The extraterrestrial SPLATs

What are SPLATs? They are explained here.

Space exploration

• All matter has mass. Objects with mass exert a force on each other. Gravity is this force: it holds us on the earth, and it keeps the earth orbiting the sun.

• Our sun is a star like other stars, but it is much closer than the other stars we can see in the night sky. All of our energy comes from the sun originally.

• Gravitational forces operate in space and in a vacuum, although when a spacecraft is in free fall, it may seem to those inside as though there is no gravity.

• The accelerational force due to gravity diminishes with distance, in accordance with the inverse square law: double the distance, quarter the effect.

• Objects in free fall are always influenced by gravitational forces, mostly those of the nearest massive bodies, even if the forces are not detectable.

• The escape velocity from a body depends on the mass of the body being escaped from, and the distance from it. It is usually given as a value from the surface.

• One method of accelerating spacecraft for flight to other planets is the gravity assist, which adds velocity to the craft by taking some from a large body.

• A rocket operates in accordance with Newton's laws of motion, using reaction as a means of propulsion. Rockets can work even better in a vacuum than in air.

• A rocket is the only sort of vehicle which can operate in space, because it does not require oxygen to burn fuel, or need anything to push against.

• In 1869, Edward Everett Hale foresaw space stations when he wrote The Brick Moon. This was an artificial satellite placed in orbit as a navigational aid.

• In 1895, Konstantin Tziolkovsky proposed the use of liquid-fuel rockets for navigation in space, because they could be controlled, turned on and off.

• In 1903, Konstantin Tziolkovsky wrote of using rockets to reach outer space, space suits, and colonization of the solar system, the use of liquid oxygen.

• In 1919, Robert Goddard suggested a rocket could be used to reach the moon. He actually wanted to shoot for Mars, but felt the Moon was more plausible.

• In 1952, Wernher von Braun discussed the technical details of a manned exploration of Mars in The Mars Project. Like Robert Goddard, Mars was his big dream.

• In 1990, the launch of Hubble Space telescope took place, complete with faulty optics that took until 1993 to fix, when the first servicing mission flew.  

  The principles of Earth in space

• The Earth is made up of different layers: the crust, the mantle and the core. The crust is made up of separate tectonic plates that move across the surface.

• Every body in the solar system has an albedo, a reflectivity factor which makes some objects easier to see so long as they are bright, even when they are small.

• All planets have a natural albedo, and this influences their overall temperature. When there are more clouds, the Earth gets colder as more heat is reflected.

• The Van Allen belts are layers of charged particles trapped by the earth's magnetic field, one about 3200 km from the Earth, the other at 15,000 to 19,000 km.

• The Moon takes a lunar month, a little more than 29 days, to make one complete passage around the Earth. The Earth's rotation makes it seem much less.

• Strictly, the Moon does not in fact orbit the Earth, but the Earth and the Moon both orbit a common point in space which is their combined centre of gravity.

• As the Moon works its way around the Earth, relative to the Sun, so we see different parts of the Moon's 'day', from full 'day' to full 'night' and back again.

• Meteors are quite common in space. A meteorite is a meteor fragment that reaches the Earth's surface, but most meteors burn up in the atmosphere.

• An asteroid striking the earth could cause massive extinctions, as has happened before. The impact would produce clouds of dust that would chill the planet. 

 The principles of the solar system

• Every body in the solar system has an albedo, though some have less than others. For small bodies, the albedo depends only on what they are made of.

• The closest point of a planet's orbit to the sun is called the perihelion, the most distant point of a planet's orbit from the sun is called the aphelion.

• Orbiting bodies obey Kepler's laws of planetary motion, whether they are planets around the Sun, or moons (or spacecraft) orbiting one of the planets.

• The planets obey Kepler's three laws of planetary motion, which can all be shown to follow naturally from the operation of gravitational forces.

• Kepler's first law says that all planets revolve around the Sun in elliptical orbits, with the Sun lying at one focus of the ellipse traced out.

• Kepler's second law says that for any planet, a radius line joining that planet to the Sun sweeps out equal areas of space in equal lengths of time.

• Kepler's third law says that the square of the period of revolution (year) of a planet is proportional to the cube of its mean distance from the Sun.

• In 1626, Godfried Wendilin verified Kepler's laws of planetary motion for the moons of Jupiter, showing that the laws apply to all orbiting bodies.

