ASTR 1210 (O'Connell) Study Guide
1. INTRODUCTION: SCIENTIFIC DISCOVERY
AND THE SCALE OF THE UNIVERSE
The European Southern Observatory Very
Large Telescope, Chile.
This introductory lecture places astronomy in the broader context of
science. It discusses the nature of science, how science is
distinguished from other modes of thought, the difference between
science and technology, and some of the main results of science.
Astronomy has had a strong influence on other sciences and defines the
limits of the scientific universe. We will illustrate some of the
mind-boggling cosmic spatial and temporal scales revealed by
A. What is Science?
Science is the systematic understanding of empirical
"Empirical" = experienced or observed
Science is both a body of knowledge and a way of thinking.
Scientific values & methods are relatively new in human
history, starting ca. 1500 AD.
- Logical; rational
- Clear, orderly; choose the simplest alternative ("Occam's razor")
- Cumulative development
New interpretations are required to be consistent with all established
Given all that we now know about nature, this is a tremendously challenging requirement!
- Science is based on an empirical criterion
of truth: ideas are tested by objective experiment/observation in
the real world.
- Evaluation of evidence must be rigorous, objective, and public.
- Any valid scientific proposition is falsifiable by
empirical tests. I.e. it is well enough defined that you can specify
in advance those outcomes that would show the idea to be wrong.
- The results of tests must be repeatable.
- Confidence in ideas grows with the number of independent
tests or validations. "Independence" implies verification not only
by different people but also by different methods of
inquiry or lines of evidence.
The scientific method in practice
Scientific methods were not invented or prescribed wholesale by
some individual or group. Rather, they emerged over a period of several
centuries as the set of analytical techniques that proved most
successful in the struggle to understand nature.
The usual formalized statement of "The Scientific Method"
(e.g. Hypothesis ===> Prediction ===> Experiment ===> Interpretation
===> Repeat) is misleading:
Scientists do not necessarily work from "hypotheses." They frequently
simply explore the characteristics of new phenomena, without
any particular intent to distinguish between interpretations but with
the hope that they might prove interesting or important.
A number of sciences, including astronomy, deal with phenomena that
cannot be manipulated by humans. Experiments are impossible in
these cases. These sciences must rely instead on passive
For astronomy, the only exception is that we can,
with difficulty, sample and experiment with the surfaces and
atmospheres of some of the other bodies in the solar system.
Science and "Truth"
Scientific ideas are not claimed to be absolute
truths. They are always provisional, to a greater or lesser
degree. They are regarded as approximations to the truth,
subject to revision as new evidence emerges. They systematically
improve with time, by discarding older, less successful
Science and "Common Sense"
The characteristics of scientific thinking should sound familiar to
you: this is really nothing more than slightly refined, standardized,
and tough-minded "common sense." Scientific thinking deviates
from "common sense" mainly in that it insists on validating ideas in
the context of a vast store of existing knowledge that goes
far beyond everyday experience.
The subjects and conclusions of science, however, often
differ drastically from the "common-sense perspective"
that we intuitively develop in our everyday lives. The familiar
structures that surround us (e.g. trees, rivers, mountains) are
utterly different from those that characterize spatial scales only a
couple of orders of magnitude removed, either larger or smaller. And
nature comprises an almost unimaginable range of physical scales, as
illustrated at the right.
Humans directly experience only a minuscule range of the
distances, timescales, masses, densities, velocities, and energy
releases that prevail in the universe around us, and those are
often completely non-intuitive for us.
In fact, most of science deals with phenomena that
are "invisible" in everyday life even if they, like electrons
and bacteria, are actually ubiquitous in the world around us. They
have been recognized by scientists only gradually through systematic,
painstaking observations, experiments, and measurements.
One of the difficulties in
communicating science to others is leading the audience to
appreciate this real but invisible landscape.
We will lay the groundwork for going beyond the "common-sense
perspective" to a cosmic perspective in
Section G below.
