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ASTRO 2233

TOPICS IN ASTRONOMY AND ASTROPHYSICS

Fall 2008

Lectures 1 & 2

Telescopes

August 28 & September 2, 2008

Don Campbell

ARECIBO RADIO TELESCOPE

D = 300 m => Res = 20 arcsec at λ = 3 cm

EARLY GREEK ASTRONOMY:

Obliquity of Earth - Angle between plane of the Sun’s motion in the sky (the

ecliptic) and the plane of Earth’s equator.

Known in the 6th century BCE – measured angle differences for

shadows at the summer (northern) soltice and the winter soltice

≈ 470 - Tropic of Cancer +23.50; tropic of Capricorn -23.50

Eratosthenes (276 – 194 BCE) measured angle difference of 11/83 of a circle

= 470 43’

Real value NOW = 460 26’ – has decreased by ~15’ since antiquity

ECLIPTIC and the ZODIAC:

Looking from Earth, Sun moves in the Ecliptic plane – defined by Lunar

eclipses since you can’t see the stars around the Sun.

Ecliptic plane lies in the Zodiac – the constellations through which the

Sun and planets pass during a year.

Babylonian astronomers knew about the Zodiac in the 6th century BCE,

Greeks in the 5th century.

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“Because of the precession of the equinoxes, the vernal equinox moves

through all the constellations of the Zodiac over the 26,000 year precession

period. Presently the vernal equinox is in the constellation Pisces and is

slowly approaching Aquarius. This is the origin of the "Age of Aquarius"

celebrated in the musical Hair: a period when according to astrological

mysticism and related hokum there will be unusual harmony and

understanding in the world. We could certainly use a dose of harmony and

understanding in this old world; unfortunately, it is unlikely to come because

of something as irrelevant as the position of the vernal equinox with respect

to the constellations of the Zodiac. “ (Unknown author)

The Dawning of the Age of Aquarius (Almost)

Celestial coordinates

- Right Ascension (RA) and

Declination (δ or Dec)

PRECESSION => RA and δ

coordinate frame rotates with

26,000 yr period => must

specify year with RA and δ

e.g. 2,000 coordinates (common)

DISTANCES

Astronomical Unit (AU): Mean distance from Earth to the Sun (149.598 106 km)

Light year: Distance light travels in one year (9.5 1012 km) (vel. of light = 3 105 km s-1)

Parsec: Distance at which 1.0 AU subtends 1 arc sec (= 2 105 AU ~ 3.26 light years)

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THE APPARENT MAGNITUDE BRIGHTNESS SCALE

Logarimithmic since the sensitivity of the eye to brightness is logarithmic

Inverted scale – all the fault of the Greeks.

Greeks set brightest star to have

brightness of ~1

Dimmest observable star to have

brightness of ~6

Suppose we have two stars with

apparent magnitudes m1 and m2.

We can calculate the ratio of their

brightnesses b1 and b2 by the formula:

m1 - m2 = -2.5 log (b1 / b2)

Let's compare Sirius, the brightest star

visible in the night sky, to the Sun.

(-1.5) - (-26.8) = -2.5 log bSirius / bSun

log bSirius / bSun = -10.1

bSirius / bSun = 10-10.1 = 7.9 x 10-11

bSirius / bSun = 1/13,200,000,000.

Sirius appears 13,200,000,000 times

fainter than the Sun.

But Sirius is actually more luminous than

the Sun. It is just much more distant.

Apparent magnitudes of some familiar objectsFor the apparent brightness, we usually use the apparent magnitude, conventionally written as m.

