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Telescopes

Galileo's telescope
Replica of Newton's telescope
Herschel 1.2 meter reflector
Herschel 1.2 meter reflector
Yerkes 1 meter refractor

Hale 1.5 meter
Hooker 2.5 meter
Palomar 5 meter
Palomar
Keck 10 meter

Keck 10 meter
Hubble 2.4 meter
Webb 5 meter
30 Meter Telescope

Telescope            Diameter  Resolution  Year
                     (meters)  (microrad)

Human eye                .005    291
Lippershey's telescope    ?        ?       1608   First telescope.  Refractor
Galileo's telescope #1   .015     34       1609   Refractor
Galileo's telescope #2   .038     10       1620   Refractor
Newton's telescope       .033     12       1668   First reflecting telescope
Herschel telescope      1.20       2.5     1789   Reflector
Yerkes refractor        1.02       2.5     1897   Refractor.  End of refractor age
Hale 60-inch            1.52       2.5     1908   Mount Wilson observatory
Hooker 100-inch         2.54       2.5     1917   Mount Wilson observatory
Hale 200-inch           5.08       2.5     1948   Palomar Observatory
Keck                   10          2.5     1993   Mauna Kea Observatory
Hubble                  2.4         .20    1990   Earth orbit
Webb Space Telescope    6.5         .10       ?   L2 Lagrange point
Thirty Meter Telescope 30           .20       ?   Mauna Kea Observatory

Refracting telescope

Focus
Focus
Refracting telescope

Refraction depends on wavelength, which introduces "chromatic aberration". This limits the size of refracting telescopes. Reflecting telescopes don't suffer this limitation.


Reflecting telescope

Parabolic mirror
Gregorian
Newtonian
Cassegrain
Ritchey-Chretien

1608  Lippershey constructs the first refracting telescope
1663  Gregory publishes a design for a "Gregorian" reflector
1668  Newton constructs the first reflecting telescope, a "Newtonian" reflector
1672  Cassegrain publishes a design for a "Cassegrain" reflector
1910  Ritchey-Chretien reflecting telescope, the basis for modern reflectors

Visual resolution

A person with 20/20 vision can distinguish parallel lines that are spaced by an angle of .0003 radians, about 3 times the diffraction limit. Text can be resolved down to an angle of .0015 radians.

   
        Resolution     Resolution    Diopters
        for parallel   for letters   (meters-1)
        lines          (radians)
        (radians)
20/20     .0003         .0015          0
20/40     .0006         .0030         -1
20/80     .0012         .0060         -2
20/150    .0022         .011          -3
20/300    .0045         .025          -4
20/400    .0060         .030          -5
20/500    .0075         .038          -6
"Diopters" is a measure of the lens strength required to correct vision to 20/20.

If you are looking at a screen that is .2 meters from your eyes, the minimum resolvable pixel size is

Pixel size  =  .0003 * .2  =  .00006 meters  =  .06 mm

Diffration

Aperture size = Wavelength
Aperture size = 5 * Wavelength

The resolution of a telescope is limited by diffraction.

Wavelength of light  =  L
Mirror diameter      =  D
Resolution angle     =  θ  =  1.22 * L / D
If we assume blue light with L=440 nm,
                     D        θ

Eye                 .005   .00011
10 cm telescope     .1     .0000054
Hubble telescope   2.5     .00000021

1 Degree    =  60 arcminutes  =  3600 arcseconds
1 arcsecond =  4.8e-6 radians

Twinkling stars

Moonlight distorted by the atmosphere
Mirage caused by refraction
Distortion of a wavefront by the atmosphere

A star without atmospheric distortion
A star with atmospheric distortion

The atmosphere blurs light from outer space, limiting telescopes to a resolution of 5e-6 radians or 1 arcsecond. This is the resolution of a 10 cm telescope. A telescope larger than 10 cm has the same resolution as a 10 cm telescope. The advantage of the larger telescope is more light.

