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The Scale of the Cosmos

Little round planet
In a big universe
Sometimes it looks blessed
Sometimes it looks cursed
Depends on what you look at obviously
But even more it depends on the way that you see

from Child of the Wind, Bruce Cockburn (1991)

We live in an enormous universe! A major part of this course is devoted to finding out just where we are in relation to the stars and other celestial phenomena. Prepare to be amazed! One of the most challenging parts of learning astronomy is coming to terms with both the enormity of the universe and the huge range in size (scales) that are needed to comprehend this wonderful and mysterious cosmos. In this course you will find yourself going from the unbelievably small world of the atomic nucleus to the vast expanses of nearly empty space between galaxies. Along the way you will learn how to use units of measure appropriate to these scales.

The Universe - A BIG Place!

By the end of the 19th century it was becoming clear just how enormous our universe is. This had direct impact in culture and helped to shape our understanding of ourselves in relationship to the rest of the world. As an example consider the writing of Thomas Hardy and his book Two on A Tower, published in 1882. In this book he explores love between two very different social classes (with the usual cheery end of most Hardy novels!). He also introduces the dread that living in such a vast universe casts on us all. In the following excerpt, Lady Constantine and Swithin St.Cleve discuss the immensity of the universe:

	'We are now traversing distances beside which the immense line stretching from the earth to the sun is but an invisible point',said the youth. 'When just now, we had reached a planet whose remoteness is a hundred times the remoteness of the sun from the earth, we were only a two thousandth part of the journey to the spot at which we have optically arrived now.' 'O pray don't; it overpowers me!' she replied, not without seriousness. 'It makes me feel that it is not worth while to live; it quite annihilates me.''If it annihilates your ladyship to roam over these yawning spaces just once, think how it must annihilate me to be, as it were, in constant suspension amid them night after night.'
Figure 1.1 Cover of the late 19th century novel Two on a Tower
This "cosmic angst" has been with us for more than a century and has clearly contributed to our thought of "who we are". Consider the chilling conclusion of Jacques Monod"
“Man knows at last that he is alone in the universe’s unfeeling immensity, out of which he emerged only by chance”
	Chance and Necessity, 1970

The following applet summarizes some of this for you. How we determined these distances will occupy us in future lectures.

Figure 1.2 Interactive applet that takes you on a "tour" of the cosmos from the sub-nuclear realm to the edge of the universe.

Technical Stuff

If you spent just a few minutes with the applet in Figure 1.2 you will have seen a variety of terms used to express the different length scales. Table 1.1 summarizes the conventional units used and relates these to "powers of 10". Recall how powers of 10 work:

Getting the Right Units for the Job!

10^N means 1 followed by N zeroes

10^-N means a decimal and then 1 moved N spaces over (and preceded by zeroes)

Realm	Exponent Power of 10(m)	Unit	Unit Prefix Name
	-18	am	atto
Nuclear	-15	fm	femto
Atomic to Cellular	-12	pm	pico
	-9	nm	nano
	-6	um	micro
Human Scale
	-3	mm	milli
	-2	cm	centi
	0	m
	3	km	kilo
Astronomical	6	Mm	Mega
	9	Gm	Giga
	12	Tm	Tera
	15	Pm	Peta
	18	Em	Exa
	21	Zm	Zetta
	24	Ym	Yotta
Table 1.1

Example 1.1 What are the following: a) 10⁷ in long form, b) 10^-4 in long form, c) 1000 expressed in power of 10 form, d) 0.00001 expressed in power of ten form

Solution: a) 10⁷ is 1 followed by 7 zeroes so 10 000 000 or ten million; b) 0.0001 or 1 ten thousandth, c) 10³, d) since the 1 is shifted 5 spaces over it is 10^-5.

Scientific Notation and the Exponent Rules

Throughout the course we will deal with large numbers. Mathematicians and astronomers have developed scientific notation to help facilitate this. For example, instead of writing the distance between the Earth and sun as 149 000 000 000 m it is much easier to express this as either 149 Gm ("one hundred forty nine Giga metres") or as:

Using scientific notation also simplifies mathematical computation and follows a number of simple rules summarized in Table 1.2.

