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Northern Lightsthis week

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Suppose we want to find the energy (rate) fluxradiated from the surface of a sphere……

First, find the peak intensity of the blackbody radiation

and use Wien’s law to get the temperature:

T =

Then, the energy emitted per second per unit area from a surface is proportional to absolute temperature

of the surface to the fourth power (T4). This is called energy flux. This is Stefan’s Law:

__________________2.9 x 10-3 (meters)(K)

wavelength (in meters)__________________2.9 x 10-3 (meters)(K)

wavelength (in meters)

Energy flux (in J/s/m2) = σT4

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We want to find the total energy per second radiated from a spherical surface having temperature T

We multiply the surface area times the energy flux: (surface area 4πR2 [meters2]) x (energy flux [Watts/m2])

This is the Stefan-Boltzmann Law for the rate of energy radiated from a spherical surface:

L = (4πR2)σT4 (Watts or J/s)

L is luminosity, the total energy/sec (power) radiated.

σ is the Stefan-Boltzmann constant: 5.67x10-84

The surface temperature of the Sun is ~ 5800 Kand the radius R of the Sun is ~ 7 x 108 m

Stefan’s Law shows that the energy flux at theSun’s surface is approximately 64 million Watts/m2,

and there are lots of square meters of surface area on the Sun (~ 6.1 x 1018 m2)

We use the Stefan-Boltzmann equation and findthat the total energy output of the Sun, per second

(i.e., its luminosity is (area x flux):

L = 3.9 x 1026 Joules/second or Watts

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The Sun’s luminosity L = 3.9 x 1026 Watts (constant)

Suppose a sphere with a radius the size of the Earth’s orbit encloses the Sun,

then the total energy of the Sun goes through the surface of this sphere (with many more sq. meters).

The surface of this sphere is 4π(1 AU)2 ≈≈≈≈ 2.83 x 1023 m2

Divide the Sun’s luminosity by this surface area andwe have an energy flux of 1380 Watts/m2

This number is called the solar “constant”.6

Sun

Earth

Mars

dEarth

Total power (L) of the Sun goes through all three spheres

energy flux = Luminosity L area of sphere

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Suppose we go out to the orbit of Mars and create a new sphere that completely encloses the Sun.

The entire luminosity of the Sun must go through this sphere also. (A sphere with even more sq. meters)

The energy flux through this sphere is

Fmars = Lsun_________

4π(1.52 AU)2

and we have a solar constant for Mars: ~ 600 W/m2

We see the nearest star with a flux of ~ 10-10 W/m2

This is why we need telescopes…….

Astronomical

Tools

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Topics

• Telescope concepts ♦

• How telescopes work ♦

• What a telescope does ♦

• Telescope types

• Space telescopes

• Detectors and Instrumentation

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TELESCOPES

• The general purposes of any telescope are to gather light and to bring that light to a focus.

• Telescopes can be designed for either visible or invisible radiation.

• The most important component of any telescope is the objective lens or mirror.

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POWERS OF A TELESCOPE

• LIGHT GATHERING POWER

• RESOLVING POWER

• MAGNIFYING POWER

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LIGHT GATHERING POWER

• Is the ability to see faint objects

• The most important power for astronomers

• Varies directly with the surface area of the objective (diameter2)

• The human eye has an aperture of about 1/5" and can see about 6,000 stars.

• A 2" telescope sees about 110,000 stars.

RESOLVING POWER

• Is the ability to see fine details

• Varies directly with the diameter of the objective

• The human can resolve an angle of about 70 arc seconds.

• The theoretical limit for the largest telescopes on Earth is less than 0.1 arc second.

• Resolving Power = D/λ λ λ λ

or Diameter / wavelength

MAGNIFYING POWER

• The ability to enlarge an image

• Magnifying power = fobjective/feyepiece.

• A practical limit to magnifying power can be found: 50 x Diameterobjective

(inches).

• Normally it is the least important for

astronomers.