Telescope     Resolution           Reason for
diameter      (radians)            resolution limit
(meters)

  < .1        5e-7 / Diameter      Diffraction
  > .1        5e-6                 Atmosphere
A space telescope doesn't experience atmospheric distoration and the limit is from diffraction only. The 2.5 meter Hubble space telescope has a better resolution than the 10 meter Keck Earth telescope.

Telescopes equipped with "adaptive optics" can correct atmospheric distortion and reach a resolution better than 5e-6 radians.


Sensitivity

Astronomers measure brightness in a goofy unit called "magnitudes". It was defined by Hipparcos in Ancient Greece and it's still with us.

The "Apparent luminosity" of a star is its brightness as viewed from the Earth.
The "Absolute luminosity" is the power generated by a star in Watts.

R  =  Distance to star
L  =  Luminosity in Watts
l  =  Flux in Watts/meter2
M  =  Absolute magnitude
m  =  Apparent magnitude              

Flux corresponds to the brightness of an object as viewed from the Earth.

l  =  L / (4 π R2)

L  =  3.29e28 * 10-M/2.5  Watts

l  =  2.16e-8 * 10-m/2.5  Watts/meter2

M  =  m + 87.71 - 2.17 log(R)
The fainter an object, the larger its apparent magnitude "m".

Nearby stars, with color, size, and brightness to scale. Overlapping stars are binary stars.

                  Distance  Luminosity  Flux        Absolute   Apparent
                   from       Watts     Watts/m2    magnitude  magnitude
                   Earth       (L)         (l)         (M)        (m)

Sun                1    AU   3.8e26      1360        4.8        -26.7
Full Moon        .00257 AU   4.8e15      2.6e-3     32.1        -12.7
Mars                .52 AU   2.3e16      3.1e-7     30.4         -2.9
Jupiter            4.2  AU   1.5e18      3.1e-7     25.8         -2.9
Saturn             8.5  AU   6.8e17      3.4e-8     26.7          -.5
Uranus            18.2  AU   1.5e16      1.6e-10    30.9          5.3    Discovered 1781
Ceres              1.77 AU   4.3e13      4.9e-11    37.2          6.6    Discovered 1801
Neptune           29.1  AU   3.8e15      1.6e-11    32.3          7.8    Discovered 1846
Pluto             28.7  AU   1.8e13      7.8e-14    38.2         13.6    Discovered 1930
Alpha Centauri A   4.36 ly   5.9e26      2.7e-8     4.4           0.0
WISE-0855          7.2  ly   3.4e21      5.9e-14   17.5          13.9    Rogue planet
Sirius             8.58 ly   9.8e27      1.2e-7     1.4          -1.5    Brightest star
Exo-Sun           10.0  ly   3.8e26      3.4e-9     4.8           2.0
Exo-Earth         10.0  ly   5.4e16      4.8e-19   29.5          26.6
Betelgeuse       640    ly   5.8e31      1.3e-7    -6.0            .4    Massive star
Andromeda    2560000    ly   9.9e36      1.3e-9   -21.6           4.2
Values for solar system objects are for when they are closest to the Earth.

Uranus is at the limit of human vision. It's conceivable that an ancient civilization could have detected Uranus. Ceres is just beyond human vision.

WISE-0855 is a brown dwarf with a mass somewhere between 3 and 10 Jupiter masses. It has a temperature of 240 Kelvin and was detected by the WISE infrared space telescope.

"Exo-Sun" and "Exo-Earth" are values for if the sun and the Earth are at a distance of 10 light years.

GRB 080319B is the most luminous recorded gamma ray burst.

The horizontal lines represent the limits of the Pan-STARRS, Keck, Hubble, and Webb telescopes. Exo-Earth is detectable by the Keck telescope.


