Getting Started

A few idle thoughts

The Uniqueness of AstronomyAmong 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!)

Dimensional analysis- Thinking about g

g ~ 10 m/sec2 But why seconds2 ?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)

More on dimension

• Think about the Hubble constant, Ho (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 Ho = 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

More on Ho

The dimensionality of Ho is velocity/distance = [L/T] / [L] = 1/[T]

Noting that 1 Mpc = 3.1 x 1019 km, we can ‘cancel out’ the kms and get

Ho = (75 / 3.1 x 1019) sec -1

So 1/Ho = 4.1 x 1017 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’

Periods for SatellitesFor 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 = Gα Mβ Rγ 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

[P] = [L3α] [M-α][T-2α] [Mβ] [Lγ] = [T]

Look at T to deduce -2α = 1, so α = -1/2Look at M to deduce β-α = 0 so β = α = -1/2Look at L to deduce 3α + γ = 0 so γ = -3α = 3/2

Consequently P depends on G-1/2 M-1/2 R3/2

so P goes like 1/ ( √G √ (M/R3) )

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.

Angular measure

- radian: definition and implications

- the parsec by definition: review this!

- simple conversions1 radian ~ 57.3 degrees1 radian ~ 2 x 105 seconds of arc

Angular size / solid angle

- steradians

The Whole Sky

= 4 π steradians= 4 π (57.3)2 square degrees = 41,259 square degrees~ 160,000 full moons

Surveys

• Palomar Sky Survey: (Schmidt telescope)

• plates are 6.6 degrees on a side

• full sky survey requires ~1000 plates or more

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

Various image sizes

Small Field of ViewThe Hubble Telescope ACS (Advanced Camera for Surveys) has a field which is 202 x 202 arcsec

I radian is ~ 2 x 105 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

One Such Microscopic Pointing:The HST Ultra-Deep Field