What Will Telescope Cost?

Amateur telescopes come in a wide range of prices, from a low of under $200 to a high of $5,000 and more, much more. There really is no upper limit. Someone out there will be happy to take as much money as you’d care to spend. In fact, the Beck Telescope (a Cassegrain-focus telescope with a 30” diameter primary mirror) located in Bradley Observatory at Agnes Scott College was originally owned privately by one Henry Gibson, who had it housed in a dome near his house. He sold the telescope to the College in 1947 for $15,000—a lot of money back then! The beginner need not invest in the four-digit range; however, spending less than about $300 on a new telescope (except in the case of certain rich-field instruments, which we will get to shortly) is likely to result in disappointment.

If you’ve been hitting the malls and looking at telescopes in department stores, camera stores, hobby shops, and even some optical stores, you may be surprised that most of the instruments you’ve seen will not provide you with a satisfying observing experience. The market is full of telescopes in the $100 to sub-$300 range—and they sell! But they’re mostly not worth their “bargain” prices. That’s not a subjective judgment. It’s a cold, hard fact. Here are some typical attributes of cheap telescopes:

• A cheap, wobbly mount. If the view wiggles, you will have a very frustrating time looking at the sky, especially if there is the slightest breeze, or you bump the telescope trying to focus the image. We’ll discuss mounts in just a few minutes, but be aware that a shoddy equatorial mount is inferior to a simpler altazimuth mount—if that mount is steady and well made.
• A telescope that trumpets its magnification but makes little or no mention of its aperture. Aperture, the diameter of the telescope’s objective lens (if it’s a refractor) or primary mirror (if it’s a reflector), determines how much light you will be able to collect. After you get tired of looking at the moon, you’ll find yourself increasingly interested in the dimmer objects of the night sky. Buy the largest aperture you can afford; aperture size and component quality are far more important than magnification numbers. A 2.75-inch (70 mm) aperture is a very good minimum for a refractor, and a 4-inch (100 mm) aperture is a good minimum for a reflector. Excellent Maksutov-Cassegrain instruments start at 90 mm, but the entry-level Schmidt-Cassegrain is a 5-inch model.
• Poor optical quality. Stars should focus as bright, sharp points of light, not smears, blurs, or flares. Unfortunately, it is rarely possible to field test a telescope before you buy it, so purchase only an instrument that comes with a noquestions-asked return policy. Put the telescope through its paces by focusing on a reasonably bright star. You may want to find Altair, Betelgeuse or Arcturus, for example. On a night with good seeing, the star should focus to a clean point. Next, using the highest magnification, slightly unfocus the image by turning the focus knob first one way and then the other. With good optics that are properly collimated (the optical elements made perfectly parallel with one another), the out-of-focus image will look the same regardless of which way you turn the knob. If the two out-of-focus images are significantly different, the optical collimation is poor.
• Small eyepiece. The modern standard for an eyepiece barrel diameter is 1.25”. Two-inch diameter eyepieces are common on larger, more expensive telescopes (14” diameter mirrors and greater). A short-barrel eyepiece can restrict the field of view at low power and is generally a sign of an inferior telescope.
• A junk finderscope. The finderscope (or finder)—the small telescope attached to the side of the main telescope—is very important for locating the objects you wish to study, especially if your telescope lacks go-to capability. An inferior scope is of little use. Look for one with an aperture of at least 30 millimeters. Also make sure the bracket that mounts the finder is easily, firmly, and accurately adjustable. You’ll need to align the finderscope with the main instrument frequently. You may want to also replace the factory finderscope with a “bullseye” on the sky, powered typically by a small red LED.
• Obscure and/or skimpy instructions. Not only is a clear and ample manual an important aid to using and enjoying a telescope, it is a sign of the quality of thought that has gone into making the instrument.

Telescope shopping advice

Here are a few words of shopping advice—much of which applies to telescopes as well:

• Examine and feel the binoculars. They should strike you as a well-crafted precision instrument.
• Test the focusing mechanism. It should be smooth and offer steady resistance.
  
• Look for antireflection coating on all lenses. This thin coating will make the lenses appear blue, yellow, magenta, or purple when held at an angle to the light.
• Look through the binoculars. Try focusing on a point of light (a distant bulb, for example). It should be absolutely sharp, at least until the point of light gets very near the edge of the field of view.
• Focus on a vertical straight line such as the corner of a building. Even with very good binoculars, the straight line will bend at the extreme edges of your field of view. However, if the line remains bent a third of the way from the edge, the quality of the optics is poor.
• The twin barrels of binoculars must be perfectly parallel with one another. If they aren’t, you will see a double image. Your eyes will work hard to compensate and fuse that double image, but ideally, there should be no double image to fuse.

Do You Really Need a Telescope?