Limit of telescopes
                  Flux        Apparent
                  limit       magnitude
                 Watts/m2      limit

Human eye          3.4e-11       7
Pan-STARRS         5e-18        24
Keck 10 meter      1e-19        28
Hubble             1e-20        31
Webb               5e-22        34

Atmospheric transmission

              Observable from the ground?
Gamma ray     No
X ray         No
Ultraviolet   No
Visible       Yes
Infrared      No
Millimeter    Yes, if the air is dry
Radio         Yes

Wavelength range of telescopes

Wavelength in meters

The SOFIA tel escope can see in the infrared because it flies on a Boeing 747 at an altutude of 12 km, which is above most of the atmosphere's water.


Radio telescopes

Square Kilometer Array
Arecibo
Green Bank

Square Kilometer Array
Square Kilometer Array
Square Kilometer Array, artist's conception

                                       Min & Max
                      Aperture  Year   wavelength
                         (m)            (meters)
Arecibo                  300    1963   .03    1.0  Puerto Rico
Green Bank Telescope     100    2000   .0026  3.0  Green Bank, West Virginia. Largest steerable dish
Astron                    10    2011   .01    1.0  High Earth orbit. Used for large-baseline interferometry
Square kilometer Array  1000    2019   .01    4.3  Australia and South Africa

Millimeter telescopes
                       Min & Max
      Aperture   Year  wavelength
      (meters)           (mm)
CSO      10.5    1986  .3    2.0  Mauna Kea                 Caltech
Maxwell  15      1987  .3    2.0  Mauna Kea
ALMA     12      2011  .3    9.6  Atacama Desert, Chile     54 12-meter dishes and 12 7-meter dishes
LMT      50      2011  .85   4.0  Sierra Negra, Mexico      Large millimeter Telescope
CCAT     25      2017             Cerro Chajnantor, Chile   Wavelength range similar to ALMA

CSO  = Caltech submillimeter observatory
CCAT = Cerro Chajnantor Atacama Telescope
ALMA = Atacama Large Millimeter Array

Space telescopes for the cosmic microwave background radiation
        Diameter  Resolution   Mass    Min    Max    Year    Location
          (m)      (urad)     (tons)   (mm)   (mm)

Planck      1.9    4100         .21     .3    11     2009    L2
WMAP        1.6   12000         .76     .32    1.30  2001    L2
COBE         .19               1.41                  1989    Geocentric

Infrared telescopes

The SOFIA telescope on board a Boeing 747

       Aperture  Year  Min    Max  Location
       (meters)        (mm)   (mm)

WMAP      1.6    2001  .003  .015  L2 Lagrange point     NASA   Observes cosmic microwave background
Spitzer    .85   2003  .003  .180  Sun orbit             NASA
WISE       .40   2009  .003  .025  Earth orbit           NASA
Herschel  3.5    2009  .055  .672  L2                    ESA
SOFIA     2.5    2010  .001  .655  Boeing 747 at an altitude of 12 km
SOFIA = Stratospheric Observatory for Infrared Astronomy
X ray telescopes
         Aperture  Resolution  Low   High   Focus   Mass   Year
           (m)      (urad)    (keV)  (keV)         (tons)

NuSTAR       .32       46       3      79  10.15    .17   2012  Geocentric  NASA
Hitomi soft                      .3    12   5.6    2.7    2016  Geocentric  JAXA
Hitomi hard                     5      80  12      2.7    2016  Geocentric  JAXA
INTEGRAL     .31     3500       3   10000          4.0    2002  Geocentric  ESA RKA NASA
Swift        .30                                    .61   2004  Geocentric  NASA GSFC
NuSTAR has a collecting area of 847 cm2 at 7 keV and a collecting area of 60 cm2 at 78 keV. The field of view is 12 arcminutes.

The Hitomi lost attitude control and went into an uncontrollable spin, destroying the telescope.