• In 1684 Isaac Newton proved that planets moving under an inverse-square force law obey Kepler's laws of planetary motion, that gravity is the same everywhere.

• In 1787, William Herschel found the planet Uranus, which he called a star, and claimed to have found volcanoes on the surface of the moon, but he got better.

• In 1613 Galileo Galilei used sunspots to demonstrate the rotation of the sun on its axis, and he also outlined the principle of inertia at the same time.

• In 1675 Giovanni Cassini reported his discovery that Saturn has separated rings and that they must necessarily be composed of small orbiting objects.

• We can measure the distances to the moon using radar transmission and reflection, though other methods can be used to get a reasonable estimate of the distance.

• Our solar system is made up of the Sun and nine planets and many smaller bodies, including asteroids, comets, moons, dust and Kuiper Belt Objects.

• Planets form from dust and debris from old supernovae that is drawn into the gravitational field of a star that is forming, where something pulls it together.

• Around 1640, René Descartes used a strange notion of vortices to present a model of the solar system which matched Galileo's, but avoided annoying the Church.

• In 1755 Immanuel Kant proposed his theory that the universe formed from a spinning nebula in an infinite hierarchy, which seemed like a good idea at the time.

• In 1905, Percival Lowell suggested there might be a ninth planet beyond Neptune, which he called Planet X. He photographed it before he died, but never saw it.

• In 1977, James L. Elliot discovered five rings around the equator of the planet Uranus, by the occultation of a star. Voyager 2 found four more rings in 1986.

• In 1980 Voyager 1 sent back pictures of Jovian system, in which researchers discovered the rings of Jupiter ,and these were further investigated by Voyager 2.

• Orbits are elliptical. Very rarely, the ellipse may be close to circular, but the circle remains just a special form of the ellipse, with equal semi-axes.

• Gravity acts everywhere: while people say that things in space are weightless, that is only because the entire frame is responding to gravity in the same way.

• Asteroids are relatively small bodies orbiting the sun, some of them in eccentric orbits that cross the Earth's. Some asteroids are large enough to have moons.

• In 1757 The Catholic Church removed Galileo Galilei's Dialogue on the Two Chief World Systems from its list of banned publications, after more than a century.

• There are places, the Lagrangian points, where objects may 'float in space', because they are points of stability where different gravitational fields balance. 

The principles of stellar physics

• Astronomers can use Wilhelm Wien's displacement law to estimate the surface temperature of a distant star by measuring its intensity at different wavelengths.

• In 1863, William Huggins suggested that stellar spectra indicated that the stars are made of exactly the same elements as can be found on Earth.

• In 1920, Harkins and Arthur Eddington suggested that the fusion of hydrogen to form more massive atoms and release energy could be the energy source of stars.

• In 1924, Eddington developed the main-sequence mass-luminosity relationship, that stars of similar composition and energy are brighter when they have more mass.

• In 1938, Hans Bethe, Critchfield, Carl von Weizsäcker worked out that stars were powered by nuclear fusion, involving the carbon-nitrogen cycle.

• In 1939, Hans Bethe and Carl von Weizsäcker proposed the proton-proton chain as the thermonuclear energy source for the sun, where four protons form helium.

• In 1942, J. J. L. Duyvendak, Nicholas Mayall, and Jan Oort deduce that the Crab nebula was a remnant of the 1054 supernova observed by Chinese astronomers.

• In 1967, Jocelyn Bell and Anthony Hewish discovered radio pulses from a pulsar, the first of four that Bell found. Some 350 pulsars are now known.

• Pulsars are rotating bodies that emit directional radio signals, so that in certain positions, the signals are intermittent, forming a series of pulses. 

  The principles of eclipses and other events

• Eclipses and occultations happen when three bodies all lie on a straight line, so that the light from one of them is prevented from reaching another.

• Eclipses of the Sun happen when the Earth, Moon and Sun line up so the Moon is between the Sun and the viewer. Total eclipses only affect a narrow belt.

• Eclipses of the Moon may be seen from half of the Earth. They happen when the Earth moves between the Sun and the Moon so as to entirely shade it.

• The fact that we can observe a solar eclipse proves that the Moon is closer to the Earth than the Sun, and this was known by the ancient Greeks.

• In a lunar eclipse, the surface of the Moon appears red because some of the Sun's light is refracted by the Earth's atmosphere, which filters out blue light.

