Common abbreviations and
prefixes used in
class, which you need to learn:
nano: 1/1,000,000,000
micro: 1/1000,000
milli: 1/1000
kilo: 1,000
mega: 1,000,000
giga: 1,000,000,000
Here is a handy table and
explanation for conversion between the standard length units
(A, nm, microns, mm, m, km). You must learn these units and
how
to convert between
them for this course. Most of the time, the factors change in
a
systematic way, so once
you learn the various prefixes (nano, micro, milli, kilo, mega,
giga)
you should be able to handle the units.
Myr = megayear (1 million years)
Gyr = gigayear (1 billion years)
AU = Astronomical Unit, distance from Earth to Sun (about
150,000,000
km)\
pc = parsec, a "cosmic yard" (3.26 light years). Astronomers
generally use pc (and kpc and Mpc),
not light years, for
distances, because distances in pc are easy to convert to parallaxes
(which are easy to measure).
Know the difference between ROTATION (spinning; rotation about an
axis
inside of
an object like a planet, star or galaxy) and
REVOLUTION (motion in an orbit
around a center of gravity, following Kepler's Laws)
SOME of the more common chemical element symbols to know which are
important in astronomy.
I'll introduce others as they come.
The most important are:
H hydrogen
He helium
C carbon
N nitrogen
O oxygen
Fe iron
Less commonly used but still useful to know because I'll use them
are:
Li lithium
Ne neon
Na sodium
Mg magnesium
Al aluminum
Si silicon
S sulfur
K potassium
Ca calcium
Pb lead
U uranium
It would be a very good idea
(hint) to know the conversions between Kelvin, Celsius and
Fahrenheit:
Kelvin = 273+Celsius
Celsius = (Fahrenheit - 32)/1.8
Links to
supplemental material for
Astronomy 107, chapter by chapter
This is VERY helpful if you need more explanation for key concepts.
There are also links for Astronomy 307, a more advanced course, if
you're interested.
Useful Equations
Equations
you
MUST know
(memorize)!:
Geometry:
circumference C of a circle and sphere: C=2 pi r
area A of a circle: A = pi r^2
area
A of a sphere: A = 4 pi
r^2
volume V of a sphere: V = (4 pi/3)r^3
1
radian = 180/pi degrees and 1 degree = pi/180 radians
1 degree = 60 arcminutes
= 3600
arcseconds
1 arcminute = 60
arcseconds
Physics:
density = mass/volume
(rho = M/V)
speed x time = distance or vt=d
acceleration x time = velocity or at=v
Kepler's 3 laws:
1) The planets orbit the Sun in ellipses, with the Sun at one
focus.
2) The line joining the Sun and a planet sweeps through equal
areas in
equal times.
3) The square of the orbital period of a planet is
proportional to the
cube of its semi-major axis: P2=a3.
Newton's 3 laws:
1) Law of Inertia: Bodies in motion tend to remain in motion,
in a
straight line with constant speed, unless
acted upon by an external force.
2) Law relating force,
mass and
acceleration: force =
mass x acceleration or F=ma
3) For every action,
there is an equal
and opposite reaction.
Einstein's relation
of mass and
energy:
energy = mass x (speed of
light)^2
or E=mc^2
Know what an inverse
square law
is: [something] propto
1/r^2
where [something] can be gravitational force, light flux,
sound
intensity etc.
---------------------------------------------------------------------------------------------------------------
Otherwise, I'll generally
provide
equations you need for quizzes/tests
These are other equations you will run into for homework and
tests.
They'll be on your equation sheet for quizzes/tests.
Chap
2:
Light, Matter and Energy:
Wien's Law:
lambda(max) T = 2.9 x 1e7 A K
where lambda is in Angstroms and temperature T is in Kelvin
So, a star with T=5800K (like the Sun) has a peak wavelength of
2.9 x 1e7 A K/5800K = 5000 A (so the Sun appears yellow to our
eyes)
Stefan-Boltzmann Law:
E = sigma T^4
where E = energy PER UNIT AREA (e.g. square meter),
shttp://news.bbc.co.uk/2/hi/health/6540449.stmigma is a constant
and temperature T is in Kelvin
So, for two stars, star A with T=5000K and star B=10000K, the
ratio of
energy per unit area of B to A is
E(B)/E(A) = (10000/5000)^4 = (2)^4 = 16
Chap
3:
Light and Telescopes:
Diffraction limit (maximum
resolution) for a telescope:
theta(arcsec) = 0.25 lambda(micrometers) / diameter (meters)
So, a 2.5m telescope at 1 micrometer has a 0.10 arcsec
diffraction
limit (like the Hubble Space Telescope).