Gamma ray telescopes
X rays from the Vela pulsar
         Year    Low    High      Mass
                (MeV)   (MeV)    (tons)

Hitomi   2016      .06       .6    2.7    Geocentric     JAXA
Fermi    2008    30    300000      4.3    Lagrange #2    NASA

Shotgun telescopes
           Aperture Magnitude  Field of  Exposure   Full-sky      CCD      Year
           (meters)  limit      view     (seconds) survey time  (Gpixels)
                              (degrees)            (days)
Pan-STARRS   3.6      24.0       3.0        60         8          1.4      2010   Hawaii
LSST         8.4      24.5       3.5        15         2          3.2      2021   El Penon, Chile
The Pan-STARRS and LSST telescopes are designed to find solar system objects, which is why they use short exposures.
Photons
Frequency         =  F
Wavelength        =  W
Planck constant   =  h          =  4.1357⋅10-15 eV seconds
Speed of light    =  C  =  F W  =  2.9979⋅108   meters/second
Energy            =  E  =  h F
Aperture diameter =  D
Diffraction angle =  A  =  1.22 W / D


                Energy  Wavelength   Temperature
                 (eV)      (nm)       (Kelvin)

Gamma ray     124000          .01
X-Ray            124        10     290000
Bohr energy       13.6      91      32000
UV-Extreme min    12.4     100      29000
UV-C min           4.43    280      10350
UV-B min           3.94    315       9200
Human UV limit     3.10    400       7244
Violet             3.06    405       7155
Blue               2.79    445       6512
Cyan               2.58    480       6037
Green              2.33    532       5447
Yellow             2.10    589       4920
Orange             2.03    610       4750
Red                1.91    650       4458
Human IR limit     1.63    750       3864
Infrared            .12    104        290
Microwave           .0012  106          2.90       300 GHz
Radio                      109           .0029     300 MHz


1800   Herschel discovers infrared light by its effect on a thermometer
1801   Ritter discovers UV rays by their effect on AgCl
1835   Melloni builds a thermoelectric infrared detector
1878   UV rays are found to kill bacteria
1879   Stefan-Boltzmann law:  Power = Constant * Area * Temperature^4
1901   Planck hypothesizes that E=hF
1905   Einstein discovers the photoelectric effect
1960   UV rays found to be harmful to DNA

Antarctic telescopes

The Antarctic plateau

"Ridge A" in Antarctica is a 4 km high plateau where the environment is cold, dry, and has no wind, making it the best place in the world for a telescope. Resolution is up to 3 times higher than what can be achieved by telescopes at the equator. It is also ideal for submillimeter astronomy, which requires cold dry air.

Properties of Ridge A:
Altitude                     = 4053 meters.
Distance from the South Pole = 1000 km.
Distance from Dome A         = 144 km.     Dome A is the highest ice feature in
                                           Antarctica, with an altitude of 4091 meters.
Annual snowfall              = 2 cm.
Average temperature          = -70 Celsius.

Earth Lagrange point telescope farm

The Webb telescope will operate from the Earth L2 Lagrange point, an ideal place for telescopes. From there you can place a barrier that blocks out the sun, the Earth, and the moon all at the same time, allowing the telescope to reach a low temperature. This is essential for infrared astronomy, which is used to detect exoplanets and distant galaxies.

A manned base station at L2 can be used to contruct large space telescopes. Segmented mirrors are launched from Earth and assembled on site.

A manned base station needs 4 tons/meter2 of ice for radiation shielding, which can be obtained from the moon. It also needs to have both a zero-gravity module for telescope construction and an Earth-gravity module for habitation.

Assuming a launch cost/kg of 1000 $/kg and a cost of 1 billion dollars, 1000 tons of material can be launched. Each telescope will have a mass in this range, with most of the mass being mirrors.

In the following table, the first section lists the largest existing space telescopes and the second section lists the kinds of telescopes that could be constructed at L2.

