Today’s lecture
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Scientific method
Night sky
Celestial coordinate systems
Parallax
Angular size
To understand the universe, scientists use the
“Scientific Method”
1. Observe - Observe something. Write down the
observations and make sure that other people can repeat
them on their own.
2. Guess - Make a guess about how that something
happens. The guess has to be in the form of an
explanation that can be used in other contexts. The guess
must help to make predictions about other observations.
3. Test and Criticize - Observe similar things to see if the
guess (the explanation) is correct or needs to be modified.
4. Repeat - until you get it right.
Types of Guesses
Hypothesis
•
One or more ideas to explain an observation or set of
observations. Must be useful in making predictions about
other observations, be testable, and be falsifiable.
Model
•
Hypotheses that have withstood observational and
experimental tests.
Theory
•
A well-founded body of related hypotheses and models
that form a self-consistent description of nature.
Law
•
A theory that has been very well tested and is applicable
over a wide range of different situations.
Which are legitimate scientific hypotheses?
1. Any two objects dropped from the same height
above the surface of the moon will hit the lunar
surface at the same time.
2. Our universe is surrounded by another, larger
universe, with which we can have absolutely no
contact or interaction.
3. All horses are brown.
Science, religion, and pseudo-science
• Scientific theories are experimentally verifiable (or
falsifiable) and predictive. They address how questions (e.g.
How do stars form? How is a lunar eclipse caused? How
did the Universe evolve?)
• Religious and ethical statements are (generally) not
verifiable. They address why questions (e.g. Why does the
Universe exist? What kind of life is worth living?). These are
not intrinsically less worthwhile than scientific inquiries, they
are simply addressing different questions. Religion and
science come into conflict when religion supplies answers
for questions that can now be addressed by science, i.e.
evolution of humans, age of the Universe.
• Pseudo-science theories pretend to be scientific but are
either not falsifiable (e.g. séances, ) or supporters or use
anecdotal evidence to support claims (e.g. astrology,
‘creation’ science).
Skepticism and Truth
• Role of skepticism. An essential part of the scientific
method. Scientists always question the basis for an
scientific assertion. This is often considered ‘impolite’
behavior in social settings, but is not impolite in
scientific discussion.
• ‘What is truth?’ - Scientific theories are not
statements of truth. They are the best available
explanation for observed facts, but are subject to
revision or falsification.
• Scientists must be able to admit that they are wrong.
Occam's Razor
• What if two or more competing hypotheses both pass some
initial tests - how do you choose between them?
• If the hypotheses generate different predictions it will be a
simple matter to pick the best one - as long as it is feasible to
carry out the experimental tests. What if the competing
hypotheses don't give distinguishable, feasible predictions?
Enter "Occam's Razor".
• William of Occam was a medieval scholar and logician, and, in
modern form, the principle that has come to be known as
Occam's Razor says:
If two hypotheses can't be distinguished experimentally, choose
the simpler one.
How does one locate an object on
the night sky?
1. By drawing imaginary patterns on the sky
(the constellations) and then locating the
object relative to the stars in the
constellations.
2. By drawing an imaginary coordinate
system on the sky, then specifying the
objects coordinates.
Eighty-eight constellations cover the
entire sky.
• 6000 stars visible to
unaided eye (only half
are above the horizon).
• 88 semi-rectangular
groups of stars called
constellations.
• Some stars in the
constellations are quite
close while others are
very far away.
Finding M51
Finding M51
Finding M51
We use angles to denote the positions and
apparent sizes of objects in the sky.
Your hand at arm’s length is about 10 degrees wide
Your thumb at arm’s length is about 2 degrees wide
Coordinate system
Coordinates are
Latitude = degrees
North or South of the
equator
Longitude = degrees
East or West of the
“Prime meridian”
Prime meridian is
historically defined as
longitude of the Royal
Observatory in
Greenwich, England
Sky coordinate system
Introduce the
‘celestial sphere’
This is an imaginary
sphere drawn in space
with the earth at its
center.
We align the sphere
with the Earth.
Coordinates are:
Declination = degrees
North or South of the
equator.
Right ascension =
degrees East of the
“Vernal equinox”.
Vernal equinox is
defined as the position
of the Sun on the first
day of spring. Note it is
a point on the sky, not
the earth.
Motion
of stars
on the
sky
The rotation of the Earth causes the stars to
appear to move on the sky.
Precession
• If you spin a top, its very hard to get it to
spin exactly straight – usually it wobbles
around in a circle
• The spinning Earth wobbles in exactly the
same way – this is called precession
Precession of the Earth
Precession causes celestial coordinates to change slowly with time.
When observing, one must have coordinates for the correct epoch.
Angular Measure for Small
Angles
1º = 60 arcminutes = 60′
1′ = 60 arcseconds = 60″
e.g., On January 1, 2004, the planet Saturn
had an angular diameter of 19.7″ as viewed
from Earth.
How can you measure the distance
to an object you can’t reach?
• Use triangles…
Triangles
The small triangle has the same shape as the large
one.
By measuring the two sides of the small triangle and
the short side of the big triangle, we can calculate
the length of the long side of the big triangle.
Measuring distance
a
A
d
D
D d

A a
d
DA
a
So, how can we measure the distance
to stars?
p
p
Take two telescopes some distance apart and
observe the same star.
Measure the tilt between the two telescopes – this
sets all the angles for the triangles.
Then we can find the distance to the star from the
distance between the telescopes and the angle of
the tilt.
So, how can we measure the distance
to stars?
• We want to use the largest distance we can
for the short side of the big triangle
• What is the largest distance we can get
between the two telescopes (if both of them
have to be on Earth – no spacecraft).
So, how can we measure the distance
to stars?
• The largest distance is not by placing the
two telescopes at opposite ends of the Earth.
• Instead, we can use one telescope and just
let the earth move.
A.U. = Astronomical Unit = distance from Earth to Sun
Stellar Parallax
As Earth moves from one
side of the Sun to the
other, a nearby star will
seem to change its
position relative to the
distant background stars.
d=1/p
d = distance to nearby
star in parsecs
p = parallax angle of that
star in arcseconds
Closer star – larger parallax
Example: Using parallax to
determine distance
The bright star Vega has a measured parallax of 0.1
arcsec (p = 0.1″)
This means that Vega appears to move from +0.1″ to 0.1″ with respect to distant stars over a year’s
observation
D(pc) = 1/p(″) = 1/0.1 = 10 pc
Vega is 10 pc (parsec) from Earth
(remember: 1 pc = 3.26 light years)
Sizes of Astronomical Objects
• How can we measure the sizes of
astronomical objects?
• The same way that we measure distances –
using triangles
The Small-Angle Formula
D
D = linear size of object
 d
θ = angular size of object
(in arcseconds)
206265
d = distance to the object
Example: On November 28, 2000, the planet
Jupiter was 609 million kilometers from Earth
and had an angular diameter of 48.6″. Using the
small-angle formula, determine Jupiter’s actual
diameter.
D = 48.6″ x 609,000,000 km / 206265 = 143,000 km
The Small-Angle Formula
D
 d
206265
D = linear size of object
θ = angular size of object
(in arcsec)
d = distance to the object
Review questions
• What do we mean by a model in science?
• Determine the distance to Alpha Centauri
which has a parallax of 0.75 arcseconds.
• If one can measure stellar positions to an
accuracy of 0.01”, what is the farthest distance
that can be measured to an accuracy of 10% or
better?
• If the distance to the Sun is known, describe
how one could determine its physical size.