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Ian Randal Strock was curious about how far away we’d have to be from the sun before it started to appear to be a point rather than a disk. To answer the question, first we have to look at how humans see distant objects: The angular size of an object is proportional to its physical size divided by its distance from us. So if you double the size of an object, it’s going to cover an angle twice the size. If you move the object twice as far away, the angular size will be halved. It’s a simple proportionality.
The sun occupies 30 arc minutes, and that’s calculated by solar diameter and the distance from earth (1AU).
If you went to 30 AU (approximately at Neptune, which is 31 AU), then the sun (which stays the same size of course) would go to 1 arc minute. So at Neptune and beyond, the sun would look like a point of light (rather than a disk) to the human eye.
How far away does the human have to be before they can’t see the sun at all? We’ll answer this tomorrow, promises Brotherton.
This is independent of brightness. It’s sheerly a function of resolving power. Though, if it’s too faint, it can’t be seen.
Brotherton switches subjects. He mentions that Grazier gave a very academic talk yesterday about the solar system, focusing on hows and whys rather than what. The what is relatively easy to find, in things like text books (Launch Pad has generously given each of us a basic astronomy text book, although they represent a variety of different editions and titles, so we don’t all have the same ones). Brotherton has collected some online resources on his blog. He’s collected a lot of videos about the solar system, often from the TV show universe. There are also some videos of lectures.
Before we get into today’s lecture, Brotherton discusses what we’re going to do after lunch–we’ll be playing with thermal glasses, for instance, and he mentions that this will teach us how to defeat predators. He also mentions that if you look at someone wearing glasses with thermal vision, their face will seem to glow, but their glasses will be black.
LIGHT AND OTHER FORMS OF RADIATION: THE ELECTROMAGNETIC SPECTRUM
We refer to light as everything from radio to gamma rays and everything in between.
In astronomy, we don’t have laboratories (apart from some esoteric astrophysics). We can’t really crash Mars into the earth. We can do it with numerical simulations, that’s as close as we can get. But mostly we can only observe.
The way we watch is by collection photons. We have to understand light. We need to understand the processes that create and modify light so that we can understand distant objects.
Particle/wave duality: light has both wave and particle-like properties. When we talk about light waves–oscillating, transverse electromagnetic fields propagating through space at the speed of light. These have speed (300,000 km/s), wavelength, and frequency. There’s a relationship between speed, wavelength, and frequency. Frequency equals speed divided by wavelength. (In mathematical language, frequency and wavelength are represented by Greek letters.)
The speed of light is constant in a given medium. We think of it as constant, but it’s not quite–when it hits the atmosphere, for instance, it slows down. It goes even slower in water. Anything that refracts light will slow light. Under extreme lab conditions, some astrophysicists have slowed light to meters/sec.
There’s a relationship b/w the wavelength of light and its color. In the case of a visible light spectrum, a rainbow or white light coming through a prism and being dispersed into its colors–ROYGBIV (red, orange, yellow, green, indigo, violet–though violet may not be real) (also, there are no green stars, and we’ll be talking about why over the next couple days) (stars, as they increase temperature go from red to blue, but are never green)–each wavelength corresponds to a different color. Longer wavelengths are closer to ROY and then move even longer into infrared. Shorter are closer to BIV and then move into the ultraviolet. Short wavelengths do get into the atmosphere; they can burn your skin; some animals can see them; and eventually the ozone layer kicks in and prevents further entrance.
Anyway, prisms. Blue light bends more than red light when it goes through a prism, and this is because the red and blue light travel at different speed as they go through the prism.
Units–wavelengths of light are very very short. Waavelengths of light are measured in units of nanometers or angstroms. Astronomers tend to one, and physicists to the other. 1 nanometer is 10(-9) meters. (I’m using parentheses to denote exponents because I can’t be arsed to look up how to HTML it.) One angstrom is 10(-10)meters or .1 nanometers. Visible light has wavelengths between 4000 angstroms and 7000 angstroms (400-700 nanometers).
The electromagnetic specturm extends beyond what we can see with our own eyes. When we put it in a logorhythmic scale, visible light comprises only a very small part, somewhere in the middle, of the range.
There’s violet, and shorter than that there’s ultraviolet, and then even shorter than that, there’s x-rays, and even shorter than that, there’s gamma rays. These are higher energy particles, or photons, as you continue in this direction. The wavelength shortens and the frequency gets larger.
From red, we go higher to infrared, then higher to microwaves (microwaves shoot a lot of light energy into your food and cook it because of a feature we’ll discuss later), then radio waves (in theory there are radio waves with lengths that are tens of meters).