Science and mathematics
Mathematics is integral to science. In most physical sciences,
including astronomy, mathematics is an essential technical ingredient
in interpretation. Large swaths of modern biology and medical
science, based on interpretation of the structures of huge nucleic
acid and protein molecules, are likewise highly quantitative.
Mathematics is needed in the design and analysis of experiments. For
example, it is used to determine how the inevitable uncertainty in any
measurement affects the reliability of scientific inferences,
especially since these often depend on combining measurements of
dozens of different quantities, each with its own limitations. But
even where complicated mathematics is not required, the rules of
logic, as elaborated by mathematics, are still essential.
It is actually surprising that mathematics, developed for the most
part in the abstract, is capable of describing the real, empirical
universe with exquisite accuracy. This mysterious "unreasonable
effectiveness" of mathematics has been the subject of
a number of thoughtful studies.
The symbiosis between science and mathematics is evident even in the
historical context. The first society to develop a scientific outlook
was ancient Greece, whose thinkers were
simultaneously laying the foundations of mathematics. And
whose 17th century experiments were the breakthrough that ignited
modern physics, believed that without mathematics "we are wandering in
vain through a dark labyrinth" --- i.e. that the clarifying insights
of mathematics are essential to understanding the universe.
B. Alternative Modes of Thought
It is worthwhile distinguishing science from some other important
modes of thinking.
Explanations are sought by appeal to a spiritual realm beyond the
natural world ("super"-natural).
Prior to the development of science, important physical phenomena were
usually interpreted as the product of deliberate and purposeful
manipulation by supernatural agencies, with motives largely beyond
human understanding. Knowledge of these agencies was thought to be
possible only through intentional revelation by them.
By contrast, science deals only with the natural world.
It seeks explanations of natural phenomena in terms of other natural
Supernatural explanations are not acceptable to scientists because
there is no way to test them.
Objective empirical tests are impossible for the supernatural world.
Science cannot predict supernatural behavior or its
intervention in our world since, by definition, the laws of nature
However, science could in principle detect supernatural
intervention in the natural world a posteriori (after the
fact) because it would appear as a breakdown in the laws of nature.
The fact that discontinuities in natural law have never been verified
shows that direct intervention is rare at current levels of
detection. Frequent intervention would produce an arbitrary and
largely unintelligible world.
When revelation was the dominant means of trying to understand the
world there might have been as many different interpretations of a
given phenomenon as there were religious traditions. By applying
empirical tests, science replaced this confusion with a unified,
pan-cultural vision of the universe.
Dependence on revelation to interpret the world produces
a hierarchy of privilege. Access to understanding, and the
corresponding power, is normally accorded only to a few (priests,
prophets, gurus). This is a central danger to this kind of thinking,
which is not consistent with a democratic society.
Idealism gives priority to the human mind and its constructs
over evidence from the external world. It asserts that truthful
conclusions about the natural world can be reached purely by analysis
Idealism was first championed by ancient Greek philosophers, most
Deductions about the physical world are made from abstract, a
priori postulates. It is assumed that empirical evidence
is corrupted and unreliable.
While this approach may be fine for mathematics (in which the Greeks
excelled), it is badly flawed as a means of assessing the real
Ideas are tested by appeal to the pronouncements of an individual or
small group. These cannot be questioned or superseded. Again,
a non-democratic system.
The most familiar, and dangerous, variety of authoritative
"truth" is found in dictatorships. But authority is also the basis of
the case law system ("precedent") in American jurisprudence.
Social systems based on revelation almost always invoke authority
Despite the public impression, science is not based on
authority. Instead, it operates by consensus. Any scientist
is entitled to question and retest any idea at any time and attempt to
convince others to change their minds. Science is democratic.
Scientific "authorities" are respected not because of
who they are but instead because of what they say.