5 magnitudes = 100

N.B. Magnitude differences can change depending on the wavelength

ABSOLUTE MAGNITUDE (M) = APPARENT MAGNITUDE (m) IF OBJECT WAS AT A DISTANCE OF 10 PARSECS

M = 5 + m - 5log (d)

where d = dist of object in parsecs

ONE PARSEC = DISTANCE AT WHICH 1 AU SUBTENDS AN ANGLE OF 1.0 ARCSEC

We are probably nearing the limit of all we can

know about astronomy.- Simon Newcomb, astronomer, 1888

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Ionospheric absorption

Interstellar

absorption Atmospheric absorption

• BEFORE 1950’s OBSERVATIONAL ASTRONOMY USED ONLY OPTICAL TELESCOPES – 200 inch PALOMAR TELESCOPE COMPLETED 1948

• FIRST RADIO ASTRONOMICAL TELESCOPES IN 1950’s

• FIRST SPACE BASED TELESCOPES/MISSIONS IN 1960’s

Infrared, UV, x-rays, γ-rays

• VERY LARGE ARRAY (VLA) 1976 – Synthesis radio telescope

• COSMIC BACKGROUND EXPLORER 1989 – Cosmic Microwave Background

• HUBBLE SPACE TELESCOPE 1990

• 10 m KECK TELESCOPE 1993

• CHANDRA X-RAY SATELLITE 1999

• SPITZER INFRARED TELESCOPE FACILITY (SIRTF) Aug 25 2003

1770’s Charles Messier compiled list of 100 “fuzzy” or diffuse non-stellar objects (nebulae) in the sky – Messier objects

1864 – General Catalogue of Nebulae by John Herschel

1888 – New General Catalogue (NGC numbers) by J. Dreyer

Some of these nebulae showed spiral structure – debate raged until 1920 as to whether these nebulae were in our galaxy or external to it.

Issue resolved by Edwin Hubble in 1922 using new 100 inch Mt Wilson telescope in California using Cepheid variables as standard candles.

New and better telescopes allow problems to be solved.

ATMOSPHERIC ABSORPTION

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Sky brighness temperature and atmospheric transmission over Cerro

Chajnantor (near ALMA site in Chile) with 1 mm of precipitable water

overhead and over the VLA site in New Mexico with 4 mm of precipitable

water overhead.

Cerro Chajnantor, Chile site ~5,600 m

CCAT – Cornell-Caltech sub-mm telescope

Galileo Galilei (1564 (?) – 1642

Galileo’s telescope –

about 2 cm effective

aperture

2009

– 400 YEARS OF ASTRONOMICAL TELESCOPES

ORBITS: Confirmation of the heliocentric model of the solar system

Galileo (1609 and 1610)

- Observed that Venus showed “phases” like the Moon

- not possible on the epicycle model

- Discovered the Jovian (Galilean) satellites

- clearly in orbit about Jupiter – mini-solar system

Jupiter and its moons (1609)

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ELECTROMAGNETIC WAVES

Oscillating electric and magnetic fields that propagate with a velocity;

v = (ε µ)-1/2 where ε = the electric permittivity

µ = the magnetic permeability

For a vacuum: v = c = (ε0 µ0)-1/2 = 2.997 108 ms-1 ≈ 3 108 ms-1

where ε0 & µ0 are the values for a vacuum

Image courtesy of W. Blake, U. Rochester

In vacuum c = λ x ν

where λ = wavelength

ν = frequency

In 1864 James Clerk Maxwell derived a set of equations – Maxwell’s

equations – which showed the relationship between electric and magnetic

fields

=> a propagating electromagnetic wave in a vacuum

- a very new concept!!

Propagation in a Dielectric (non-conducting) material – e.g. glass

v = (ε µ)-1/2 ms-1 and, for a vacuum, c = (ε0 µ0)-1/2 ms-1

Substituting: v = c x (ε0 µ0)1/2 / (ε µ)1/2

= c/n where n = the refractive index = (ε µ)1/2 / (ε0 µ0)1/2

For Earth’s atmosphere at radio wavelengths n ≈ 1.0003 - mainly due to H20 vapor

For non magnetic materials: n ≈ (ε/ε0)1/2 since µ ≈ µ0 (almost all materials)

Plane and Spherical Wavefronts and Huygens’ Principle

Plane

wavefront

Spherical

wavefront

Point source will generate a spherical wavefront.