• When scientists in the Mediterranean saw eclipses of the Moon, these showed them that Earth was a sphere, based on its shadow.

• Further evidence of a spherical Earth in lunar eclipses came when scientists compared the time of night when eclipses were seen in different longitudes.

• Solar eclipses also showed Greek astronomers that the Sun was further from the Earth than the Moon was.

• When the moons of Jupiter are eclipsed by Jupiter, this happens at intervals which can be predicted. Navigators could use this to find longitude. 

The principles of comets

• Comets are volatile bodies orbiting the Sun. When they get close to the Sun, some parts of the comet boil off, forming a 'tail', which points away from the Sun.

• Comets travel in eccentric orbits. Some travel in elliptical orbits, which means they will return, some only make one pass, as they are on hyperbolic paths.

• The first comet to be predicted for a return was Halley's comet, which returns in its orbit to a point reasonably near the Earth about every 76 years.

• In 1950, Jan Oort suggested the presence of a cometary cloud. Now known as the Oort Cloud, orbiting the Sun, some distance beyond the orbit of Pluto.

• New comets that we see entering our part of the solar system are probably ejected from the Oort Cloud, although the cause of their ejection remains unknown.

• According to many astronomers, comets are probably ejected by the gravitational effects of Kuiper Belt Objects pulling them from their previous stable orbit

The principles of observational astronomy

• In 1572, Tycho Brahe saw a new star in the sky, a 'nova' as we say now. This was the first evidence against the ancient view that the heavens were unchangeable.

• In 1610, Galileo Galilei saw four 'new stars', actually moons of Jupiter, further evidence that the skies were not, as orthodox rulers claimed, unchangeable.

• Stars have an absolute magnitude that is always the same, no matter where they are. They also have a relative magnitude depending on where they are seen from.

• Stars have an apparent brightness from a particular viewpoint, with distant objects appearing dimmer than similar objects that are nearer to us.

• Relative magnitude follows the inverse square law. Of two stars of identical absolute magnitude, the one twice as far off has a quarter the relative magnitude.

• In 1826, Heinrich Olbers posed his paradox: if the universe is infinite, he asked, why is the sky so dark at night? The answer involves the red-shift.

• Armand Fizeau was the first to point out that a star, moving away from us, should show an observable Doppler effect red-shift in the spectral absorption lines.

• Distant objects have a larger redshift, which is taken by astronomers to indicate that they are travelling away from us faster than nearby objects.

• The Hubble constant relates distance to redshift, and tells us how fast the universe is expanding, from which we can deduce that the universe will not collapse.

• In 1869, William Huggins used red-shift data to estimate that the star Sirius is moving away from the Earth at about 30 kilometres (20 miles) a second.

• Barnard's star is the fastest moving star as it shifts position in the star field: it takes 180 years to move across half a degree of sky, the moon's width.

• Cepheid variables are stars that have a frequency of variation which relates to their absolute magnitude, which means we can use them as 'standard candles'.

• In 1912, Henrietta Leavitt discovered the period to luminosity relationship for Cepheid variable stars from studies of the Large and Small Magellanic Clouds.

• In 1914, Ejnar Hertzsprung estimated distance to the Small Magellanic Cloud using Cepheid variables, as 3000 light years, a lot lower than the current 210,000.

• In 1918, Harlow Shapley set out to use Cepheid variables and offered a model for the shape of the Milky Way. He was unaware there are two types of Cepheids.

• In 1924, Edwin Hubble used Cepheid variables in a nebula, Messier 31 in Andromeda to show the nebula was some 750,000 light years away, outside our own galaxy.

• Spectrum analysis of the absorption and transmission in light from distant objects can reveal a great deal about them and the elements that they are made of.

• Astronomy includes the study of cosmology, the branch of science that tries to explain how the universe and everything in it began, using the laws of physics.

• In 1782, John Goodricke noticed that the variations in brightness of Algol are periodic and proposes that it is partially eclipsed by a body moving around it.

• In 1803, William Herschel found, as John Michell had suggested, that binary stars existed. Michell felt this was more likely than stars being near each other.

• In 1863, Richard Carrington discovered that sunspots rotate at different speeds at different latitudes on the sun, revealing that the Sun was in some way fluid.

• In 1975, Gerald Smith, Frederick Landauer, and James Janesick use a charge-coupled device to observe Uranus, the first astronomical CCD observation.

