How do we do experiments in astronomy? We receive the information in the form of light. 
We can't do experiments directly! 

(Diffraction experiments with fingers blocking a bright light). CD 
diffraction. 

Let's talk about light, (or, in more generality, electromagnetic
radiation).  Light is an oscillating field of electrical and magnetic
fields, which travels at the speed of light (i.e., c=3x10^5 km/s) in
vacuum.  A wave of light is characterized by its wavelength lambda, or
its frequency nu, such that c = lambda times nu.   For visible light,
lambda is related to color; blue light has short wavelengths and red
light has long wavelengths.  

Amazingly, the speed of light is measured to be the same by everybody,
no matter how fast they are moving relative to the object giving off
the light.  We'll discuss this in detail in Prof. Gott's part of the
course.

    But it turns out that the speed of light in empty space is
different than when it goes through different materials (for example,
light going through water goes about 30% slower), and this slowdown is
slightly different for light of different wavelengths.  The effect of
this, it turns out, is to cause light to bend ("refract") as it
crosses the boundary between air and water.  In a prism, for example,
different wavelengths are bent by different amounts, and white light
is spread out into a rainbow.

  Frequency: number of peaks that go by in one second (#/sec).  
  Amount of time between peaks is: t=1/nu
  Distance the wave goes by in this time: lambda (wavelength)
  Speed is : d/t=lambda/(1/nu)=lambda nu = c. 
  Wavelength <--> color, short lambda -- bluer color, longer lambda 
  -- redder color.
  
  Yellow light: wavelength lambda=0.5 microns = 5 x 10^-7 meters
  nu = c/lambda = 3 x 10^8 m/sec / (5 x 10^-7 m) = 3/5 x 10^14=6x10^14 (sec^-1)

   Your eye is sensitive to light with wavelengths from 400 nanometers
   (blue) to 700 nm (red).  Longer and shorter wavelengths exist as
   well!
   In order of increasing wavelength, the electromagnetic spectrum: 
     gamma rays  X-rays   Ultraviolet  Visible   Infrared  Radio

  Our atmosphere is transparent to visible light and radio waves, and
  some infrared, but is opaque to ultraviolet, X-ray and gamma-ray
  light, and some of the infrared.  

  The energy the light is carrying depends on its wavelength; the
  greater the frequency (the smaller the wavelength), the greater the
  energy per photon (about which we will have much to say later).  

  An object with a certain temperature will radiate electromagnetic
  energy at a certain rate.

  Infrared and ultraviolet light -- longer and shorter wavelengths. Our
skin can feel the infrared light (and gets burned by ultraviolet light!). 

Spectrum: gamma-rays (<10^-6 microns) X-rays (10^-6-.01 microns) 
UV (0.01-0.1micron) IR (0.07 microns -- 200 microns) 
Microwaves (0.02mm - 5mm) Radio (>5mm)

  A hot object glows brightly.  Heat up a fireplace poker, and it will
glow first red, then orange, and then eventually white.  The color an
object emits depends on the temperature; the hotter the object, the
shorter the wavelength at which the object emits.  The Sun's surface
has a temperature of 6000 K, and its emission peaks at 500 nanometers,
i.e., yellow light.  The actual color of the Sun our eye perceives is
the sum of wavelengths from blue to red; the Sun is actually pretty
close to white overall.  More on this in future lectures.  

  One refers to the emitted radiation as blackbody radiation (so
called because this is true for an object which absorbs all energy
which falls upon it), or thermal radiation.  The spectrum of radiation
coming off a blackbody (strictly, the energy per unit time per unit
surface area emitted by the emitting body, at each wavelength) depends
*only* on the temperature of the body.  This spectrum extends over a
very broad range of wavelengths.  Even objects too cool to glow
red-hot are emitting light, in the infrared part of the spectrum
(which we sense as heat).

  Indeed, any object at a given temperature radiates (at least
approximately) as a blackbody.

  A perfect blackbody is one that absorbs all the radiation upon it 
  and then re-emits the energy.  This is why it is called 'black',
  because a perfect black color absorbs all the light (i.e., reflects
  none of the light) falling on it.  You will also here the term
  'thermal radiation' rather than 'blackbody radiation'.  

  For blackbodies, the emitted spectrum of light (i.e., the quantity
  of energy given off each second from the object's surface, per unit
  wavelength) depends only on the temperature and the surface area.  

  Several key formulas:
    The Stefan-Boltzmann Law:
      The power (energy/time) emitted by a blackbody of temperature T
      per unit surface area, summing over all wavelengths is:
         P = sigma T^4
	 where sigma is a constant; 
	   sigma = 6 x 10^{-8} watts/m^2/K^4. 

  Thus the total power emitted by the Sun (i.e., its luminosity)
  would be given by the above expression, times the Sun's surface
  area (= 4 pi R^2, where R is the radius of the Sun).  

  All this power radiates out (at the speed of light) spreading out
  over a larger and larger area, as one gets further from the Sun.  In
  particular, at a distance r from the Sun, it is spread out over an
  enormous sphere of radius r, and thus surface area 4 pi r^2.  Thus
  the luminosity per unit area we receive, i.e., the *brightness*, at
  a distance r, from an object with luminosity L, is:
   b = L/(4 pi r^2).  
   (This is called the "inverse square law").  

   Make sure you understand the distinction, then, between brightness
and luminosity!  Many people use them interchangeably, but they are
*not* the same!

  For sunlight (L = 4 x 10^{26} watts) at the distance of the Earth (1
AU), this works out to 1000 watts/m^2.  You can do a similar
calculation to ask how much photosynthesis could be carried out, e.g.,
in Jupiter's moon Europa, given the brightness of the Sun at that
distance.

  Wein's law expresses the statement that the peak wavelength of the
  blackbody spectrum is shorter for higher temperature objects: 
    lambda_peak = 2.9 \times 10^{-3} meters/T (Kelvin)


  

© Copyright 2009 Christopher Chyba, Michael A. Strauss, and Anatoly Spitkovsky