          Diameter  Resolution  Flux    Focus  Mass     Min       Max
            (m)      (urad)     (W/m2)   (m)  (tons)    (um)      (um)

Spektr-R     10                            4.22   2.5   13000     930000     Geocentric
Planck        1.9   4100                           .21    300      11000     L2
Herschel      3.5                         28.5     .32     55        672     L2
Webb          6.5       .10      5e-22   131.4    6.5         .6       28.5  L2
Gaia          1.45      .000034                    .71                       L2
NuStar         .32    46                  10.2     .17    3 keV    79 keV    Geocentric
Fermi                                       -     4.3    30 MeV   300 GeV    L2

Radio       1000                       10000   1000                          L2
Millimeter   200                        2000   1000                          L2
Infrared     100                        2000   1000                          L2
Visible + UV 100                        2000   1000                          L2
X              5                        1000   1000                          L2
Gamma          5                           -   1000                          L2
Astrometry
Radio: Metal can be mined from the moon and used for a radio telescope. Radio telescope mirrors can be manufactured in space whereas all other mirrors have to be manufactured on the Earth. Multiple radio telescopes can be deployed at various points in the solar system for large baseline interferometry.

Millimeter: Useful for measuring the cosmic microwave background. Occultation can be used to reach high resolution.

Infrared: Use a segmented mirror coated with gold. This telescope is optimized for finding high-redshift objects and exoplanets.

Visible+UV: Use a segmented mirror coated with aluminum.

X-Ray: An extremely long focus length can be used, which is helpful because X-rays can only be deflected by small angles.

Gamma Ray: Deploy 4 high-mass telescopes separated by thousands of kilometers. The spatial resolution allows precision measurement of the source direction using time-of-arrival of gamma bursts.


Cosmic rays


Gravity wave telescopes

         Year   Range (Hertz)
LIGO     2002   300 - 7000          Washington
LISA    ~2025   .00003 - 0.001      Sun orbit

Crowd computing

Projects such as SETI, Kepler, LIGO, and Pan-STARRS require massive data and computation and are well suited to crowd computing.

                    TFlops

Folding@home       39700     Protein folding
GPUGRID.net         2570     Simulations of proteins
Milkyway@home       1175     Construct a 3D map of the Milky Way
Einstein@home       1138     Search for pulsars
Collatz conjecture   623
SETI@home            594     Search for alien radio signals
Asteroids@home       135
theSkyNet             46     Analyze data from the Square Kilometer Array

Neutrino telescopes

                                  Neutrino   Min   Volume    Source   Year
                                    type    energy
                                            (GeV)
Super-Kamiokande                    E M T            .00005  S A G  1996       Pure water
Cubic Kilometer Neutrino Telescope                  5                          Mediterranean
IceCube Neutrino Observatory                100                            1 km3 of Antarctic ice
India-Based Neutrino Observatory
ANNIE                                          .8            S A G           Neutrinos from Fermilab

Proton decay

Grand unification theories conjecture that protons can decay.

Proton  ->  Positron  +  Pion0                      The Pion0 has a charge of 0
Proton  ->  Kaon      +  Neutrino                   The Kaon has a charge of +1
Proton decay has thus far not been observed. The best limit on proton decay comes from the Super-Kamiokande experiment.
Lower limit on the proton halflife   =   1e34 years
Protons in 1 kg of hydrogen          = 6.0e26
Mass of protons for 1 decay/year     =  17000 tons

Future

Telescope size in meters


Problems

Diffraction

You can simulate diffraction using the "Waves" simulation at phet.colorado.edu.

W  =  Wavelength of the wave
D  =  Size of the aperture
A  =  Diffraction angle of the wave
Using the simulation, how would you construct a relationship between W, D, and A?


Human vision
Limit of the human eye   =  Magnitude 7
Eye diameter             =  5 mm
If you are looking at a magnitude 7 object, how many photons/second are you seeing?


Finding Planet X

How many arcseconds does Pluto move across the sky during a 10-hour observing session?

Suppose for an asteroid:
Distance from Earth        =  0.1 AU
Speed transverse to Earth  =  10 km/s
Albedo                     =  0.2
Brightness                 = 24 magnitudes
How long does it take to move 1 arcsecond across the sky?

