IV: The Solar System
Analysis of light is by far the major way in which astronomers gather information about the Universe. So, we need to collect as much as possible and study it in great detail.
- Use telescopes to gather more light than our eyes can, and to provide greater clarity.
- We record and measure light with electronic detectors.
- Use spectrographs, etc. to obtain more information about the physical conditions from which the light escaped.
- Study the entire electromagnetic spectrum — not just visible light. Use radio and space telescopes, etc.
- Use computers for detailed, quantitative analysis
Purpose of Telescopes
The primary purpose of a telescope is to collect more light.
We characterize the brightness of an object as some number of photons being collected per unit area per unit time. Brightness is therefore the amount of radiation received by us. We cannot change how bright an object is. But we can change the number of photons we collect.
- increase the amount of time over which we collect photons
- increase the area of whatever we are using to collect photons
Think of photons arriving at Earth like raindrops falling to the ground. If you want to collect more raindrops you can put a bucket in the rain and leave it there for a long time or you can put out a bigger bucket. Or better yet, you can do both!
For human eyes the collecting area is only the total area of your two pupils. It’s not very big. Furthermore, your eyes only collect light for about 1/30th of a second before they send the info to your brain and start collecting again (like frames of a movie). That’s why when you look through a telescope at, say the Orion nebula, it does not look as impressive as it does in the pretty pictures in text books. Plus we cannot record precisely what our eyes saw and study it later quantitatively. So, we need telescopes…
We typically rate telescopes by the size of their collecting area. Since the collecting areas are usually circular we describe them in terms of their diameters:
A typically large telescope has a diameter of Dt = 4 m, whereas your dilated eye has a diameter of about De = 4 mm (4 x 10-3 m).
A = area = R2 = D2/4 , since R = D/2
Ratio of areas:
At/Ae = Dt2/De2 = (Dt/De)2
At/Ae = ((4 m)/(4 x 10-3 m))2 = 1 x 106
So with an area 1 million times greater we can see stars 1 million times fainter than the eye!
The secondary purpose of a telescope is to provide greater resolution
Resolution is the ability to detect fine detail. For example, the bright star in the bend of the handle of the Big Dipper, Mizar, looks like just one star to your eye. But in a telescope it is revealed to be two stars. Your eye cannot resolve angles small enough to separate the two stars in the image on your retina. This is is because of a wave property that light has called diffraction. As a wave passes through an aperture the planar wave is converted into a spherical wave as seen in the following figure:
In a telescope (or your eye) which has a circular aperture this leads to point sources being surrounded by rings of light. When the rings of one point source overlap the rings of another it becomes impossible to discern one point source from the next.
This effect is dependent on wavelength as you might expect from the figure. There is a simple relation for the smallest angle, , that a circular aperture, with a diameter D, can resolve for light with wavelength .
We call this the diffraction limit of a telescope. Here the angle is measured in radians. (Recall that there are 57.3° in 1 radian, and 3600″ in 1°. Hence, there are 206,265″ in 1 radian).
What is the diffraction limit of the Keck telescope in Hawaii? It has a diameter of 10 m. It is an optical telescope, so let’s use the middle wavelength of the optical spectrum as the fiducial wavelength, = 5500 Å.
1.22(5500 x 10-10 m)/(10 m) = 6.7 x 10-8 radians * 206,265″/radian = 1.4 x 10-2” = 14 milli-arcseconds (mas)
The Keck Telescope does not actually achieve this small of an angle, however. The atmosphere blurs the light of any incoming point source and spreads the light out over a larger angle than the diffraction limit of the telescope.
Types of Telescopes
There are two basic types of optical telescopes:
In a refracting telescope the light is collected by a lens and brought to a focus via the physical process of refraction of light waves. Refraction is the bending of light as it enters a new medium. This bending occurs because the light waves interact with the matter in one medium differently than the other which leads to the wave traveling at different speeds in each medium. For example let’s say that light is traveling in a vacuum and encounters a prism of glass at some incident angle. The part of the wave to first enter the glass will slow down causing the entire wave to bend (similar to when the tires on one side of a car move slower than the other side causing the car to turn).
This effect is wavelength dependent. Blue light slows down more in glass than does red light. This causes white light to spread into a rainbow of colors when it enters glass. This also means that when white light is passed through the lens of a refracting telescope the different colors will be focused to different points. Thus there will be no one place that you can put a detector and have the image all in focus. The image will have colored halos. This is called chromatic aberration.
In addition refracting telescopes have another limitation. It becomes prohibitively expensive to make lenses very large. Plus the need to support them only on their edges causes large lenses to sag in the middle and the tubes needed to hold them become gigantic. The largest refractor in the world is the Yerkes Observatory owned by the University of Chicago. It has a 40 inch diameter lens. At Lick Observatory on Mnt. Hamilton UC owns a 36-inch refractor. Hopefully, we’ll get to view through it.
Reflecting telescopes uses mirrors to bring light to a focus. In order for every ray of light that is incident on the mirror to be brought to a single focus the mirror must have a shape that is parabolic. If the mirror is spherical the light will not all come to one focus but to many foci. This is called spherical aberration. The Hubble Space Telescope suffered from this problem when it was first launched. The difference between being spherical and parabolic was less than the width of a human hair!
