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: P

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.

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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!