FOCAL LENGTH

OPTICAL TELESCOPES

(a) REFRACTORS

(b) REFLECTORS

REFRACTOR TELESCOPE

• USES A LENS AS THE OBJECTIVE TO GATHER LIGHT

• LIMITED IN SIZE

• CHROMATIC ABERRATION

• GALILEO’S TELESCOPE

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REFLECTOR TELESCOPE

• USES MIRROR AS OBJECTIVE TO GATHER LIGHT

• CAN BE MADE LARGER THAN REFRACTORS

• ARE LESS EXPENSIVE FOR A GIVEN SIZE

• ARE FREE FROM CHROMATIC ABERRATION

• NEWTON’S TELESCOPE

WORLD’S LARGEST

OPTICAL TELESCOPES

McDonald

NEW-GENERATION

TELESCOPES

• MULTIPLE MIRROR

• LIGHT WEIGHT RIGID MIRROR

• FLEXIBLE MIRROR (ACTIVE OPTICS)

• SEGMENTED MIRROR

• LIQUID MIRROR

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MULTIPLE MIRROR

TELESCOPE

• Uses two or more fully operational mirrors acting as a single telescope

• Computers are needed to keeps the mirrors properly aligned.

• MMT had six 1.8 meter mirrors.

• Very Large Telescope will have four 8 meter mirrors.

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SEGMENTED MIRROR

TELESCOPE

• Mirror segments are fit together like a puzzle.

• Computers align the mirror segments

• Keck I & II Telescopes are each 10 meters

• Hobby-Eberly Telescope at McDonald Observatory in Texas is a 9.2 meter segmented mirror design

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Curvature control of a segmented mirror

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OPTICAL INTERFEROMETER

• Combines images from two or more

telescopes

• Improves resolving

power

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KECK INTERFEROMETERKeck twin telescopes,located on the 13,800 ft

summit of Muana Keain Hawaii, are the largest

optical and infra-redtelescopes in the world.

The diameter of eachmirror is 10 meters. Each

mirror is composed of36 hexagonal segments.

Each telescope with

mounting structure weighs 300 tons.

The telescopes work

together and useinterferometry, or

interference of light,to increase resolution.

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• IMAGING DEVICES

• PHOTOMETER

• SPECTROGRAPH

INSTRUMENTS ON THE

TELESCOPE

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IMAGING DEVICES1. Drawing what was seen

through the telescope

2. Photography greatly increased the "light gathering power" of the telescope by allowing an image to build up on the film.

3. Electronic (digital) cameras utilizing CCD(charge-coupled device) chips have taken the place of film in many applications in the last few years.

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CCD IMAGES

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IMAGE PROCESSING

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PHOTOMETER

• Measures the intensity of the light from a celestial object very accurately

• Often used to monitor variable stars

• Data can be read directly into a computer for analysis

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SPECTROGRAPH

• Records the spectrum of celestial objects

• Can be used in conjunction with a digital camera or photometer

• Data can be read directly into a computer for analysis

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INVISIBLE ASTRONOMY

FROM EARTH• RADIO

• INFRARED

FROM SPACE• INFRARED

• ULTRAVIOLET

• X-RAY

• GAMMA RAY

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RADIO ASTRONOMY

• Is done from the Earth's surface

• Radio waves pass through interstellar dust and even clouds on Earth

• Cool neutralhydrogen radiates at radio wavelengths (spiral arms of the Milky Way galaxy)

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A TYPICAL RADIO TELESCOPE

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ARECIBO RADIO

TELESCOPE

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RADIO INTERFEROMETRY

• Radio telescopes are usually quite large but have low resolving power.

• Interferometry is used to "connect" radio telescopes thus improving resolving power.

• The Very Large Array (VLA) near Socorro, New Mexico uses 27 radio telescopes simultaneously.

• Very Long Baseline Interferometry links telescopes from around the world and increases resolving power to about 0.001 arc second.

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VLA NEAR SOCORRO, NM

27 RADIO TELESCOPES

44The VLA seen from an elevation

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SPACE ASTRONOMY

• Able to observe at all wavelengths of the electromagnetic spectrum

• Increased resolving power because of almost perfect "seeing" in space

• Increased light gathering powerbecause of the extremely black background in space

• Observe almost continuously

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INFRARED ASTRONOMY

• Can be partially done from high (dry) observatory sites

• Done more comprehensively from space

• Relatively cool objectsradiate strongly in infrared (newly forming stars, planets, cool molecular clouds)

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SPITZER SPACE TELESCOPE

• Infrared telescope

• 85 cm diameter (33.5 inches)

• Wavelength

Coverage: 3 - 180 microns

• 2.5 years (minimum); 5+ years (goal)

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The constellationOrion, seen in

visible light.

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The same

constellation seein infra-red light.

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Triffid nebula invisible light and in infrared

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ULTRAVIOLET ASTRONOMY

• Must be done from space (ozone absorbs UV)

• Some critical information is only available at UV wavelengths

• Hot, energetic stars and stellar chromospheres radiate strongly in UV.

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