Reflectors do not suffer from chromatic aberration and since mirrors may be supported on their entire back surface they can be much larger. Reflectors are the type of telescope preferred by astronomers for research purposes these days. Until recently, however, 4 meters was about as big as anyone could economically make. The glass would be so large and heavy that it would deform when in different positions, plus it is difficult to build support structures for such large mirrors. There have been several solutions. The Twin Keck Telescopes in Hawaii have a primary mirror 10 meters in diameter. The mirror is made of many smaller mirror segments each attached to little servos that move to keep the mirror’s shape parabolic at various orientations. These are the largest telescopes in the world right now. Another has been to “spin up” molten glass into the correct shape and make it very very thin. This has been successfully done with several 8 meter class telescopes soon to be coming online (Gemini, Subaru, Magellan, VLT, etc.). These have the advantages of being very lightweight and inexpensive.
Telescopes at other wavelengths
Telescopes that work at radio, infrared, ultraviolet, or even x-ray light all use the same basic principles of reflection that optical telescopes do. They all have diffraction limits and are setting out to detect as many photons as possible by maximizing their collecting area. They have some individual differences that are based on the physical properties of how matter interacts with these wavelengths of light. For example, making mirrors for X-rays is difficult since the x-rays will penetrate deep into and even pass straight through conventional optical mirrors. Radio telescopes work much in the same manner as your radio sets in your car. There is a dish which is referred to as an antenna that reflects radio waves to a focus and the radio waves drive a signal from that focus to a control room where it is recorded.
Some radio telescopes are used in arrays called interferometers. These arrays observe radio waves and very carefully time their arrival. They then correlate the signals from each dish to put together an image. The result is that the array has the effective diffraction limit of a telescope with the diameter equal to the span of the the array. An international union of radio observatories has managed to use radio telescopes from all over the world to make observations that have the effective diffraction limit of a radio telescope the size of the Earth!
There are several advantages to having telescopes in space.
- There is no distortion or blurring by the atmosphere of Earth. Telescopes can reach their diffraction limit.
- The telescope mirrors do not flex under their own weight as they do on the ground.
- The sky is darker. No scattered light from nearby human populations or from the Sun. The atmosphere also glows at certain wavelengths, especially in the infrared. The infrared sky is very bright.
- You can see ultraviolet, x-rays, gamma-rays, and infrared light blocked by the atmosphere.
- Even at optical wavelengths the atmosphere absorbs some light.
Astronomers no longer use their eyes to record images. After the invention of photography in the 1800s astronomers developed photographic plates. These were glass plates that had photosensitive emulsions on them that would be placed at the focus of the telescope. Light was then allowed to collect on the plates for long exposure times. The plates were then developed just like photographs still are today.
Today, we no longer use photographic plates. We now use CCDs (Charged-Coupled Devices). They are solid-state semi-conductor chips that work on the principle of the photoelectric effect discovered by Einstein. Photons can knock electrons loose when they collide with certain elements. These loose electrons created a charge that we can measure. CCDs are used in video and digital cameras. Science grade CCDs have arrays of pixels of 2048 x 2048 or more. Each pixel stores electric charge in direct proportion to the amount of light that has been incident upon it.
CCDs have many advantages:
- Linear response: double the exposure time or star brightness, double the charge
- Extremely sensitive: up to 80% of photons are detected
- Digital Output: analyze with computers
- Wide dynamic range: very faint or bright stars are measured accurately.
Computers are an Astronomer’s Primary Tool
Overview of the Solar System
That which we call the Solar System consists of
- a central Star: the Sun (big, hot, ball of gas)
- nine major bodies that orbit it: the Planets
The Planets are Divided into categories:
- The Terrestrial Planets: Mercury, Venus, Earth, and Mars (small, rocky, near the Sun)
- The Jovian Planets: Jupiter, Saturn, Uranus, and Neptune (large, gaseous)
- Planet 9: Pluto (strange in many ways)
- Asteroids (Giant Rocks orbiting the Sun, mostly between Mars and Jupiter)
- Meteoroids (smaller rocks in interplanetary space)
- Comets (“dirty snowballs” — mostly far away)
- Moons (many moons orbit the planets)
- Dust and Gas (left-overs from the formation of the Solar System)
The size of the Solar System is about 100 AU (the comets may go out to as far as 100,000 AU, NOTE: 1 light-year 63,000 AU)
The orbits of the planets are almost all in the same plane (plane of Earth’s orbit). Small inclinations (most < 4°). They all orbit in the same direction. With the exception of Venus, they all basically spin in the same direction also (most of the planets have the same sense of North).
Nebular Hypothesis (Kant and Laplace: 18th Century): origin of Solar System
- Collapsing, spinning cloud of gas and dust
- Spins faster as it collapses (conservation of angular momentum)
- centripetal acceleration balances gravity and a disk forms
- Sun forms in center: planets in outer parts
- Sun’s early wind blows away extra gas.
(TO BE CONTINUED)