April 4, 2007, jeb

Outline

• Scientific Notation
• Temperature Scales
• Light and Electromagnetic Radiation
• Generation of Electromagnetic Radiation
• Blackbody Radiation
• Astronomical Applications
• Inverse Square Law
• Doppler Effect
• Distance Scales

Scientific Notation




10 x 10 = 100 = 10²

10 x 10 x 10 = 1,000 = 10³

10 x 10 x 10 x 10 x 10 x 10  = 1,000,000 = 10⁶

300,000 = 3 x 10⁵

5,000,000,000 = 5 x 10⁹

1/10 x 1/10  = 1/100 = 10^-2

1/1,000,000 = 10^-6

Temperature Scales 



There are three temperature scales in common usage: 

The Fahrenheit Scale: 
• we are most familiar with this one
• water freezes at 32 degrees F.
• water boils at 212 degrees F.
• when we cool to the absolute lowest temperature we reach -459 degrees (this is referred to as Absolute Zero)

The Celsius Scale:
• water freezes at 0 degrees C.
• water boils at 100 degrees C.
• Absolute Zero is at -273 degrees C.

The Kelvin Scale
• Absolute Zero is 0 K
• a temperature change of 1 degree K is the same as a temperature change of 1 degree C.
• water freezes (or melts) at 273 K
• water boils at 373 K

The Kelvin scale is the more useful scale for our course since it refers to Absolute Zero in a direct way.

Light and Electromagnetic Radiation



• We learn about the stars by studying the electromagnetic radiation that they emit.



• Visible light is one particular type of electromagnetic radiation.



• The types of electromagnetic radiation are:
• radio
• infrared
• visible light
• ultraviolet
• X rays
• Gamma rays



• Electromagnetic radiation is a wave with a wavelength and an amplitude.



• The frequency of a wave is related to its velocity and wavelength through the formula



wavelength x frequency = velocity



• wavelength is measured in units of length
  
  • meters
  • millimeter (mm) = 0.001 m = 10^-3 m
  • micrometer (&mu m) = 0.000001 m = 10^-6 m
  • nanometer (nm) = 0.000000001 m = 10^-9 m
  
  
• frequency is expressed in units of inverse time (1/sec)
  • called Hertz (1 Hz = 1/sec)



• Since electromagnetic radiation (or waves) travel at the speed of light
  300,000 kilometers/second
  
  • 1 kilometer(km) = 1000 m = 10³ m
  we have a relationship between wavelength and frequency.



wavelength x frequency = 300,000 km/sec




• The electromagnetic spectrum ranges from radio waves at one extreme to gamma rays at the other extreme.
  
  
• Radiation is composed of "photons" (packets of electromagnetic radiation)
  • the "photons" are "particles"
    • Einstein was awarded the Nobel Prize for understanding that light (and electromagnetic radiation) is composed of these "particles" ("photons")
  • the "photons" have energies related to the "color" or wavelength
    • short wavelengths -> higher energies
      • like gamma rays
    • long wavelengths -> lower energies
      • like radio waves
  
  
  
• So light is both a wave, and particles.
  • This property is known as "wave-particle duality," a basic element of the quantum theory of physics
  
  
  
• Visible light can be split into its components by a prism.
  • the bending of light in going through the prism results from REFRACTION
  • long wavelengths (red) are refracted less than short wavelengths (blue and violet)
  
  
  
• The entire electromagnetic spectrum shows the frequencies and wavelengths of the types of electromagnetic radiation.



• The atmosphere blocks much of the electromagnetic radiation from space. 
  This is referred to as atmospheric "opacity".
  There are "windows" of transparency in the radio and visible parts of the spectrum.

Generation of Electromagnetic Radiation 



Electromagnetic Radiation is generated by the movement of charged particles

Nature's primary charged particles are:
• Proton (positive charge)
• Electron (negative charge)


Electromagnetic Waves
• Changing electric fields are accompanied by magnetic fields
• The Earth has a magnetic field
  • The Earth's magnetic field is relatively static, not a wave


On Earth, we generate radio waves (a form of Electromagnetic Radiation) by moving electrons along an antenna
We also detect radio waves when they move electrons along an antenna attached to a receiver

Some Demonstrations
• The Electric Force
• Vibrating Charges and Electromagnetic Waves
• The Magnetic Force

Blackbody Radiation 



A blackbody radiator is a perfect radiator of light that absorbs and re-emits all radiation incident on it.

Its light output depends only on its temperature.

The sun and stars emit radiation like a blackbody following the Blackbody spectrum.
• This curve is known as the blackbody curve, or the Planck curve.


As an object (a blackbody) is heated, the radiation it emits will always be described by the blackbody spectrum for the temperature of the body, with the curve peaking to higher and higher frequency. 



Wien's Law
The maximum wavelength of radiation emitted by a blackbody is inversely proportional to the temperature:
max wavelength ~ 1/Temperature



Stefan's Law
The total amount of energy emitted by a blackbody is proportional to the 4th power of the temperature:
energy radiated ~ T⁴

Wien's Law and Stefan's Law are evident in the changes in the blackbody spectrum with temperature.

Astronomical Applications


The Sun appears differently in each type of radiation


Examples of the blackbody spectra from cosmic objects:
(a.) a cool, invisible galactic gas cloud, Rho Ophiuchi (T=60 K)
(b.) a dim, young star in the Orion Nebula (T=600 K)
(c.) the Sun, with a surface temperature of 6000 K
(d.) a globular cluster of bright stars, Omega Centauri (T=60,000 K)


The Milky Way Galaxy as it appears at many wavelengths
(a.) radio wavelengths
(b.) infrared wavelengths
(c.) visible wavelengths
(d.) X-ray wavelengths
(e.) gamma-ray wavelengths

Inverse Square Law



The farther away an object is the fainter it appears.

We refer to the amount of radiation for the star at our location as the apparent brightness.

The apparent brightness of a star is inversely proportional to the square of its distance:

apparent brightness ~ 1/(distance)²


This Law results from the spreading of the energy in the radiation.

The Doppler Effect



Electromagnetic radiation (of any type) always travels through diffuse space at the same speed, the speed of light:
300,000 kilometers/second


The observed speed will not depend on relative motion.

However, the wavelength of the light does change with relative motion.

Stars moving away from us appear red-shifted and stars moving toward us appear blue-shifted.

This can be illustrated by considering the wave crests of the wave motion.

Distance Scales 



There are two distance scales in use in Astronomy: 

The Light-year (ly): 
• the distance light will travel in one year
• 1 ly = 9.46 x 10¹² kilometers
• you can calculate this distance by multiplying
  • the speed of light (300,000 kilometers/second)
  • by the number of seconds in a year (3.15 x 10⁷)


The parsec (pc)
• related to the apparent motion of a close object compared to the relatively more distant background over the course of one year (see illustration - Fig 17.1 of textbook)
• if the angle of parallax is 1 second of arc, the distance is 1 parsec
• 1 pc = 3.1 x 10 ¹³ kilometers


1 parsec = 3.26 light-years

The "local" neighborhood

Summary

• There are many forms of electromagnetic radiation
  • visible light, radio, ultraviolet, etc.
  • wave characterized by period, wavelength, and amplitude
  • frequency is reciprocal of the period
• Moving electric charges generate radiation
  • Radiation moves through empty space at the speed of light
    • 300,000 kilometers per second
• Blackbody radiation laws based on temperature
• Inverse square law
• Doppler effect