1.2 S.I. Units
The following units form the basic, internationally accepted list to describe physical quantities
 
unit  symbol  
 
length  meter  m 
mass  kilogram  kg 
time  second  s 
force  Newton  N 
energy  Joule  J 
 
Example: mass of the Sun
M_{\odot} = 1.99×10^{30} kg
Derived quantities the units can be combined to describe other quantities
 
velocity  m s^{1}  
momentum  kg m s^{1}  
pressure  N m^{2} or Pascal (Pa)  
 
Example: speed of light c = 3 ×10^{8} m s^{1}
1.2.2 Units in Astronomy
1 AU 1.5 ×10^{11} m
1 pc 3.09 ×10^{16} m
1 M_{\odot} 1.99 ×10^{30} kg
1.2.3 Notes on Notation
'Astronomical' (= very large) numbers are written using powers of 10
10^{6} pc = 1000000 pc = 1 Mpc
10^{3} pc = 1000 pc = 1 kpc
10^{1} pc = 10 pc
10^{3} pc = 0.001 pc = 1 mpc
10^{6} pc = 0.000001 pc = 1 mpc
10^{9} pc = 0.000000001 pc = 1 npc
1.2.4 Notes on Accuracy
Many observed quantities in astronomy are accurate only to 110%.
Do not give more than 3 significant digits in calculations
Example: distance to the Andromeda Galaxy is 780±50 kpc.
780 kpc = 780 ×10^{3} ×3.27 ly = 2.55 Mly ¹ 2550600 ly
1.2.5 Angles on the sky
1 degree 1/360 of a circle 1 arcminute 1/60 of a degree 1 arcsec 1/60 of an arcminute 1 radian 1/2p of a circle
1.3 parallax and the parsec
Distances to nearby stars can be measured via triangulation
baseline: orbit of the Earth. Over 6 months, the Earth moves by 2 AU.
When looking at a star, we see it under a different angle. This angle
allows us the measure the distance.
Parsec: defined as the distance at which the parallax is 1 arcsec
The parsec is the fundamental unit of distance in astronomy
The distance to a star is now giwven by the following equation:
 (1.1) 
1.4 Celestial coordinates
Coordinate frame is spherical, fixed with respect to the stars
The
Constellations of
the zodiac
follow the ecliptic:
There are 88 constellations over the sky.
Latitude and altitude
Take a location on Earth with latitude f
Take a star with declination d



1.4.1 Equinox and solstice
Sun crosses the equatorial plane twice a year
Sun reaches two extrema in declination each year:
Sun rise and Sun set:
1.4.2 Right ascension
The position of the Sun at the vernal equinox:
Fixes coordinates of all stars on the sky
Coordinates of Solar system objects change due to their and our movement
1.4.3 Precession
Rotation axis of the Earth changes direction with time
Traces out a circle on the sky
We specify coordinates w.r.t equinox of 1900, 1950, 2000, ..
1.4.4 Day and Year
Length of day
Length of year
Time keeping
1.5 Solar system orbits
Orbits are almost in plane of ecliptic (except for Pluto)
Inner planet (Venus, Mercury)
Movement reflected in: apparent (angular) diameter, phases & brightness, Mayan calendar
Outer planet (e.g. Mars, ..)
1.5.1 Period of planet

where E is sidereal period of the Earth
1.6 Brightness and luminosity
1.6.1 Luminosity
The luminosity L of a star is the power (J s^{1} or W) which it emits
Unit: 1 solar luminosity = 1 L_{\odot} is the luminosity of the Sun

If a star has a luminosity


1.6.2 Flux
The flux F from a star is the power coming from the star
passing through an area of 1 m^{2}
A star has luminosity L_{*} and distance d. The flux is
 (1.2) 
A telescope with diameter of 3.6 m points at the star. It receives a power of

For A = 10 m^{2}, L=L_{\odot} and d=1 pc

1.6.3 Luminosity and temperature
The StefanBoltzmann law

The luminosity of a star is surface area times P:
 (1.3) 
where R_{*} is the radius of the star
Divide by solar values

1.6.4 Magnitude
The magnitude of a star is related to its intensity or flux:

 (1.4) 
From apparent to absolute magnitude



This equation relates the apparent and absolute magnitude to the distance:

Where the distance d is taken in parsec
This equation is normally written as:
 (1.5) 
m  M is called the distance modulus
Extinction
Light from a star may suffer from dust between us and the star.
This reduction in the flux of the star is called
extinction

where A is the extinction in magnitudes
 (1.6) 
Include A in the distance modulus:
 (1.7) 
1.7.1 Electromagnetic radiation
 (1.8) 
The wavelength l or frequency n determines the type of radiation
 
l  n  
 
Gamma rays  10^{6}  10^{2} nm  10^{22} Hz  
X rays  10^{2}  10 nm  10^{18} Hz  
UV  10  400 nm  10^{16} Hz  
visible/optical  400  700 nm  5×10^{14} Hz  
IR (infrared)  700 nm  1 mm  10^{14} Hz  
radio/microwave  1 mm  1 m  10^{10} Hz  
 
Sometimes the nonSI unit angstrom is used:

1.7.2 Telescopes
1.6.3 Diffraction limit
Angular resolution of a telescope is the smallest angle it can resolve
Angular resolution depends on
The angular resolution of a perfect telescope is given by the diffraction limit
 (1.9) 

To get higher resolution
Angular resolution of the eye
Angular resolution of a refracting telescope

Example: a resolution of 0.5 arcsec at
l = 500 nm requires

Angular magnification of a refracting telescope
 (1.10) 
Length of a refracting telescope

To match the angular resolution of telescope and eye requires

Example
To look through a refracting
telescope to see 0.5 arcsec details requires

If the eyepiece has f_{oc} = 50 mm


Interferometry
Radio astronomy: l ~ 1 cm
Resolution of 1 arcsec requires
D=2.5 km
Solutions: combine signals from two telescopes 2.5km apart
Commonly used for radio telescopes