Astronomical Observation

As we have seen, we can only directly measure the angle between two objects, not their distances from us. But if we know their distance from us, we can compute the distance between the two objects. More usually, we are measuring the size of a single object from the angle it subtends:
size = distance * angular diameterradians
where a radian is 180/π degrees. Here are some examples of variation of angular diameter with distance:

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Perigee is the point of closest approach during the orbit of a satellite about the Earth. Similarly, perihelion is the point of closest approach during orbit of the Sun. Apogee is the point of greatest distance from the Earth during orbit, and aphelion is the point of greatest distance from the Sun during orbit.
By setting the angular diameter in the equation above to the resolution of a telescope, we can compute the size of the smallest object it can see at any given distance. The resolution is determined by interference effects and depends on the size of the optics (usually a mirror) and the wavelength being observed:
angular resolutionarcsec = .0025 * wavelengthAngstroms / mirror diametercm
For instance, the Hubble Space Telescope (below) has a mirror diameter of 2.4 meters, or 240 cm. At optical wavelengths (for instance, 5600 Angstroms), its angular resolution would be
.0025 * 5600 / 240 = .0583 arc seconds,

times π / (180 * 3600) radians in an arc second = 2.828 * 10-7 radians.

Looking at Saturn at closest approach (8.004 AU, or 1.197 * 1012 m), the Hubble could resolve an object whose
size = 1.197 * 1012 * 2.828 * 10-7 = 338.6 km wide.
The light gathering power (literally, how much electromagnetic radiation the instrument can gather in a given amount of time) is proportional to the square of the mirror radius. This is important because intensity decreases with the square of the distance: if you move twice as far away, the intensity drops to one quarter of what it was at the original position. This is why we distinguish between apparent magnitude and absolute magnitude (M):
M = apparent magnitude + 5 - 5 * log10 distancepc.
Absolute magnitude is the magnitude a star would have at a fixed distance of 10 parsecs; the apparent magnitude (m) will be larger than M if the star is more than 10 parsecs distant, and less than M if it is closer. You can barely see a star of apparent magnitude 6 with your eyes, if you are in a region of dark skies. Under the same conditions, binoculars takes you to magnitude 10 and 8 inch telescopes to about magnitude 13. The Hubble telescope can just see objects of apparent magnitude 30.

There are severe limits to which types of electromagnetic radiation can be observed from the Earth's surface. The Earth's atmosphere is transparent to radio waves with wavelengths between about 10 meters and 1 cm, and to infrared and visible wavelengths from 105 Angstroms to the near ultraviolet (around 2900 Angstroms).

Turbulence in the atmosphere blurs point-like Betelgeuse into a "seeing disc" (1/10 speed) (source):

The degree of the effect is referred to as "good" or "poor" seeing. For these reasons, many modern observatories are based in space.

Much of what we observe requires extremely long exposure times.

This image of the Orion-Eridanus Superbubble required 40 hours of exposure time. (source)


One of the most common telescope designs in use today is the Ritchey-Chretien. (source)

The Ritchey-Chretien design is a variation on the basic reflector telescope, and differs from the Cassegrain reflector in that the main mirror is shaped like a hyperbola instead of like a parabola, improving the image quality.

Some of the premier telescopes in recent use are:

Here are sample images from these telescopes:

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And here is a movie of M 20 (1.74 Mb), taken by Spitzer's Multiband Imaging Photometer. (source).
(View Cosmos DVD 6, episode 10, dramatization of red shift discoveries at Mt. Wilson.)

Portfolio Exercise: Research 3 additional telescopes, each in a different region of the electromagnetic spectrum.
Note that many telescopes, both ground-based and space-based, have multiple instruments. Be specific about which instruments you are discussing.
For each, identify the range(s) of wavelengths it is sensitive to, and its resolution at those wavelengths. Use published resolutions if you can find them; otherwise, compute the resolution from the equation above. What is the smallest object it could discern at 1 parsec? 1000 parsecs? 1 million parsecs? For 1 and 1000 parsecs, compute your answers in both parsecs and A.U.

For each telescope, include an image in representative colors taken by the telescope, and explain what observational wavelengths correspond to each primary color.

Include references for wavelength and resolution information, and for the images.

Amateur Observing

So what can you expect to see through a reasonably good amateur telescope? Unfortunately, not as much as you might expect. Here are sample images from an 8 inch Meade LX-90, using a 12.4 mm eyepiece:

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These images were taken in suburban Cincinnati on a clear night, through the eyepiece with a Cannon G-1 and an Orion SteadyPix camera mount. When taking photographs through the lens, alignment is a major headache. However, these photos give a pretty good idea of what you see with your eye. While detail is lacking and the colors are somewhat washed out, there is certainly something very exciting about seeing light from the planets with your own eyes, and no one fails to express awe when they look at Saturn. But what about deep sky objects?

