Physics 55Monday, October 17, 2005

1. What light can tell us, continued2. Application of thermal emission to greenhouse warming.3. Doppler shift with application.

Mimas and Saturn’s Ringshttp://www.saturntoday.com/

The Big Picture of What Produces Light Spectra

Solar Spectrum Is Complex!

Thermal Radiation From Dense Media

Astronomical Spectrum Revisited

Why Stars Have Different Colors:They Have Different Surface Temperatures!

M80 globular cluster in ScorpiusOrion asterism

Answer 1: Sun emits most of its energy in visual range of spectrum.

Answer 2: Water vapor in atmosphere blocks most light except the visual range.

Why are living creatures (plants and animals) tuned to the visual spectrum?

If in the future we discover life on some remote planetand

If the remote star is similar to our Sun in temperatureand

If the planet is the right distance from the Sun for water to be in liquid and gaseous form

Then:The creatures of that planet will likely see in the visual range

just like life on Earth.

We Can Make a Prediction

Quantitative Rules of Thermal Radiation I: Wien’s Law

Wavelength of peak intensity in thermal emission gives surface temperature T!

nm(Kelvin)

000,900,2max T

Example: Sun’s surface temperature of 6000 K implies max of 480 nm, greenish light.

Conversely, measuring the light intensity spectrum I() and locating the wavelength of largest intensity gives us the surface temperature of the Sun.

PRS Question: Wavelength of Peak Thermal Emission for People?

nm(Kelvin)

000,900,2max T

A person’s healthy body temperature is about 36o C. The wavelength of peak thermal emission for a human is therefore:

1. ~80,000 nm (80 microns)2. ~10,000 nm (10 microns)3. ~1,000 nm (1 micron).

See site http://coolcosmos.ipac.caltech.edu/ for more info and examples.

Quantitative Rules of Thermal Radiation II: Stefan-Boltzmann Law of Emitted Power

Intensity I of emitted light (energy emitted per unit

time per unit area) grows as the 4th power of surface

temperature T, where T is measured in kelvins (absolute

temperature).

Note: A degree symbol o is not used with the Kelvin scale, one writes 290 K, not 290o K.

4

82 4

wattwhere ~ 5.7 10

m Kelvin

I T

Some Astronomical Vocabulary

Luminosity of some object is the total energy emitted per second (power), has units of watts (W).

Apparent brightness is the amount of energy being received per second per unit area of measuring device. Apparent brightness is easily measured.

2 4

2

luminosity = "surface area" "thermal emission intensity"

= 4

apparent brightness = intensity at distance

luminosity =

4

r T

R

R

Example of Stefan-Boltzmann: Equilibrium Temperature of Earth

2

Total energy radiated by Sun each second into space

= luminosity of Sun

= "surface area of Sun" "intensity of light emission"

= (4 ) SunR

4 ( )

Total energy received by Earth each second

= fraction of solar energy received at Earth's orbit

= (cross-sectional area of Earth/area of sphere) power

SunT

22 4

2

2 4

= (1-reflectivity) 44

Total energy radiated out into space each second by Earth

= 4

Equate power received from Sun to power radia

EarthSun Sun

Sun Earth

Earth Earth

RR T

d

R T

1/ 2

1/ 4

1/ 251/ 4

8

ted by Earth to get:

1-reflectivity2

7 10 km (1 .36) 6000 K

2 (1.5 10 km)

~ 260 K, colder than freezing!

SunEarth Sun

Sun Earth

RT T

d

See Mathematical Insight 11.1 on page 301 of text.

Greenhouse Gas Effect

The Doppler Shift for Waves

Love That Doppler Shift

Use Spectra To Calibrate Doppler Shift

Note: A blue shift does not mean spectral line is itself blue, same for red shift. These terms mean qualitative way that any wavelength changes under motion, even for wavelengths that can not be perceived by humans (microwaves, X-rays).

Doppler Shift Formula

c

v

Speed v is the radial speed toward or away from observer.

This formula is valid only for speeds v less than speed of light, say v < ~0.1c.

Speed v is positive if object moving away (change in wavelength is positive), negative if moving toward.

Doppler Shift Gives Only Radial Speed

Quantitative Doppler Shift ExampleRest wavelength of certain hydrogen line is 656.285 nm.Same wavelength in spectrum of Vega is 656.255 nm.

Conclude that radial speed of Vega is toward us, toward since is negative, i.e., wavelength has been blue-shifted to a shorter wavelength. The value of the radial speed is then:

-5

(656.255 656.285) nm

656.285 nmkm

= - 4.6 10 -13.7s

v

c

v c

c

c

This is lower bound of Vega’s actual speed since we don’t know Vega’s tangential speed with respect to Earth.