• Quasars got their name from being quasi-stellar objects. Each is believed to be powered by a black hole, a very dense object, from which light cannot escape. 

The principles of galaxies

• Stars occur in groups called galaxies, and unlike constellations, these stars really are grouped together, but they are all a very long way off.

• Our local galaxy is called the Milky Way, and it may be seen at night if you look up, so long as you are away from bright city lights which obscure it.

• In 1785 William Herschel suggested the Sun is part of a larger system of several million stars forming a thin disc, the start of our notion of the Milky Way.

• Over twenty years of observation, William Herschel was able to catalogue some 2500 stars of the Milky Way, using telescopes to measure their distances.

• William Herschel estimated that there might be as many as several million stars in the whole of the Milky Way, but this turned out to be a severe underestimate,

• The Milky Way galaxy is about 100,000 light years across, and contains around 300 billion stars. The centre of the galaxy is 27,000 light years away.

• The nearest star to the Sun is part of a three-star system, Proxima Centauri, 4.3 light years away, most stars are a great deal further away.

• In 1927, Jan Oort proved Bertil Lindblad's view of the Milky Way as a rotating spiral and found its rotational speed by analysing the motions of distant stars.

• When we look at any galaxy other than the Milky Way, all we can see is a single blob of light, because the individual stars are too far away to see.

• The nearest galaxy to ours is 2.2 million light years away. Forget galaxies far, far away, we can't even get to the nearest one in our lifetime.

• Galaxies are very large groupings of stars: there are about a hundred billion stars in our galaxy and there may be a hundred billion galaxies that we can see.

• There are probably 100 billion galaxies in the universe, containing an average of around 100 billion stars in each, and an unknown number of planets near them.

• The farthest known galaxy from Earth is known as 4C41.17. On red-shift data, it is around 15 billion light years away from our galaxy, and moving further away.

• The largest known galaxy is Abell 2029, which has an estimated 100 trillion stars and a diameter of 6 million light years, 60 times that of our galaxy.

• The groups of stars that we call constellations are generally all within a few hundred light years, though some are just a few light years away.

• As they are seen from earth, nearby stars seem to form constellations, but from another direction, these constellations would appear quite different.

• In 964, the Islamic scientist Al-Sufi noted in his 'Book of the Fixed stars' that he had seen a small fuzzy object, which we now call the Andromeda Nebula.

• All the other elements in the universe are formed from hydrogen, because stars carry out a form of fusion which produces energy and forms heavier atoms.

• Clouds of dust occur in interstellar space, and sometimes make it hard to see the stars lying beyond them. This dust in space may become stars in the future.

• Some stars emit gamma radiation or X-rays, rather than (or as well as) light and so may only be seen by using a directional antenna capable of detecting X-rays.

• The universe is expanding: distant stars show a redshift proportional to their distance. The Hubble constant can be used to relate distance to red-shift. 

 The principles of ETs and SETI

• At the time of the Manhattan Project, Enrico Fermi posed a famous question: if extraterrestrials exist, where are they, and why have we not yet met them?

• Later, this was subverted: if extraterrestrials exist, where are their von Neumann machines? These are self-replicating machine which exist to copy themselves.

• One of the answers is that any species smart enough to make von Neumann machines would realize the consequences of doing so and avoid making them.

• Another answer may be that life as we know it is a von Neumann machine, programmed to spread itself across space, a notion that would appeal to Fred Hoyle.

• The von Neumann machines have a modern parallel in the 'grey goo' of the technophobes who fear and fail to understand nanotechnology and see it running wild.

• Many stars have planets: this can be shown in a variety of ways, even when the planets themselves remain invisible, by looking for wobbles in the star.

• In 1989 Wolszczan and Frail reported the first detected extra-solar planet orbiting a pulsar, when a large planet was detected, orbiting the pulsar PSR 1257+12.

• In 1995 Mayor and Queloz reported the first confirmed extra-solar planet orbiting an ordinary star, orbiting the star 51 Pegasi.

• The science of looking for life elsewhere is called exobiology. The most likely near-Earth sites to find traces of life right now are Mars and Europa.

• Planets which are large enough, and so have enough gravity, will have and retain an atmosphere, but that does not necessarily mean that it will be breathable.

• There is less evidence available to indicate if other stars have planets like Earth, located in the gap between hot and cold, where life is likely to be found.