Point source at “infinity” (a large distance) will give a plane wave or

use a lens

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Huygens principle: “Each point on a wavefront may be considered a point

source of secondary waves – wavelets. After time ∆t the new location of the

wavefront is the envelope – or tangent surface – to these secondary wavelets.”

Reflection and Refraction:

Reflection: θr = θi

Refraction: n1 sin θi = n2 sin θt

Refractive index

n1

n2

Refraction is just the application

of Huygens principle and the

different propagation velocities

in the two media.

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For small angles sinθ = θ and First Null is at θ = λ/a radians

Plane wave incident on a slit Fraunhofer Diffraction Pattern

I(θ) = I0 [sin (πaθ/λ)/ (πaθ/λ)]2

HOW DO TELESCOPES WORK?

For circular apertures first null is at 1.22 λ/a

Intensity at the focal point as telescope

scans a “point” source of radio waves

Single or a few

pixels only at cm

wavelengths

Telescope

resolution ~ λ/D

radians RESOLUTION = λ/D radians1 rad = 2 105 arcsec

At optical wavelengths 10 cm diameter gives ~ 1 arcsec resolution

Hubble Space Telescope: 90 cm aperture => 0.1 arcsec at 0.6 µm

Earth based telescopes: Atmospheric turbulence limits resolution to, at

the very best, about 0.25 arcsec.

Adaptive optics a partial solution

100 m radio telescope at a wavelength of 10 cm gives ~ ??

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Achromatic lenses invented by

Fraunhofer ~1815 – solved the

problem

Lenses produce chromatic aberration: light of different

wavelengths comes to focus at different points.

OPTICAL TELESCOPESFUERTES OBSERVATORY

12 inch diameter refractor

Joseph van Fraunhofer 1787 - 1824

Fraunhofer Diffraction Patterns

Fraunhofer lines in the solar spectrum

Fraunhofer achromatic lenses

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Resolution: The minimum angle at which two point sources of light (or

radio waves) can be distinguished. Very close to λ/D

Field of View: Solid angle over which a telescope can focus an incoming

plane wave – dependent on ratio of focal length to diameter – F/D ratio

Number of independent pixels over the field of view ≈ FOV x D2/λ2

e.g. FOV = 1 square degree; resolution = 1 arcsec

Number of pixels ≈ 107 ≈ # of pixels in a good digital camera.

N.B. Single dish radio telescopes typically have 1 to a few pixels

WE WANT MORE!

200 inch

PALOMAR

TELESCOPE

Gemini North 8 m telescope on Mauna

Kia showing the Cassegrain focus.

SEEING!

Japanese 8 m Subaru telescope on Mauna Kia, Hawaii showing

Nasmyth focus

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KECK 10m TELESCOPES

D = 10 m => res = 0.01 arc sec at 0.5 µm

(Earth’s atmosphere is the limit on the res.)

Planned Large Optical/IR TelescopesExpected 2015 to 2020

OWL – European

Overwhelmingly

Large Telescope

40 m diameter

Thirty meter telescope (TMT)

Caltech/California project

HUBBLE SPACE TELESCOPE

D = 2.4 m => resolution = 0.04 arcsec at λ = 0.5 µm

JAMES WEBB SPACE TELESCOPE

D = 6 m

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Large Synoptic Survey Telescope

(LSST)

PanSTARRS 1.8 m telescope

LARGE BINOCULAR TELESCOPE

Mt Graham, Arizona

SPITZER INFRARED TELESCOPE CHANDRA X-RAY TELESCOPE

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LASER INTERFEROMETER GRAVITATIONAL OBSERVATORY (LIGO) AT HANFORD, WA

AND LIVINGSTON, LOUISIANA