CLASSNOTES 2
Chapter 1

Read this chapter carefully. The sequence of Figures 1-1 to 1-12 are especially informative. Three natural systems may be identified:

• the Solar System: Sun plus nine planets plus miscellaneous pieces
• the Galaxy: billions of stars plus gas and dust and
• the Universe: billions of galaxies plus...

Consider the questions on page 8. The problems on page 8 are on the whole too mathematical for us. But I suggest you think about no. 4 and 5.

Scientific Notation
Seeds introduces this on page 4 and in more detail in Appendix A. Here, adapted from another text, is another introduction:

Powers-of-ten notation (also called scientific notation) is a shorthand method for expressing and working with very large or very small numbers. With this method, we express numbers as a few digits times ten to a power, or exponent. The power indicates the number of times that ten is multiplied by itself. For example, 100 = 10 x 10 = 10². Similarly, 1,000,000 = 10 x 10 x 10 x 10 x 10 x 10 = 10⁶. Note that we do not need to always write out 10 x... Instead, we can simply count the zeros. Thus, 10,000 is 1 followed by 4 zeros so it is 10⁴.
We can write 1 and 10 itself in power-of-ten notation as well:1 = 10⁰ and 10 = 10¹.
To write a number like 300, we break it into two parts 3 x 10². Similarly, we can write 352 = 3.52 x 10².
We can also write very small numbers (numbers less than 1) using powers of ten. For example, 0.01 = 1/100 = 1/10². We can make this even more concise, however, by writing 1/10² as 10^-2. Similarly, 0.0001 = 10^-4. Note that for numbers less than 1, the power is 1 more than the number of zeros.
We can write a number like 0.00052 as 5.2 x 0.0001 = 5.2 x 10^-4.

Suppose now we want to multiply numbers expressed in powers of ten. The rule is simple: we add the powers. Thus 10³ x 10² = 10⁵. Similarly, 2 x 10⁸ x 3 x 10⁷ = 2 x 3 x 10⁸ x 10⁷ = 6 x 10¹⁵. In general, 10^a x 10^b = 10^a+b.
Division works similarly, except that we subtract the exponents. Thus 10⁵/10³ = 10^5-3 = 10². In general 10^a/10^b = 10^a-b.

Contents of the Universe

Nearest 50 AU
The astronomical unit (1 AU) is the semi-major axis of the Earth's orbit around the Sun (mean Earth-Sun distance = 150 x 10⁶km). For us, semi-major axis is equivalent to the radius. All planets are within ~ 40 AU of the Sun. A few spacecraft have gone beyond 50 AU.

Nearest 5 parsecs
The parsec (1 pc) is the distance at which 1 AU subtends an angle of 1 arcsec:
1 pc 2 x 10⁵ AU 3 x 10¹³km 3 light years
Nearest star (at ~ 1.3 pc): Proxima Centauri, currently the nearest member of the triple system Centauri.

Other stars:
--well spaced out, interstellar space is very empty. Mean distance between stars
~ 1 pc ~ 4 x 10⁷ their radius (don't collide within lifetime of Galaxy, ~ 10¹⁰ years);
--majority are fainter, cooler, and of lower mass than the Sun;
--about half are double or multiple systems.
Space between stars: contains gas and dust. Gas may be cold or hot, dense or tenuous.

Nearest 20 kpc (1 kiloparsec = 10³pc)
--includes most of Milky Way (our local Galaxy);
--mostly stars: single, double, multiple and clusters, containing from
a few hundred stars (open or galactic clusters) to 10⁵ -10⁶ stars (globular
clusters). Total: ~ 10¹¹ - 10¹² stars;
--gas and dust (~10% by mass);
--high-energy particles (cosmic rays) and magnetic field.

The structure of the Milky Way is a flattened, smooth star distribution (disc) plus a low-density, roughly spherical halo. The Sun is in the mid-plane, about 8 kpc from the center, and dust hides the center in the optical (the center, in the constellation of Sagittarius, is visible in the infrared and radio). Bright stars and gas are concentrated in spiral arms. The gas is clumped in clouds, though there is also a diffuse
background of gas.