• According to the Zoo Hypothesis, intelligent life has detected us on Earth, and is carefully observing us from a distance, just as we would regard zoo animals. 

The principles of cosmology

• All things are possible: one model of the universe we know sees it, and so us, as being contained within the event horizon of an extremely massive black hole.

• Stars are separated by large distances, and the gaps beyond and between are known as interstellar space. The stars have almost no effect on interstellar space.

• Around each star, there is a boundary where the stellar wind slows down and eventually stops as it comes in contact with material in interstellar space.

• The edge of the Sun's sphere of influence, the heliosphere, lies three times as far away as Pluto. Voyager I will take 40 years to get to the heliosphere.

• Around 150 BC, Hipparchus estimated that the Moon is 30 Earth diameters away from our planet, by taking sightings of the Moon at zenith from two places.

• Around 1450, Nicolas Cusanus asserted that the world was round, and moved, but nobody reacted to this as they would later react to Giordano Bruno and Galileo.

• In 1543, Nicolaus Copernicus suggested a heliocentric model of the solar system, but there was no great reaction, possibly because he died as the book appeared.

• Bruno of Nola, Giordano Bruno, was burned at the stake in 1600 for, among other things, saying that the Earth went around the Sun, not the Sun around the Earth.

• In 1671 Giovanni Cassini completed an accurate measurement of distance to Mars and used that, combined with a known scale of the solar system to measure it all.

• In 1796 Pierre-Simon de Laplace stated his nebular hypothesis, that the solar system was formed from a nebula of gas and dust as it became organized.

• In 1992 the Catholic Church formally acknowledged its error over Galileo Galilei, after his book was taken off the Vatican's banned list in 1835.

• Cosmology is the study of how and why the universe is as it is. These studies rely on inference based on the theories of physics, and careful observation.

• Understanding how the universe developed requires careful measurement and thought, but without the right observations and measures, can still be in error.

• The universe started with the Big Bang, a point in time when all of the material we know about was in a very small volume, after which the material spread out.

• The Big Bang happened about 15 billion years ago, and while most of the interesting changes happened fast, forming galaxies took several billion years.

• Once upon a time, there was no time. That was when the cosmic egg, the super-atom, or the Big Bang happened. Then once that had happened, there was time.

• Three minutes after the Big Bang, the temperature had dropped to 1 trillion degrees, and protons and neutrons were able to begin forming nuclei of atoms.

• Since the Big Bang, the universe has been expanding outwards. So far, there is no evidence to suggest that it will slow down and collapse in a Big Crunch.

• A few hundred thousand years after the Big Bang, the universe had cooled enough so electrons could link to nuclei and form atoms of hydrogen and helium

• Stars can change over time, and as they develop through standard sequences, types of star can be recognized, and their future development can be predicted.

• In 1910, Ejnar Hertzsprung and Henry Norris Russell studied the link between magnitudes and spectral types of stars, leading to the Hertzsprung-Russell diagram.

• Annie Jump Cannon sorted Edward Pickering's arbitrary star classes to an order that made sense: she put the spectral classes in the order O, B, A, F, G, K, M.

• Blue-white, helium-rich stars like Rigel, are known by the letter B, while G is used for the Sun and other yellow stars, and M for red stars like Betelgeuse.

• We now know that a G star like the sun is at the cool end of the range, hotter only than K and M stars, while all of the rest are bluer and hotter.

• A class A star is a white star like Sirius or Vega, in whose spectra we see a very strong series of dark lines caused by hydrogen in its atmosphere.

• Between A and G are the F stars; between G and M, the K stars. The letters B, A, F, G, K, M, stand for six divisions, including a great majority of the stars.

• Stars beyond a certain size must inevitably collapse to form black holes, dense objects which exert enough gravitational force to stop even light escaping.

• Space can be thought of as curved, the curvature being caused by the influence of gravity on space. This helps explain many otherwise puzzling observations.

• The heavier elements in the universe have been formed as the result of fusion reactions in early stars, and later stellar explosions forcing nuclei together.

• Today, the universe is thought to be made up of about 74 percent hydrogen and 25 percent helium, the other elements amounting to only about 1 percent in total.

• Edwin Hubble made his first measurement of the Hubble constant in 1929, relating redshift to distance, leading to the conclusion that the Universe is expanding.