Looking through this telescope, M-31 (Andromeda) is a faint smear of dust. M-42 (the Orion Nebula) has a clear shape but no color, and the LCD screen on the camera is not sensitive enough to focus properly at any rate. So why can't you see what the Hubble sees? Even though you are on the ground, you'd think you could do better than that!

The whole problem is one of intensity. Your eye can't add up the light received over a long period, as a digital camera might. When the intensity is so low, your color-sensitive cone cells are inactive, and so you only see in black and white. The beautiful deep-sky photos shown by the Hubble were long exposures, with the light accumulated over minutes or hours; for instance, the photo of M-104 took 10.2 hours. The deep-field photo above took over 48 hours.

And so amateur astronomers who want pictures like those taken by the professionals use CCD cameras specifically designed to fit the telescope in place of the eyepiece. They take black and white photos of the same object three times, through red, green and blue filters, and then composite them into a color image. And they take many photographs a second, using computer software to scan through the tens or hundreds of thousands of images, discarding those blurred by momentary atmospheric turbulence, and then "stack" the images (literally adding the intensities) to produce the final product. A stroll through the Astronomy Picture of the Day Archive will show many examples of amateur photographs which rival some of those taken professionally.

Cosmic Ray Astronomy

Cosmic rays are not radiation at all: they are high-energy atomic nuclei, mostly protons. Their energies range from 1 GeV (109 electron volts) up to (rarely) 1020 eV. Those up to around 1015 eV are thought to originate from within our galaxy, while the more energetic cosmic rays are thought to originate outside of the galaxy. The energy density of cosmic rays in the galaxy is around 10 MeV per cm3, maintained largely by
exploding supernovae and stellar winds. Those cosmic rays originating outside the galaxy come from within a radius of about 250 million light years. Above approximately 4 * 1019 eV, cosmic rays interact with the Cosmic Microwave Background Radiation; this limits the range of the most energetic cosmic rays.

When cosmic rays hit the atmosphere they produce a shower of particles. It is this shower which is detected by cosmic ray observatories such as the Pierre Auger Cosmic Ray Observatory in western Argentina. Their goal is not to produce an image of a cosmic ray source, but to simply identify the sources and measure the energies associated with cosmic rays. To do this, the Auger Observatory has constructed 1600 detectors covering an area of about 3000 km2. Events with energies over 1019 eV have a flux of about 1 per km2 per year.

Neutrino Astronomy

The purpose of neutrino astronomy is much the same as that of cosmic ray astronomy: to detect sources and measure energies. Neutrinos are electrically neutral, almost massless, and interact so weakly that the flux of solar neutrinos through the Earth of approximately 65 billion per cm3 passes through the Earth each second with only a handful of interactions. These facts makes this perhaps the most difficult astronomical undertaking besides the detection of gravitational waves.

The Kamioka Observatory in Japan has been instrumental in confirming our understanding about supernova explosions, and in determining that neutrinos indeed have mass. Its instrument, Super-Kamiokande, is comprised of 13027 photomultiplier tubes in 50000 tons of pure water. The tubes detect Cherenkov Radiation: electromagnetic energy emitted by charged particles whose speed is greater than the speed of light in water (about 2.25 * 108 m/s). When a neutrino interacts with an atom in the water, an electron or muon is created whose track the tubes can measure. The instrument typically detects less than 14 solar neutrino events per day.

The latest high-energy neutrino observatory is currently under construction using 1 km3 of Antarctic ice: the IceCube Neutrino Observatory. It will focus on neutrinos entering the opposite side of the Earth so that the lower-energy neutrinos associated with cosmic ray showers will not be confused with those of extraterrestrial origin.

Gravitational Wave Astronomy

In 1974, Taylor and Hulse found a binary system of neutron stars, one of which is a pulsar. After two decades of observation, they determined that the change in the rate of spin of the pulsar matched the predictions of General Relativity for such a system emitting gravitational waves:

The changing orbit of binary pulsar PSR 1913 + 16 meets General Relativity. (source)

But no one has ever directly detected a gravitational wave. It is the purpose of LIGO - the Laser Interferometer Gravitational-wave Observatory - to change that.

LIGO consists of two L-shaped detectors, each 4 km long, one in Hanford, Washington, and the other in Livingston, Louisiana. In each, laser light travels repeatedly from one end to the other, reflected by mirrors. A passing gravitational wave will change the relative lengths of the two beams, and the change in the interference pattern will be registered by a photodetector. The fifth science run (recently completed) achieved a sensitivity of one part in 1021 from 70 Hz up, enabling detection of binary inspiral of 1.4 solar mass neutron stars at a distance of 12 Mpc. No news yet on what if anything they have seen.

There's a nice TED talk by Janna Levin which includes some auditory simulations of gravitational waves emitted by inspiraling black holes.

©2012, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

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