Their ideas are continuously subjected to new tests. The best idea
Young scientists often aspire to overthrow "authorities" like
Einstein; they almost always fail because their ideas are
not as good when tested against the evidence.
Advocates of pseudo-scientific investigations apply some, but not
all, of the established methods of science. These fall
short of the basic criteria listed above in some important way.
But they have credibility for many people because they resemble
science, and this opens a large arena for human folly.
Examples: astrology, extra-sensory perception (ESP), psychic
forecasts, telekinesis, UFO abductions, ghosts, personal
reinterpretations of major scientific theories like relativity or
quantum mechanics. Also, much "alternative" medicine
Hallmarks: uncritical acceptance of poorly documented phenomena; lack
of experiments or inadequate experimental controls; inexperienced
observers; logical fallicies; non-repeatability; often self-deception;
often for-profit publicity/entertainment; sometimes deliberate fraud.
The evidence is always inadequate:
The issue is not that there are no good scientific explanations
for claimed pseudo-scientific phenomena. At any time, there
are thousands of well-documented phenomena that science does
not properly understand. These are what active scientists devote
their careers to studying. By contrast, in the case of pseudo-science
many of the phenomena themselves have not been demonstrated to
exist by objective experimentation or observational evidence.
A central failure of pseudo-science is that it almost always involves
a lack of consistency with established scientific principles or facts
(e.g. foreseeing the future contradicts the verified principles of
Most pseudo-science is harmless, except for the sloppy thinking and
miseducation it encourages. But some pseudo-science poses tangible
threats to you and society. For example:
For instance, we know that penicillin kills certain types
of dangerous bacteria. But no one has ever convincingly been shown to
be able to read someone else's mind.
If credible evidence emerges
for any of the marginal "pseudo" areas, they will then receive
mainstream scientific attention.
Fraudulent or ineffective "alternative" health-care (such
in which the active therapeutic ingredients are diluted to the point
where not a single molecule remains).
criminal prosecutions (murder, child abuse, satanic rituals, etc.)
based on erroneous psychotherapy (e.g.
"suppressed" memories "recovered" by hypnosis).
We will discuss the "UFO phenomenon" as an example of pseudo-science
later in Study Guide 18.
"Cultivated skepticism" is a cornerstone of science.
All good scientists are skeptics. This means that they maintain an
attitude of doubt or of suspended judgement about
Scientists insist on the best possible evidence in support of
new ideas. The adjective that best describes the scientific approach
to evidence is "relentless."
Accepted ideas, no matter how well established, are constantly
tested against new evidence, sifted for quality. All
preconceptions are subject to scrutiny. History shows that truth only
emerges through this kind of skeptical "scrubbing" of ideas and
evidence. The ideas that survive this process are very robust.
Competition over ideas, often intense, is a hallmark of science in
practice. There are strong incentives for scientists to discover new
phenomena or interpretations that countervail the accepted wisdom.
That is how young people make careers in science.
However, scientific doubt isn't frivolous; it must be based on a
balanced evaluation of the quality of the empirical evidence.
Good scientists are scrupulous in their treatment (positive or
negative) of the evidence; their reputations suffer otherwise.
Don't confuse healthy scientific skepticism with the activist
"skeptics" who have emerged over the last couple of decades to
dispute the scientific consensus on evolution, global warming,
vaccination against disease, tobacco-induced illness, etc. These
advocacy groups mostly do not care about the evidence or hold their
judgement in suspension---rather they have a committed belief in a
contrary view or a financial stake in opposing the consensus.
This kind of agenda-driven "skepticism" is now sometimes
Skepticism based on facts is not
an established element in many
other modes of human thinking. In fact, most people
with skepticism and instead see virtue in
conviction, certainty, and strong beliefs.
Russell remarked, and as we can see daily in news reports, this
may be the
"fundamental cause of trouble in the world
occur in science, as in any human endeavor. Historically,
there have been many more wrong ideas
in science than right
ones. Understanding the natural world is hard. Every scientist has a
long list (usually private) of mistakes he or she has made. But
because of skepticism and a reliance on real evidence, there is a
strong self-correcting mechanism
operating in science: the
errors are identified and discarded.