Operation	Rule	Example
Multiplication	add exponents
Division	subtract exponents
Raising to a power	multiply exponent by power
Taking a root	divide exponent by power
Adding/Subtracting	convert both numbers to same exponent then add/subtract
Table 1.2

Other Useful Units...

Table 1.3 summarizes a number of useful constants and units along with there definitions:

Unit Name	Symbol	Conversions	Definition
speed of light	c	c = 3 x 10⁸ m/s c = 3 x 10⁵ km/s	speed of light
year	y or a	1 y = 365.25 days 1 y = 3.16 x 10⁷ s	length of year
day	d	1 d = 86 400 s	length of day
Astronomical Unit	AU	1 AU = 1.496 x 10¹¹ m	average Earth-Sun separation
Light Year	ly	1 ly = 9.46 x 10¹⁵ m	distance light travels in 1 year
Table 1.3 Useful units and conversions

When is Now?

Light travels at an enormous speed (300 thousand km/s), but the universe is vast. Look at the stars tonight - the light reaching your eyes has been travelling for decades or longer. In astronomy, we encounter a wonderful "puzzle" - we never see the universe as it "is," only as it was! Understanding this puzzle is what we focus on here.

Light Years and the Idea of "Look-back Time"

Vega, a bright star in the summer sky, is 25.3 light years away from Earth. What exactly does this mean? We answer this by starting with the definition provided in Table 1.3 of the previous section: a light-year is the distance that light travels in 1 year. Saying that Vega is 25.3 light years away tells us that light requires 25.3 years of travel time to get from Vega to you. In other words, the light you see tonight from Vega is 25.3 years old - it's like looking back in time! We call this the "Look-back Time" effect.

Example 1.2: How long does it take light to travel from the Sun to us?

Solution: To calculate this, we need the speed of light (c = 3 x 10⁸ m/s), and the distance between the Earth and the Sun (1 AU = 1.496 x 10¹¹ m).

The look-back time effect poses some interesting problems for space exploration - even within our solar system. Consider the following example.

Example 1.3: How long would the following conversation take if you were ground control talking to an astronaut preparing to leave orbit and descend to Mars? At the time of the conversation, Mars was 1.9 AU from Earth. Assuming each sentence takes one second? Assuming transmission occurs at the speed of light?

Ground Control: Mars Lander - do you copy?
Mars Lander: Roger that.
Ground Control: Do not initiate landing procedure. Repeat - do not initiate landing procedure.

Solution: For this calculation, we need the speed of light (c = 3 x 10⁸ m/s), and the distance between Mars and Earth (1.9 AU; 1 AU = 1.496 x 10¹¹ m). Each part of the transmission requires the following amount of time to reach the listener:

Therefore, this conversation would require 3 X 15.8 = 47.4 minutes!!

Practice

What is the most appropriate unit of distance to when expressing distances to nearby stars? Provide several examples (Hint: use Stellarium.)
Venus is, on average, 0.723 AU away from the sun. Express this distance in km.
You are a technical reviewer for a Mars rover project. The plan calls for a rover-mounted camera that would enable an earth based "driver" to make any last moment corrections to the motion of the rover if an emergency should arise. Why is this "plan" seriously flawed? How far is Mars, on average from the sun (express the answer in both AU and km)?
Estimate the closest that Neptune approaches the earth. Express this in both AU and km.
Use Stellarium to find the distance to the star Deneb (part of the Summer Triangle). How long would it take to travel to Deneb if you could travel at the speed of light?

The Virgo Cluster is a "nearby" cluster of galaxies that you can see with a medium-sized telescope. The Virgo Cluster is only about 65 million light years away! How far back in time are you looking when you see the Virgo Cluster?

To understand the scale of the cosmos and appropriate ways to describe this