Astronomers also have to worry about the atmosphere. All forms of light don’t travel through the atmosphere equally well. Infrared doesn’t go through glass (this relates to why thermal goggles make glasses seem dark), but it interacts very strongly with some molecules. If you had eyes that detected microwave or far infrared, everything would look cloudy and foggy because those molecules absorb infrared, particularly water vapor and greenhouse gases, making the atmosphere opaque.
We have telescopes we use in airplanes, and telescopes we fly in space, because we need to get above the water vapor so we can see. In visual light, the atmosphere is pretty transparent, you can see to the ground.
But if you want to observe ultraviolet or x-ray light to find out what kinds of objects are emitting those parts of the spectrum, then you have to look from space. And if you want to look at x-rays, you also have to use other materials; for instance, you don’t use glass, you use gold.
A quanta is a discreet amount of energy. I don’t really understand this, but Ian says it means that a photon can only have X amount of energy, or Y, but not in between. Maybe someone will ping in and explain. (Mike Brotherton says they used to think that there could be any amount of energy in a quanta, but then discovered it didn’t work that way.)
Light can also appear as particles, called photons. A photon has a specific energy E, proportional to the frequency f: (E=h*f where h is the planck constant, and h=6.626×10(-34) Joul seconds).
The energy of a photon DOES NOT DEPEND on the intensity of the light! We could have a little, pathetic blue laser with a very low, milliwatt intensity, much lower than the energy in your microwave. But every individual blue photon has more energy than every microwave photon. To analogize, think about hail. You can have an intense hail storm with very small hail that won’t damage your car. Or you can have a brief hailstorm with golf-ball sized hail that damages the hell out of your car. Or, consider this: ultraviolet light damages your skin, whereas you can bathe in infrared all day.
Photons interact with matter as individual photos. There’s a certain amount of energy in each photon and it interacts with matter in different ways because of that.
Most of the time, it works to think of thermal or heat energy as relating to kinetic energy, or the moving of atoms and molecules. Moving molecules/atoms are hot. When you cool them down, their motion slows. Hot material has more energy available. You can use that energy to create chemical reactions, nuclear reactions (at very high temperature), escape of gasses from planetary atmospheres, and very hot objects can create light. Creating light happens when collision bumps electrons up into a higher energy orbit, or when the object emits extra energy as light when it drops back down to a lower energy orbit. The reverse can happen in the absorption of light.
Temperature scales: The Celsius scale is arbitrary, relating to freezing and boiling of water, and farenheit even moreso. Astronomers prefer a scale that measures the energy of heat, so they work with Kelvin, starting at absolute zero (-273 celsius). Kelvin uses the same degrees (even though these are arbitrary) as celsius, but starts its scale in a different place.
Now with a little of this background, there’s an important physics concept we can tackle: Planck Black Body Radiation. Planck came up with his constant as he tried to explain black body radiation. The idea is that hot objects glow, or emit light. Heat (and collisions) in material cause electrons to jump to high energy orbits and as electrons drop back down, some of the energy is emitted as light. We see this in stove tops, etc.
The radiation emitted by this body is the black body radiation. The “black” part refers to the fact that it’s a perfect absorber, that does not reflect light. It absorbs light that hits it. The light that comes off is emitted by virtue of heat.
In a “solid” body, the close packing of the atoms means that the electron orbits are complicated, and virtually all energy orbits are allowed. So all wavelengths of light can be emitted or absorbed. A black material is one which readily absorbs all wavelengths of light. These turn out to be the same materials which also readily emit all wavelengths when hot.
Now, Mike Brotherton is showing us three different diagrams of black body spectra. Placnk formula gives intensity of light at each wavelength. This is complicated, so we’ll use two simpler formulae which can be derived from it:
Wien’s law tells us what wavelength has maximum intensity.
Stefan-Boltzmann law tells us total radiated energy per unit area.
At 5000K, close to the surface of the sun, the peak energy emission is red. As we increase the temperature, the body emits more light at all wavelengths, but the peak moves into the green. So why are there no green stars? To answer the question, we have to think about how the eye works.
The issue is that when a star emits lots of green light, it also emits lots of red and violet. Its temperature is high, so its peak may be green, but its emitting lots of all kinds of light. All these colors blend to create white. And so we see white light.
A star that emits relatively little light will emit mostly red, and so be seen as red. Its temperature is low, so its peak is red, and it’s mostly emitting red.
An object like the sun has a temperature at 6000 degrees kelvin. Where is the peak of that wavelength? Use Wien’s law, and you get 500 nanometers.
In the infrared part of the spectra, we use microns, which are 1 millionth of a meter. Room temperature is about 300 degrees Kelvin, human bodies are 310 degrees Kelvin. What part of the spectrum does the peak fall in when we calculate Wien’s law using 300 degrees? 10 microns, which is in the infrared.