• Stars can orbit each other in binary systems, orbiting about the joint centre of gravity, which lies between, at a place determined by their respective masses. 

The principles of black holes

• In calculating the Milky Way's mass, based on its rotation, astronomers find there should be more mass: they call the deficit "the missing dark matter".

• The matter contained in stars and black holes makes up most of the known mass in the universe, possibly all of it, but nobody is sure at this stage.

• In 1783, John Michell outlined the nature of a Newtonian black hole, based on the idea that light consists of particles, and so would be affected by gravity.

• In 1916, Karl Schwarzschild offered a singular static solution of gravitational field equations which describes a minimal black hole, and sent it to Einstein.

• In 1916, while fighting on the Russian front, Karl Schwarzschild applied relativity to the inner workings of a star, then died of a battlefield illness.

• Black holes are so massive that no light can escape past a limit of the black hole, a surface called the event horizon. This is not the edge of the black hole.

• A black hole is typically surrounded by an accretion disc, a fast-rotating disc of dust and other material which eventually falls down into the black hole.

• Schwarzschild concluded that when a star contracts under gravity, there is a point when the gravitational field is so huge, nothing, not even light, can escape.

• The radius of a star of any given mass when it reaches the stage of collapse at which it traps all light is now known as the Schwarzschild radius.

• Our Sun has a Schwarzschild radius of 2.5 km, and if it ever actually shrinks below that radius, will become a black hole, from which nothing can escape.

• In 1967, John Wheeler, introduced the dramatic term 'black hole' to describe a concept that went back to earlier times, but never with such a name.

• In 1972, James Bardeen, Brandon Carter, and Stephen Hawking proposed four laws of black hole mechanics in analogy with the laws of thermodynamics.

• As material falls into a black hole it loses electrons and is broken down into charged particles, and as these accelerate, they emit large amounts of radiation.

• In 1973, Ostriker and Peebles found the amount of visible matter in typical spiral galaxies was not enough for Newtonian gravitation to keep the disks together. 

The principles of radio astronomy

• A radio telescope uses a large dish to collect and focus the weak radio signals from a distant star in much the same way that telescopes process visible light.

• In 1933, Karl Jansky announced that he had detected radio waves coming from the direction of Sagittarius, after first thinking they came from the Sun.

• In 1942, Grote Reber made the first radio map of the sky and J.S. Hey detected solar radio waves, while wartime radar operators were also detecting signals

• The Square Kilometre Array radio-telescope or SKA, if it is built, would place about a thousand antennas in an array to give superb resolution.

• The SKA would work on the principle of an interferometer, combining the separate signals from the many antennas to build up a single very clear picture. 

The principles of X-ray astronomy

• X-rays are a form of radiation, just like light, heat, gamma rays, microwaves and the radiation we use to transmit radio and television signals.

• Soft X-rays range from 10 to 0.1 nanometres (nm) (about 0.12 to 12 keV). Hard X-rays range from 0.1 nm to 0.01 nm (about 12 to 120 keV).

• Stars generate electromagnetic radiation at X-ray and radio broadcast wavelengths as well as visible light. This is the basis of radio and X-ray astronomy.

• X-ray astronomy needs to be carried on from spacecraft in space, as the Earth's atmosphere blocks all of the radiation at X-ray wavelengths, to our good luck.

• The first X-rays detected in space were found in 1969, with instruments sent into space by Americans using a captured German V2 rocket.

• The first distant cosmic X-ray source known was Scorpius X-1, discovered in 1962. This won Riccardo Giacconi the Nobel Prize in Physics in 2002.

• Scorpius X-1 emits 10,000 times as much energy in the X-ray range as it does in the vislible light part of the spectrum.

• Most X-ray telescopes use charge-coupled devices (CCDs) to build up an image, pixel by pixel.

• Black holes are said to give off X-rays, but these are from matter that collides as it falls very fast towards the black hole. 

There are other SPLATS to be found, but you will need to go back to the main SPLATS page to find the links.

© The author of this work is Peter Macinnis, who asserts his sole right to the product as it is packaged here, recognising that many of the ideas are common. You are free to use this as a model to do your own version. Copies of this whole file or site may be made and stored or printed for personal or educational use. You can contact me at macinnis44@gmail.com, but only if you add my first name to the front of that email address — this is a low-tech way of making it harder to harvest the e-mail address I actually read.