"He believed in the primacy of doubt, not as
a blemish upon our ability to know
but as the essence of
---- J. Gleick, writing about physicist Richard Feynman.
The Golden Gate Bridge, a premier example
of 20th century
D. Science vs. Technology
Although science and modern technology are often intertwined, they have
different goals and value systems; and we need to clarify the
distinctions between them. Science and technology are symbiotic
- Science: The attempt to understand nature; to build
a conceptual framework.
Adjectives used: "unapplied," "pure" or "basic"
Examples: principles of gravitation, electromagnetism, biochemistry,
- Technology: Application of basic concepts to
Examples: structural engineering, electrical generators, weapons,
All technology has a societal motivation
, whether for ultimate
good or ill, but the main motivation for "basic" science is
simply curiosity and the desire to understand
- Scientist: "be curious"
- Technologist: "be useful"
E. Results of Science
The basic result of science
Nature is understandable and operates
according to a small set of universal principles, or "laws"
We may take this for granted today, but it is an astonishing fact.
None of the early scientists who wrestled with trying to interpret
nature could have predicted it. The notion that a rainbow, lightning,
and the shape of a snowflake are all governed by exactly the same
underlying principles would have sounded absurd to them.
Some other key results
- The laws of nature are the same everywhere in the observed universe
- All matter, including living systems, is organized hierarchically from
a smaller set of subunits
- The structure of molecules & atoms is determined by electromagnetic force
- The Sun is a star
- The Earth is a planet
- Genetic information is transmitted by DNA molecules
- Most communicable diseases are caused by microorganisms
- The universe is very ancient, and its structure and contents have changed
systematically with time
Very few of the important results of science had recognizable
precedents in earlier modes of thought (prior to 1500 AD).
The main exceptions are Greek physics and astronomy, e.g. the
models of the solar system by Ptolemy, ca. 130 AD, or the atomic
theory of Democritus, ca. 420 BC. The Greeks made great progress.
However, because of their inclination to idealism, they disdained
empirical testing of scientific ideas, which circumscribed their
ultimate accomplishments. And those were forgotten or actively
suppressed in the Western world for nearly a thousand years starting
about 400 AD. See Study Guide 6.
How well determined are scientific results?
Some scientific results are known with effective certainty
(e.g. Earth is a planet; only one Sun in the solar system).
Aside from reaching reliable conclusions, scientists have been able
to measure many important aspects of nature with amazing
precision. Even in astronomy, where we cannot exert control over the
things we are measuring, a number of quantities -- e.g. the distance
between the Earth and the Sun -- have been determined to a precision
of better than one part in ten billion.
But, as noted above, scientific results are subject to revision
based on new evidence. Scientific ideas normally systematically
improve by discarding older, less successful interpretations.
You can picture the progress of science as an inward spiral toward
the truth as better evidence accumulates.
At any given time, some scientific results are much less well
established than others, so there is a huge range of validity
(say from 99.999% certain to less than 50% certain) throughout the
Among science that is less well established are many "interesting"
results in areas like human psychology and the influence
of lifestyle on health (especially diet). Unfortunately, these
tend to get wide publicity (isn't it great to hear that chocolate is
good for your heart?). And when contrary studies appear later, this
diminishes confidence in science overall.
Difficulties in these areas arise because it isn't ethical to
experiment on human subjects in ways that might produce more
definitive conclusions. Large samples are often hard to gather, but
small samples yield large experimental scatter and also prevent
assessment of the effects of the huge range of personal
characteristics. And in the absence of hard statistics, investigators
are sometimes swayed by random variations in ambiguous data sets that
seem to confirm their hypotheses. You shouldn't judge the reliability
of basic scientific conclusions by the muddled impression
emerging from the popular press.