The stuff you’ve seen in Predator, and military and cop movies, operate between 7 and 14 microns with 10 microns in the middle, so they’re very sensitive to temperature ranges that we find here on the surface of the earth, around 300 Kelvin. We (humans) are warmer than that so we stand out. Many things are cooler. As it gets dark, and the background cools, living things stand out a lot more.
The Stefan Boltzmann law says the energy radiated by a body per unit surface area… um, look this one up if you want to know, eh? Here’s Wiki. Anyway, the deal is that as the temperature increases, the energy increases a lot. If you double the temperature of an object in degrees Kelvin, how much more energy in black body radiation does it put out? 16 times more. And if you cool an object so it’s only half the temperature it will be a factor of 16 times less bright by black body radiation.
Now, Stefan-Boltzmann also depends on surface area, so it depends on the size of the radiating surface. S-B tells you how much total energy is coming out, but not how it’s distributed. Wien’s law tells you the peak. Planck’s calculates everything, but the simpler Wien’s and S-B still give you important information.
We’re visiting this site: Animations for Astronomy 101 by Instructor Eric Sandquist where there are lots of cool things, including some notes on black body radiation.
How you perceive the spectrum of light mapped by a Planck’s formula arc will have to do with how bright the object is. So even though an M-star has a lot, lot, lot of red light, you will still see other colors. Also, the eye is preferential to middle ranges, picking up green more effectively than red. So if you compare a red and green laser, the red will look dimmer, even though they’re the same brightness.
Can you overlay a Planck’s formula diagram with a diagram of the sensitivity of the human eye to figure out what you’d see? Sort of. It’s complicated, and even when astronomers are trying to discern what an object would look like, the filters we use affect our photography.
Reminder: don’t put a planet around a really hot star, because while you can put the planet far enough away that it won’t fry you, the star will have a short life and explode, like building near a nuclear bomb. On the other hand, with cold stars, you have to have your planet snuggly into the star, but that raises problems, because solar flares could fry the planet. It’s hard to find the “Goldilocks” zone where life can persist.
In principle, every once in a while, humans zing off a few photons–not very many because we’re not *that* hot, but some because we are–but we can’t see them because they’re insignificant.
Hot solids emit continuous spectra.
Hot gases try to do this, but can only emit discrete wavelengths.
Cold gases try to absorb these same discrete wavelengths.
So, we can look at what’s being emitted by a hot solid (or a really dense hot gas) and see what it’s emitting, and then figure out how hot it is. However, for gases that is very thin, you can’t figure that out; they don’t emit energy in the same way as black bodies. In a thin gas, the particles don’t collide often. Cold gases absorb radiation that passes through it, but it doesn’t absorb it in a black body pattern. These emissions and absorptions happen at discrete wavelengths.
If you’ve got an individual atom with nuclear charge so it has some electrons held around it electrically, there are sets of quantum mechanical rules that dictate how the electrons can arrange themselves, relating to specific energy states. When they move between states, they have to either absorb or emit energy in the form of a photon. This can also happen in collisions between objects, but we’re focusing on the radiation process.
Binding energy: there’s a certain amount of energy needed to bind the electron to the atom. If it gets more, the electron escapes, and the atom ionizes. Most atoms will settle down in the lowest energy state they can, until something prompts them to alter. If they need to gain energy, they will absorb light. If they need to lose energy, they will emit light.
The photon coming out of an atom that falls from high to low energy state must correspond to the energy difference the emitter is undergoing, and what energy difference is will have to do with the specific atom, molecule, or ion. So we can take a spectrum and see what changes in energy we see, and then figure out what in a gas is absorbing or emitting light.
An example we can see in visual light comes from the different states of hydrogen. See wiki on hydrogen lines.
We can fingerprint what elements are out there by looking at the emission/absorption spectra.
When you look at the sun, the first thing you want to do is get rid of most of the light because it’s too much, then you might want to focus on interesting features like transitions in hydrogen–the sun is mostly hydrogen–and you can see where hydrogen is being absorbed and emitted.
Telescopes: Won’t focus just on optical, but will start there. Historically optical telescopes are important, but since WWII, we’ve done optical and radio, but radio still gets short shrift even though it really is the same thing as the visual astronomy. As we’ve been able to put telescopes into space we’ve been able to observe the whole electromagnetic spectrum. Telescopes can be mounted in the sides of airplanes; they can be sophisticated aircrafts; they can be rays spread across hillsides. In order to observe forms of radiation other than visible light, very different telescope designs are needed.
There are some common facets, though: they’re ways to gather large amounts of light, wherever that light is on the spectrum.
More on optical telescopes: A refracting telescope lens focuses light onto the focal plane. Reflecting telescopes involve concave mirrors that focus light onto the focal plane. Basically, you can make telescopes with either mirrors or lenses. It turns out that it’s hard to make good, high-quality, giant lenses, and much easier to make giant mirrors, so most high-quality modern telescopes use mirrors.