Telescope light gathering
power
propto area propto D^2 where D=diameter
Telescope
resolving
power:
R propto D/lambda
where D=diameter, lambda = wavelength
(must be in SAME units, because R is a dimensionless number!)
Chap 4: Observing Stars and Planets
Magnitudes:
5 magnitudes is a factor of
100 in
brightness, with low magnitudes brighter.
So
1
mag = 100^(1.5) or
approximately 2.5.
brightness-magnitude
relation:
b_A ~ 2.5^(m_B-m_A)(b_B)
where b is brightness and m
is
magnitude for objects A and B.
Chap 5: Gravity & Motion
Orbital velocity propto
1/r^{1/2}
where r is radius from Sun (or central body)
Newton's form of Kepler's
3rd law:
P^2 = {4 pi^2 /
[G(M+m)]}a^3
where P=period, M and m are the masses of the bodies in orbit
around each other and a is the semi-major axis
G is the gravitational constant.
If one body m is MUCH smaller
than
the other body M (like a planet and a star) then use the
approximation
M+m~M
where M is the bigger body (the smaller body doesn't matter).
This makes Newton's form of Kepler's 3rd law MUCH simpler:
P^2 = a^3/M
where P is in years, a is in AU and M is in solar
masses. USE THIS
IF YOU'RE DEALING WITH A STAR WHICH IS NOT THE SUN.
If you're just taking a
proportion
for two objects in orbit around the
same central body (like
planets
around the Sun), then P^2 propto a^3
If you are dealing with the
Sun and
objects in orbit around it,
and use AU for distance and
Earth-years for the period, then the
constant of proportionality is
one:
P^2 = a^3
Newton's law of acceleration: F=ma (memorize that one!)
Newton's law of gravity: F=GMm/r^2
where r is the distance to the
center of the attracting body (e.g. Earth), M is the mass of
Earth
and m is the mass of the body in question.
Orbital velocity as a function of radius: v propto
r^(-1/2)
Chap 10: The Sun
small
angle
approximation:
sin theta ~ theta for small theta (measured
in RADIANS)
Chap 11: The Stars
stellar luminosity as a
function of
temperature and radius:
L = (sigma T^4)(4 pi r^2)
relative velocity shift -
relative
wavelength shift relation (for v~<0.1c,
where c=speed of light,
300000 km/s):
Delta v/c = Delta lambda/lambda
trigonometric parallax:
d=1/(pi")
where d is in pc, pi is the
parallactic angle in arcsec
1 pc = 1 parsec ~206000 AU
apparent
magnitude--absolute
magnitude--distance relation:
m-M = 5 log d - 5
where m = apparent
magnitude, M =
absolute magnitude, d = distance in pc
relative location of the barycenter between two stars:
m1 v1 = m2 v2
where stars have
masses m1, m2 and
distances r1, r2 from the barycenter
Chap 16: A Universe of
Galaxies
redshift:
z =
[lambda(obs)]/lambda(rest) - 1
where lambda(obs) is the observed wavelength of a spectral
line and
lambda(rest) is the rest (or laboratory) wavelength of a
spectral line
recession velocity of a galaxy (pretty close for
v~<0.2c):
v~cz
Hubble's Law (for
nearby galaxies,
good for about z~<0.2):
v=(H0)(d)
where H0 is the Hubble
constant
(about 71 km/s/Mpc)
and d is the galaxy's
distance in Mpc
Chap 17: Quasars and
Active Galaxies
relativistic Doppler
shift:
(1+z) = lambda(obs)/lambda(rest) = sqrt[(1+v/c)/(1-v/c)]
This is exact, and good
for all
0<v<c. Note that v can never equal c,
the speed of light.
Student
Questions
Q. How long do sunspots last? Chris Watson, 27 Feb 2007
A. Small ones last for a few days. Large ones, with
umbral
diameters of
30000km and penumbral diameters over 2x as large, can last
for months.
Other
resources:
Astronomy
Picture of the Day
Websites
showing constellation
maps, mythology etc.
Munich
constellation
site (English/German/Italian)
Wisconsin
constellation
site (Chris Dolan's, has clickable map)
"Top
Ten" bright
constellations
Hawaiian
Astro Society
skymaps
Help do
astronomy research with
galaxy
classification!
Galaxy Zoo:
classify Sloan Digital
Sky Survey
Galaxies!