)sin(90 " $)cos H % cos z = sin # sin$ + cos# cos$ cos H. So use cosine formula: Z z H P S

17 How many hours above 2 airmasses (al/tude of 30 o )? Cosine formula gives H in degrees: cosh = cosz! sin! sin" cos! cos" Divide H by 15 to convert to hours (i.e., 360 degrees = 24 hours) Object rises above 2 airmasses when z=60 deg. H gives /me un/l meridian crossing Object is observable for twice this dura/on

18 Example The GAMA9hr field is at RA=9 h and Dec=0 o, es1mate: When would be the best date to observe this field? If observed from the Anglo- Australian Telescope, how long would this object be at more than 30 degrees above the horizon per night? If observed on the 1 st Feb at what local /me would this field rise above 30 o and at what local /me would it set below 30 o? The AAT is at Siding Springs Observatory, NSW Longitude =149.1 o East of Meridian La/tude = 31.3 o South of Equator [Al/tude = 1150m above Sea Level] not required for this ques/on

19 Solu/on to example Knowns: Z=60 o φ= o δ=0.0 o RA=9 h Best /me to observe field: 12 h overhead on 21 st March (Vernal Equinox) Sky moves on 2hrs per month 9hrs overhead would be 1.5months earlier Best /me to observe would be approximately 7 th Feb Time above 30degrees: Use formulae to find Hour angle (H): cosh=(cosz- sinφsinδ)/cosφcosδ cosh=(cos(60)- sin(- 31.3)sin(0))/cos(- 31.3)cos(0)

20 cosh=0.585 H=54 o Earth rotates once every ~24hrs, i.e., 1hr=15 degrees Therefore it will take 3.6hrs to rise from Z=60 to the meridian And another 3.6hrs to fall from the meridian to Z=60 Object will spend 7.2hrs above Z=30 At what local /me would the object rise and set on 1 st Feb: RA overhead on 7 th Feb is ~9h (see answer to part1) RA overhead on 1 st Feb is ~8.5h (2hr per month so ~0.5hr per week) Object therefore overhead on 1 st Feb at half past midnight Rises 3.6hrs earlier = 8.9pm or 8:54pm Sets 3.6hrs later = 4.1am or 4:06am Note: Precise answers will vary because: Equinox is not exactly midnight 21 st March (varies each year), Earth takes slightly less than 24hrs to rotate, need to calculate offset due to Earth s orbit precisely. However Astronomers should be able to make ballpark es/mates like the above to plan their observa/ons and use online tools if they need greater precision.

21 What /me does a star rise/set? You ve already worked out the hour angle H when the star rises above Z = 60 deg. H is nega/ve when star rises, posi/ve when it sets. Rises/sets (>/< 30deg above horizon) Local standard /me = RA - LST midnight +/- H 60 All values are approxima/ons but good enough to plan observa/ons In prac/ce many tools online to calculate them accurately for any object A good App for Macs is: iobserve

22 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 ques/on!

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

24 Siding Springs Observatory Anglo- Australian Telescope 3.9m Built 1963 Responsible for 40% of all known redshiws Australia s main onshore op/cal observatory Warrumbungle Na/onal Park Near Coonabarabran

25 Anglo- Australian Telescope (AAT)