Nearest megaparsec (10⁶pc)
Most galaxies form part of a group or cluster of gravitationally bound galaxies. Our Local Group (radius ~ Mpc) contains two dominant and similar galaxies, the Milky Way and Andromeda, each of mass ~ 10¹¹ M. Each has several satellites:

• Milky Way -- closest satellites are Large and Small Magellanic Clouds (LMC, SMC), at ~ 55 kpc; both are irregular in shape;
• Andromeda -- main satellite is a spiral galaxy.

There are about 20 other galaxies, mostly small (10⁶-10⁹ M O) and either irregular or elliptical in shape.

Irregulars -- lots of gas, dust and young stars;
Ellipticals -- almost no gas or dust, old stars, smooth shape.

Note that galaxies are much closer together, compared to their size, than stars: Milky Way to Andromeda ~ 600 kpc ~ 50 R_Gal. Collisions between galaxies occur.

Nearest 20 Mpc
Beyond the Local Group, other small groups, and larger clusters, are clustered together into the Local Supercluster, centered on the Virgo cluster within about 15 Mpc.

Nearest 100 Mpc
Many groups and clusters appear, some in other superclusters. We begin to detect:
--large-scale structure of the Universe: galaxies found in filaments and sheets,
at the boundaries of voids, which are empty of galaxies, or nearly so;
--a general expansion of the Universe, following Hubble's law:

v_expansion = H₀d

V _expansion is a galaxy's velocity of recession, d is its distance and H₀ is Hubble's constant, whose value lies in the range 50-100 km s^-1 Mpc^-1.

Nearest 10⁴ Mpc (radius of observable Universe)
Galaxies (faint!) are seen to distances of about 3000 Mpc. Quasars -- probably energetic nuclei of galaxies -- are seen to greater distances.

Our horizon is set by the fact that light, our source of information about remote objects, travels at a finite speed. The Universe is approximately 12 billion years old. This means that light now reaching us can have travelled at most 12 billion light years, or about 4 billion parsecs which is the same as 4Mpc.

Thus, the observable Universe extends to about 10⁴Mpc.

Roughly,

1 pc = 3 ly = 200,000 AU

Of course, we also use kilometer, etc.

Since some distances are enormous, we use abbreviations such as kpc and Mpc (see Seeds Table A-1, p.425)
where

1 kpc = 1000 pc
1 Mpc = 10⁶ = 1,000,000 pc.

We'll discuss these three measures in subsequent classes. But remember a light year is a measure of DISTANCE not time.

Time and the Universe
Our discussion of the Universe not only spans great distances but also long time intervals. The Universe is about 12 billion years old. Figure 1-15 from The Cosmic Perspective by Bennett et al. shows a cosmic calendar scaled to 1 year 12 billion years. Human civilization spans the last minute of the last day.

"Mandalay is rather a disagreeable town -- it is dusty and intolerably hot, and it is said to have five main products all beginning with P, namely pagodas, pariahs, pigs, priests and prostitutes." If anything attracted his interest in the city, it was the seamy side, not the relatively genteel world of Beadon and the regulars at the Upper Burma Club. He made a point of getting to know the most disreputable Englishman in Mandalay, a former army captain who had been dismissed from the military police and was leading the life of an opium addict. The man, whose name was Captain H.R. Robinson, would tell anyone who would listen that he had discovered the secret of the universe. It was all contained in a single sentence but he could never remember it after his opium trances were over. During a long crazy night of dreaming about this secret, he managed to write down the pearl of wisdom, but when he looked at in the morning, all it said was, 'The banana is great, but the skin is greater.'"

George Orwell, Burmese Days

 

Over the semester, we shall discuss 'the secret of the universe' unravelled by astronomical observations. We shall also discuss secrets not yet unravelled; for example, 90% or more of the mass in the universe has yet to be seen by telescopes. This 'dark matter' is the leading problem in contemporary astronomy.