Instead, here is a simple, practical measure of the validity of
the most important scientific ideas:
If our scientific understanding of nature was seriously flawed, then
most of our technology would simply not work. The validity of
ideas like Newton's laws of motion or Maxwell's theory of
electromagnetism or the germ theory of disease is tested
continuously in every automobile, cell phone, and hospital in the
By the way, this is also the best answer to the "cultural
constructivist" notion popular with some philosophers and social
scientists that prevailing scientific theories are more a product of
social conventions or political currents than objective data from the
real world. Scientists emphatically reject this argument. They
accept that they are subject to all the same social pressures,
foibles, and character flaws as other people. They make mistakes,
exercise bad judgement, and can have strongly subjective biases
(mostly in favor of their own ideas). However, the difference in
terms of the results of science is that empirical verification
provides an external standard for determining which ideas
have merit, and this ultimately produces robust interpretations of
Keep this success in mind when evaluating debates over scientific
results in the public arena. The same analytic procedures and
standards of evidence that produced the technologies we depend on in
our daily lives are behind the scientific consensus in areas like
biological evolution or global warming that are disputed by activist
Influence on society
As a new mode of thinking about the natural world, science succeeded
brilliantly. It demonstrated that humans can solve many problems
that at first seemed intractable: e.g. questions like "what causes
bubonic plague?" or "what are the stars?"
or "how old is the Earth?"
Success in science has been a great source of optimism
in human cultures. This was a major wellspring for the Enlightenment
and the political philosophies that culminated in the founding of
Science provides a demonstrably reliable and powerful
understanding of the physical & biological world. Over the past two
centuries it has transformed human societies. It is now the basis of
most of our technology, our wealth, and our collective and individual
well-being. The impact of science on our society is discussed further
in Study Guide 9.
The Moon and Venus at dusk
F. Astronomy as a Science
Astronomy is the study of the physical universe beyond the Earth's
It is the oldest science
, nearly universally practiced in
literate and pre-literate societies, and it has been a major stimulus to
other scientific fields from Greek times to modern physics
Relevance to society
- Astronomy investigates ultimate origins (an adjunct or alternative to religion)
- Astronomy provides our basic global perspective of time and
space, i.e. a cosmic context
- Astronomy was fundamental to the historical development of
scientific thinking and the formulation of the first generalized
physical laws by Newton.
- Study of the other planets and our cosmic environment is essential to
assessing the viability of Earth's biosphere and prospects for
long-term human survival.
History of societal influence
- All societies: practical time- and calendar-keeping, navigation
- 5000 BC - 1609 AD: awareness of the Solar System (planets, sun)
- 16th-17th centuries: astronomy leads in the
demolishment of medieval thinking
- 1609: the newly-invented telescope reveals a vast stellar system beyond the planets,
enormously expanding the horizon of human thought
- Late 1600's: astronomy leads Newton to his laws of motion, which
initiate the "scientific revolution" and modern technology
- 19th century: speculation about extraterrestrial life
- 20th century: recognition of galaxies ("island universes"), the
expanding & evolving universe, the Big Bang, exploration of the Moon
and planets by the space program, the extraterrestrial cause of mass
biological extinctions; discovery of other solar systems.
Starfield in center of Milky Way. How many
stars can you count here?
Click for a full-resolution
enlargement. (Image from the Hubble Space
G. ASTRONOMICAL DISTANCES AND AGES
Astronomical time- and distance-scales are tremendously larger
than the "common sense" scales we encounter in everyday life.
See the chart
above for scales
meters and above.
