1. Getting Started A few idle thoughts

2. The Uniqueness of Astronomy Among other things, unfamiliar scales One consequence: non-standard units (partly also for historical reasons) - distances in light-years, parsecs, Mpc - times in years, My, Gy rather than seconds - velocities (often) in km/s - masses and luminosities in solar units - wavelength scales from metres to nm - energies in eV / GeV / TeV (cf particle physics) - Or even less standard! (c = G = 1 units! Masses in km!)

3. Dimensional analysis -Thinking about g g ~ 10 m/sec 2 But why seconds 2 ? It could equivalently be written 36 km/h / sec (i.e. we pick up 36 km/h of speed every second we fall. After 2.7 seconds, we are already falling at highway speed! [100 km/h]) Or write 36 km/sec /h (which tells us that we will be moving at 36 km/s after just one hour of acceleration at a modest 1-g. There’s no need to accelerate fantastically quickly if we can find a way to provide a steady, sustained acceleration)

4. More on dimension Think about the Hubble constant, H o (not strictly a constant: it changes with time, but has a unique value over all space at any given moment. The word ‘parameter’ would be better) If H o = 75 km/sec/Mpc, the implication is that a galaxy 1 Mpc away has a recession velocity of 75 km/sec; an object at twice that distance has twice that velocity; etc - units of inverse time: the ‘expansion age’ of the universe

5. More on H o The dimensionality of H o is velocity/distance = [L/T] / [L] = 1/[T] Noting that 1 Mpc = 3.1 x 10 19 km, we can ‘cancel out’ the kms and get H o = (75 / 3.1 x 10 19 ) sec -1 So 1/H o = 4.1 x 10 17 sec ~ 13 billion years This is the ‘Hubble time’, or (in the absence of any deceleration or acceleration) the time that has elapsed since the universal expansion began: that is, the ‘age of the universe’

6. Periods for Satellites For an orbiting satellite P will be some function of G, M, and R (M = mass of body being orbited; R = distance; G = G!) Write P = G α M β R γ and solve for α,β,γ by dimensional analysis. [P], the dimensionality of P, is time [T]. [R], the dimensionality of R, is length [L]. [G], the dimensionality of G, is [L] 3 [M] -1 [T] -2

7. [P] = [L 3α ] [M -α ][T -2α ] [M β ] [L γ ] = [T] Look at T to deduce -2α = 1, so α = -1/2 Look at M to deduce β-α = 0so β = α = -1/2 Look at L to deduce 3α + γ = 0 so γ = -3α = 3/2 Consequently P depends on G -1/2 M -1/2 R 3/2 so P goes like 1/ ( √G √ (M/R 3 ) ) or, in short, P goes like 1 / sqrt (G x density) In other words, the ‘dynamical time scale’ is set by “1 over root-G-rho” SO: if we skim the surface of a tiny rocky asteroid that has the same mean density as the Earth, it will take the same period (~90 min) as a low-altitude satellite like the ISS orbiting the Earth. (Obviously it moves much more slowly around the asteroid, but the periods are the same!) Note: the larger G is, the shorter the timescale (makes sense). Likewise, the denser the object, the shorter the period.

8. Angular measure - radian: definition and implications - the parsec by definition: review this! - simple conversions 1 radian ~ 57.3 degrees 1 radian ~ 2 x 10 5 seconds of arc

9. Angular size / solid angle - steradians

10. The Whole Sky = 4 π steradians = 4 π (57.3) 2 square degrees = 41,259 square degrees ~ 160,000 full moons

11. Surveys Palomar Sky Survey: (Schmidt telescope) plates are 6.6 degrees on a side full sky survey requires ~1000 plates or more

12. Largest angular sizes studied? The whole sphere, for things like large-scale structure in cosmology (structure in the microwave background) A large swath across the sky, for something like the Milky Way But for most objects, the angular size is at most a couple of degrees (e.g. M31, the Andromeda galaxy) and usually very much less

13. Various image sizes

14. Small Field of View The Hubble Telescope ACS (Advanced Camera for Surveys) has a field which is 202 x 202 arcsec I radian is ~ 2 x 10 5 arcsec, so the ACS has a field of 0.001 x 0.001 radians 0.001 radians is the angle subtended by a 1 mm object (a grain of rice) a metre away – that is, at arm’s length The ACS area is about 10 -6 steradians, so a full-sky survey would require ~ 13 million pointings in each filter

15. One Such Microscopic Pointing: The HST Ultra-Deep Field