If we that assume the brightness of an object in the solar system is proportional to

Radius^2 * Albedo / (Distance from sun)^2 / (Distance from Earth)^2

What radius does the asteroid have to have to have magnitude 24? This sets the scale for the size of asteroids that Pan-STARRS can detect.

Suppose there exists a "Planet X" in the Kuiper belt with the following properties:
Distance from sun  =  60 AU            Beyond the "Kuiper cliff" at 50 AU
Albedo             =  .58              Same as Pluto
Radius             = 6371 km           Same as Earth
What is the brightness in magnitudes of this object?


Alpha Centauri system
Relative sizes
Artist's conception
Artist's conception
                  Mass  Luminosity  Temp  Distance  Magnitude  Age    Metallicity
                                    (K)     (ly)               (Gyr)  (dex)
Sun               1.00    1.00      5778    0.0      -27       4.57   0.0
Alpha Centauri A  1.10    1.52      5790    4.36       0.0     6      1.5
Alpha Centauri B   .91     .50      5260    4.36       1.3     6      1.6
Alpha Centauri C   .123    .0017    3042    4.24      11.0     4.85    .2    (Proxima Centauri)

Distance between Alpha Centauri A & B                   =  17.57 AU        (semimajor axis)
Orbit time for   Alpha Centauri A & B                   =  79.9  years
Distance from Alpha Centauri C to Alpha Centauri A & B  =  .21 light years

Suppose a hypothetical "Planet Z" orbits Alpha Centauri B such that
Distance from Alpha Centauri B   =  1.0 AU
Distance from sun                =  290000 AU = 4.36 light years
Radius                           =  1.0 Earth radii
Albedo                           =  .37        Same as Earth
What is the magnitude of Planet Z as viewed from the Earth?


Planetary transits

Suppose an extraterrestrial civilization is using transits to detect the Earth.

Earth orbit speed = 29.8 km/s
Sun radius        = 1.4e9 meters
Time for the Earth to transit the sun = 46600 seconds = 12.9 hours
Earth surface area / Sun surface area = .000084

This is the fractional intensity drop when the Earth transits the sun.

Suppose a star like the sun has a planet with an orbital radius like the Earth's. Using data from the web, what is the minimum mass planet that Kepler can detect? What is the minimum mass planet that the redshift method can detect?


Pan-STARRS

The Hipparcos and Gaia telescopes specialize in measuring precise star positions for parallaxes. For a star that is 100 light years away, how accurately can each of these telescopes measure their distance? How about for a star in Andromeda?

Suppose an asteroid is a distance of 0.1 AU from the Earth in the direction away from the sun (so that we're viewing it like a full moon). Suppose also that it has an albedo of 1. The smallest flux that Pan-STARRS can detect is 5e-18 Watts/meter^2. What is the smallest value for the radius of this asteroid that the Pan-STARRS telescope can detect?

Suppose an Earth-sized object is in the Kuiper belt and that it has an albedo of 1. What is the furthest distance from the sun that this object could be detected by the Pan-STARRS telescope?


Asteroids that have passed close to the Earth
Q  =  Radius of closest approach / Radius of Earth

               Q    Diameter     Date
                    (meters)
Chelyabinsk   1.00     19     2013  2 15    .44 Megaton blast
Tunguska      1.0
1972 Fireball 1.0089  ~ 6     1972          Skimmed the upper atmosphere
2011-CQ1      1.87      1     2011  2 04
2008-TS26     1.96      1     2008 10 09
2011-MD       2.94     10     2011  6 27
2012-KT42     3.26    ~ 7     2004  5 29
2013-DA14     5.35     30     2013  2 15
2012-KP24     8.99     25     2004  5 28
2012-BX34    10.3       8     2012  1 27
2012-TC4     14.9      17     2012 10 12
2005-YU55    60.00    400     2005 11  8
http://en.wikipedia.org/wiki/List_of_asteroid_close_approaches_to_Earth
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