Unfortunately, this means that astronomical scales (not to mention
atomic or molecular scales) are utterly non-intuitive
It is important for astronomers to develop a good cosmic
that transcends the perceptual biases of everyday
experience. But it is difficult for anyone to visualize the scales
involved. Because the cosmic range is so enormous, scientists make
regular use of scientific mathematical notation ("powers of
). For a review of this notation,
see Supplement I
Example astronomical scale models
Simple scale models can provide a rough, if never completely adequate,
impression of cosmic scales:
- As an example of the contrast between human perceptions and
physical reality consider the Earth's atmosphere. It seems
enormous and all-encompassing, right? Atmospheric disturbances
(rainstorms, tornados, hurricanes, droughts) easily destroy human
structures and livelihoods.
Can you propose a simple scale model for the atmosphere, using,
for example, a basketball to represent the Earth?
Click here for the answer.
Despite our impression, the atmosphere represents only a tiny fraction
(one part in 1600) of the Earth's diameter.
See this image taken
from a spacecraft, showing the atmosphere as a thin blue line on the
horizon. (The dark ridge of snow-capped mountains running diagonally
across the Earth's surface is the Himalayas, the world's highest.)
In fact, you can actually walk out of Earth's atmosphere.
Anyone who has been above 26,000 feet altitude (and there are 14
mountains this high) has been beyond the point where the air density
has dropped a factor of 2.7---the official
height" definition of the atmosphere's thickness.
- A sample cosmic time scale:
- The age of the Sun is about 5 billion years, a middling
age for an older star. Suppose we wanted to use the run of all
the letters in our textbook to represent this span of time.
How many years would we have to assign to each letter?
We discussed this in the introductory lecture, and by
"rough order of magnitude
estimation" we determined that there would be about 2000
years per letter(!) if the entire textbook represented the age of
All of recorded human history would fit within the first four
letters of the text! The existence of Homo sapiens on
Earth would extend only a couple of sentences! (Modern humans have
existed only for about 200,000 years, or 0.004% of the age of the
Here is an image of the
first two pages of our textbook with the beginning of this
time-scale model superposed.
The Earth is almost the same age as the Sun, so our scale model
graphically illustrates the vast span of time over which the surface,
atmosphere, and biosphere of our planet have been shaped into their
Your first homework assignment was simply to stare at
random pages from the textbook and try to absorb, in the context of
this scale model, the nearly unimaginable period over which the Earth
- The "dripping faucet effect": the very long time scales that
characterize planetary evolution mean that small but persistent
changes can eventually have major consequences. We will
see many examples of these (e.g. polar precession, continental drift,
- Finally, a healthy, fruit-based cosmic distance scale model:
- Use an orange to represent the Sun. This is an
appropriate choice not just because of the color but also because the mean
mass density of the Sun is about the same as an orange (1
In this model, the Earth to Sun distance (defined to be one
"Astronomical Unit") is 25 ft.
[Useful mnemonic: Earth diam : Sun diam : Astron Unit = 1:100:10,000]
- In this model, what is the scale distance to the next nearest
star (Alpha Centauri)?
An additional relevant piece of information that might help
you think about this question is that the Sun is about 10 billion times
brighter than the brightest stars as seen from Earth and that most
of this difference is a distance effect.
- Here's the surprising
answer. It illustrates how incredibly thinly matter is
spread on a cosmic scale by the standards of our everyday,
Reading for this lecture:
Bennett textbook: Ch 1 and Secs 3.4, 3.5.
Study Guide 1
Optional reading: Alan Cromer: Uncommon Sense; Bertrand Russell:
A History of Western Philosophy; Carl Sagan: The Demon Haunted
Reading for next lecture:
Bennett textbook: Ch 1 and Secs 3.4, 3.5.
Study Guide 2
Supplement I (PDF file) Skim and then refer to
this later as needed.
Optional: Cosmic History: A
Optional: browse the material on the structure &
evolution of the universe in the Bennett textbook Chs
22 and 23
May 2021 by rwo
Text copyright © 1998-2021 Robert W. O'Connell. All
rights reserved. Twilight image of Moon and Venus over Mt. Shasta by
Jane English. These notes are intended for
the private, noncommercial use of students enrolled in Astronomy 1210
at the University of Virginia.