Download Test 1 Overview - Physics and Astronomy

Review for Test #1 on February 16
Topics:
• Foundations of Astronomy - measurement, exponential notation, etc.
• The Copernican Revolution - Newton’s Laws, Gravitation, etc.
• Radiation and the Electromagnetic Spectrum - Black bodies
Methods
• Conceptual Review and Practice Problems Chapters 0 - 2
• Review lectures (on-line) and know answers to clicker questions
• Try practice quizzes on-line (in MA)
•Bring:
• Notes & Text (no books and only 1 page of notes)
• Simple calculator (no electronic notes)
Reminder: There are NO make-up tests for this class
Test #1 Review
How to take a multiple choice test
1) Before the Test:
• Study hard
• Get plenty of rest the night before
2) During the Test:
• Draw simple sketches to help visualize problems
• Solve numerical problems in the margin
• Come up with your answer first, then look for it in the choices
• If you can’t find the answer, try process of elimination
• If you don’t know the answer, Go on to the next problem and
come back to this one later
• TAKE YOUR TIME, don’t hurry
• If you don’t understand something, email me.
Test #1 Useful Equations
Kepler’s laws, including:
P2 
Newton’s laws, including:
a = Fnet / m
a3
Gravitation:
F=
G m1 m2
R2
Speed of electromagnetic waves: c = 300,000 km/s
Wien’s Law:
lmax energy 
Energy = hf
1
T
Stefan’s Law: L = A T4 where the area A = 4r2 for a sphere
Angular Measure
90o
20o
360o, or 360 degrees, in a circle.
1o = 60' or arcminutes
1' = 60" or arcseconds
1" = 1000 mas or milli-arcseconds = 103 mas
The Celestial Sphere
An ancient concept, as if all
objects at same distance.
But to find things on sky,
don't need to know their
distance, so still useful today.
Features:
- Does not rotate with Earth
- Poles, Equator
- Coordinate System
The Earth's rotation axis is tilted with respect to its orbit around
the Sun => seasons.
Summer
Scorpius
Night
Tilt is 23.5o
Winter
Day
Sun high in
northern sky
Sun low in Day
northern sky
Night
Orion
One solar day later, the Earth has rotated slightly more than 360o .
A solar day is longer than a sidereal day by 3.9 minutes
(24 hours vs. 23 hours 56 minutes 4.091 seconds).
Cycle of phases slightly longer than time it takes Moon to do a complete
orbit around Earth.
Cycle of phases or
"synodic month"
Orbit time or
"sidereal month"
29.5 days
27.3 days
Eclipses
Lunar Eclipse
When the Earth passes directly between the Sun and the Moon.
Sun
Earth
Moon
Solar Eclipse
When the Moon passes directly between the Sun and the Earth.
Sun
Moon
Earth
Types of Solar Eclipses Explained
Precession
The Earth has a bulge. The Moon "pulls down" on the side of the bulge
closest to it, causing the Earth to wobble on its axis (how do we know this?)
Earth
Moon
Vega
*
* Polaris
Spin axis
Precession Period 26,000 years!
Now
Scorpius
Night
Day
Day
Summer: July
Night
Orion
Winter: January
13,000 years from now
Scorpius
Night
Day
Winter: July or January?
Day
Night
Orion
Summer: January or July?
We choose to keep July a summer month, but then in 13,000 years, summer occurs on other side of orbit!
"Heliocentric" Model
●
Rediscovered by Copernicus in 16th century.
●
Put Sun at the center of everything.
●
Much simpler. Almost got rid of epicycles.
But orbits circular in his model. In reality,
they’re elliptical, so it didn’t fit the data well.
●
●
Not generally accepted at the time.
Copernicus 1473-1543
Copernican model was a triumph of the Scientific Method
Scientific Method:
a)
b)
c)
d)
e)
Make high quality observations of some natural phenomenon
Come up with a theory that explains the observations
Use the theory to predict future behavior
Make further observations to test the theory
Refine the theory, or if it no longer works, make a new one
- Occam’s Razor: Simpler Theories are better
-You can prove a theory WRONG but not
RIGHT
Prediction
Observation
Theory
Galileo (1564-1642)
Built his own telescope.
Discovered four moons orbiting Jupiter =>
Earth is not center of all things!
Discovered sunspots. Deduced Sun
rotated on its axis.
Discovered phases of Venus, inconsistent
with geocentric model.
Kepler (1571-1630)
Used Tycho Brahe's precise data on
apparent planet motions and relative
distances.
Deduced three laws of planetary
motion.
Kepler's First Law
The orbits of the planets are elliptical (not circular)
with the Sun at one focus of the ellipse.
Ellipses
distance between foci
eccentricity =
major axis length
(flatness of ellipse)
Kepler's Second Law
A line connecting the Sun and a planet sweeps out equal areas
in equal times.
slower
Translation: planets move faster
when closer to the Sun.
faster
Newton (1642-1727)
Kepler's laws were basically playing with
mathematical shapes and equations and seeing
what worked.
Newton's work based on experiments of how
objects interact.
His three laws of motion and law of gravity
described how all objects interact with each other.
Newton's Second Law of Motion
When a force, F, acts on an object with a mass, m, it produces an
acceleration, a, equal to the force divided by the mass.
Fnet
a=
m
or Fnet = ma
acceleration is a change in velocity or a change in
direction of velocity.
Timelines of the Big Names
Galileo
Copernicus
1473-1543
1564-1642
Brahe
1546-1601
Kepler
1571-1630
Newton
1642-1727
Review: Properties of a wave
Radiation travels as waves.
Waves carry information and energy.
wavelength (l)
crest
amplitude (A)
trough
velocity (v)
l is a distance, so its units are m, cm, or mm, etc.
Also, v = l n
Period (T): time between crest (or trough) passages
Frequency (n): rate of passage of crests (or troughs), n =
(units: Hertz or cycles/sec)
1
T
The Electromagnetic Spectrum
1 nm = 10 -9 m , 1 Angstrom = 10 -10 m
c= ln
Example: Blackbody - the microwave
background
Emits mostly in the radio, with a peak around 200 GHz
Approximate black-body spectra of astronomical objects
demonstrate Wien's Law and Stefan's Law
cold dust
hotter star (Sun)
“cool" star
very hot stars
frequency increases,
wavelength decreases
Types of Spectra
1. "Continuous" spectrum - radiation
over a broad range of wavelengths
(light: bright at every color).
2. "Emission line" spectrum - bright at
specific wavelengths only.
3. Continuous spectrum with
"absorption lines": bright over a broad
range of wavelengths with a few dark
lines.
Kirchhoff's Laws
1. A hot, opaque solid, liquid
or dense gas produces a
continuous spectrum.
2. A transparent hot gas
produces an emission line
spectrum.
3. A transparent, cool gas
absorbs wavelengths from a
continuous spectrum,
producing an absorption line
spectrum.
So why absorption lines?
.
. .
. cloud of gas
.
.
.
. .
.
.
The green photons (say) get absorbed by the atoms. They are emitted again in
random directions. Photons of other wavelengths go through. Get dark
absorption line at green part of spectrum.
Why emission lines?
hot cloud of gas
.
.
.
.
.
.
- Collisions excite atoms: an electron moves into a higher energy level
- Then electron drops back to lower level
- Photons at specific frequencies emitted.
Ionization
Hydrogen
_
+
Energetic UV
Photon
_
Helium
+
Energetic UV
Photon
+
_
"Ion"
Atom
Two atoms colliding can also lead to ionization.