You still need to focus that image into your eye, which is a secondary objective. A primary lens focuses the light, and then an eyepiece refocuses it where you want it. Or you can bounce light from mirror to mirror and then refocus it somewhere else. You can also use cameras.
There are disadvantages to refracting telescopes. Chromatic aberration can occur when different wavelengths are focused at different focal lengths, though this can be corrected.
The powers of a telescope: size does matter. Light-gathering power depends on the surface area A of the primary lens/mirror, proportional to diameter squared. It’s not the length of the telescope that matters, it’s the width or collecting area. Starlight comes down to all different points,and we want to collect it all in one place, so you have to have a wide telescope.
Resolving power is another important feature. The wave nature of light means that the telescope aperture produces fringe rings that set a limit to the resolution of the telescope. Astronomers can’t eliminate these diffraction fringes, but the larger a telescope is in diameter, the smaller the diffraction fringes are. Thus the larger the telescope, the better its resolving power. Basically, it’s a ratio b/w the size of your mirror and the wavelength of light you’re studying. If you’ve got a 4 inch telescope, you can resolve in the optical spectrum about one arc second.
Most professional telescopes are larger than that, up to 10 meters. You should be able to use these to get to much finer resolution, but there’s a problem, at least from the ground. The problem is atmospheric turbulence. We call the turbulence the seeing. When the seeing is bad, everything twinkles a lot, and get distorted. It’s like driving down a hot highway that alters the background. Still air gives you good seeing.
Magnifying power–the ability of the telescope to make the image bigger–a larger magnification does not improve the resolving power of the telescope! The problem with having a high magnifying power is that it gives you a limited, narrow field of view. It takes one faint object and blows it up and suddenly the faint bits of light are spread over a larger area and harder to see. Magnification is a selling point for cheap telescopes. You need a bit, but…
Where do you put telescopes? Far away from civilization, to avoid light pollution. A lot of good astronomy was done during WWII, during blackouts.
You also want to put them on high mountaintops so you can get above the water vapor, maybe work in the infrared. You want to get away from some of the atmospheric turbulence, looking through less air. And ideally the mountaintop will have a smooth surface so the air coming is smooth and not bumpy. Put the telescope in Chile, CA, for instance, smooth air comes across the ocean.
Computer-controlled mirror support adjusts the mirror surface (many times per second) to compensate for distortions by atmospheric turbulence. The computer knows what stars should look like, so it adjusts the shape of the mirror to bring the star back into focus. If you’re looking up at a place where there is no star, then you can use a fake laser star so that the telescope can adjust around the fake star, and figure out how to compensate for the atmospheric effects that would blur what you’re trying to look at.
Building better telescopes gives you smaller angles, better resolutions. You don’t always have control over wavelength; sometimes you want to look at microwaves because you’re interested in what’s producing them. Unfortunately, it’s very hard to make sure that the diameter of your telescope is big enough to make an angle that’s small enough to see microwaves. So you use what’s called interferometry where you put together an array of telescopes, and use the distance between them to create the diameter. They can put telescopes in space to do this.
CCD imaging, every photon that hits it leaves a little electric charge, and after a while you can measure that. These are more sensitive than photographic plates. You’re reading directly into digital memory which is handy for data processing.
Radio astronomy; we have a good window for screening for radio waves. A radio telescope is similar to a radio dish. Dishes collect waves, which are processed as data.
The VLA (very large array) is a radio array with 27 dishes. They’re painted white. They’re on railroad tracks so they can be moved and every several months they change the configuration so that when they want to look at a small part of the sky in detail you put them in a spread-out array, A configuration, 36 km across, and with a system like this you can get a resolution of an arc second. For optical, you can get down to a tenth of an arc segment. In B and C configuration, you get bigger chunks of the sky for things like mapping by bringing the radios closer together.
A transit telescope faces only up, and waits for different things to pass overhead.
Radio telescopes suffer from earth-bound interference, like that generated by cell phones.
Science of radio astronomy: radio astronomy reveals several features not visible at other wavelengths, such as: 1) Neutral hydrogen clouds don’t emit any visible light, but they contain approximately 90% of all he atoms in the universe. 2) molecules often located in dense clouds where visible light is completely absorbed. 3) Radio waves penetrate gas and dust clouds so we can observe regains from which visible light is heavily absorbed.
Most infrared is absorbed in the lower atmosphere. However, you can still observe some of it from high mountaintops or high-flying aircraft.
(Lost some of this lecture when I had to step back into the room.)
When I came back, we were watching this video on Infrared–More Than Your Eyes Can See which discusses the way that night vision cameras work.
We got to use the night vision goggles afterward, and people did look clearer, but the room was still too bright even though the lights were off to get the full effect. And hey, people’s glasses really do look black through the thermal imager.