Few experiences with the night sky are more instantly rewarding than your first look at the moon, a nebula, or a planet through a telescope. Saturn, in particular, can look almost too perfect. One of us taught students (while in graduate school) who refused to believe that the planet that they were looking at through the telescope was real. This student insisted that Saturn was a sticker on the telescope lens. However, it is also true that such an experience can be singularly disappointing if that shiny new telescope you bought at the mall turns out to be a piece of wobbly, hard-to-use junk. If you are willing to invest in a good telescope (we’ll talk about the magnitude of the investment in just a moment), and if you are willing to invest the time to learn how to use it, a telescope can be a wonderful thing to have.
But will you use it?
If you are an urban dweller who never escapes the streetlights of the city and are hemmed in by tall buildings, you may be better advised to spend your money elsewhere. Then again, owning a sufficiently portable telescope gives you a good excuse to pack up every once in a while and head for the country, where the skies are darker and the seeing is better.
faint to see with the naked eye visible, all stars are so incredibly far away (the closest beyond our sun, Alpha Centauri, is about four light-years away) that a given star at higher magnification will still be nothing more than a point of light. Magnification is also largely wasted if what you look at is too dim to see well. Get binoculars with the largest aperture (the diameter of the objective, or main lens) you can afford. An aperture of 50 millimeters is a good choice. Couple this with a 7magnification, and you have a 7 50 pair of binoculars—a good allaround choice for handheld viewing.
If you want to successfully use binoculars with a magnification of more than 10or 12, you will need to mount them on a camera tripod equipped with a binocular adaptor clamp or a specially designed binocular tripod; otherwise, the sky will be a blur.
Binoculars have the advantage of being very portable, and whole guidebooks have been written about observing the sky with them (for example, Exploring the Night Sky with Binoculars, by Patrick Moore [3rd ed., Cambridge University Press, 1996]). However, at anywhere from $200 to $1,000 and more, binoculars with high quality optics are not cheap; if you’re thinking about buying a pair of big, expensive binoculars, there are other possibilities you may want to consider.

Little advice about telescope

At nearly $3 billion for the Chandra X-Ray Observatory, astronomy can be a dauntingly expensive pursuit. Fortunately, you don’t have to spend quite that much to get started. In fact, you don’t really have to spend anything. A lot of observation can be done with the naked eye, and many local communities have active amateur astronomers who would be happy to let you gaze at the heavens through their telescopes. Some veteran amateur astronomers even warn newcomers that they will be disappointed with a telescope unless they first obtain some star charts and guidebooks and make an effort to learn the major constellations, perceive differences in brightness, and learn to explain the phases of the moon. “Learn to use your eyes before you buy a telescope,” they say.

There’s some real value in this advice. You need at least a little working knowledge of the sky before you can locate much of anything with a telescope. In addition, the type of telescope you buy will depend in part on the type of observing that you want to do, and you won’t know that until you have a little experience. So our first piece of advice is to be patient: Don’t run out to a sale at your local Mega-Lo-Mart and buy a telescope just yet.

But let’s face it—part of the fun of astronomy is making faint objects look brighter and distant objects look closer. To many, a big part of the fun of astronomy is its tools.

The Hubble Space Telescope

There are other ways to escape the seeing caused by the earth’s atmosphere: You can get above and away from the atmosphere. In fact, for observing in some portions of the electromagnetic spectrum, it is absolutely required to get above the earth’s atmosphere. That is just what NASA, in conjunction with the European Space Agency, did with the Hubble Space Telescope. High above the earth’s atmosphere, the HST regularly achieves its theoretical resolution.
The HST was deployed from the cargo bay of the space shuttle Discovery in 1990. The telescope is equipped with a 94-inch (2.4-meter) reflecting telescope, capable of 10 times the angular resolution of the best Earthbased telescopes and approximately 30 times more sensitive to light, not because it is bigger than telescopes on the earth, but because it is above the earth’s atmosphere. Unfortunately, due to a manufacturing flaw, the curvature of the 2.4-meter mirror was off by literally less than a hair (it was too flat by 1/50 of the width of a human hair), which changed its focal length. The telescope still focused light, but not where it needed to, in the plane of the various detectors.

Astronauts aboard the shuttle Endeavour rendezvoused with the HST in space in 1993 and made repairs—primarily installing a system of small corrective mirrors. HST then began to transmit the spectacular images that scientists had hoped for and the world marveled at. Subsequent repair missions have installed the short-lived but productive infrared camera (NICMOS) and other instrumentation. A final servicing mission is planned for 2003, after which HST will be replaced by the Next Generation Space Telescope (NGST) near 2010.

New optical technology

The greatest limitation of ground-based observations is that Earth’s atmosphere gets in the way. The turbulence present in the upper atmosphere means that the best resolution attainable with a traditional telescope from the surface of Earth is about 1 arcsecond, or 1/1800 the size of the Moon. Now that might seem like a pretty sharp picture, but for the largest telescopes on the surface of Earth, it is only a fraction of the theoretical resolution, the resolution that a telescope should have, based on its size. It was thought to be a shame, for example, that the 10-m diameter Beck telescope, while it could collect more light, would have no better resolution than a 1-m diameter telescope.
A new technology has been developed to get around this limitation. Dubbed adaptive optics, it allows astronomers to counteract the distortions introduced by the atmosphere with distortions of their own. The distortions are made to another reflective surface inserted into the optical path, the path that light follows through the telescope. The idea is that if the distortions can be removed quickly enough, then large telescopes would have both of the advantages that they should have, namely more sensitivity and more resolution. This technology has produced stunning results recently on the Keck Telescope and the Gemini North Telescope located on Mauna Kea, Hawaii. What does this all mean? As the technology is perfected, ground-based telescopes will be able to make images as sharp as those made from space—in a more easily maintained and upgradeable package.
This technology is very dependent on fast computers and rapidly movable motors that can make tiny, precise adjustments to the surfaces of small mirrors.

Computer Assisted Telescope

Beginning in the late nineteenth century, most serious telescope viewing was done photographically. Astronomers (despite the popular cartoon image) didn’t peer through their telescopes in search of new and exciting information, but studied photographic plates instead. Photographic methods allowed astronomers to make longer observations, seeing many more faint details than could ever be distinguished with visual observing. In recent years, chemical-based photography has increasingly yielded to digital photography, which records images not on film but on CCDs (charge-coupled devices), in principle the same device at the focal plane of your camcorder lens. CCDs are much more sensitive than photographic film, which means they can record fainter objects in briefer exposure times; moreover, the image produced is digital and can be directly transferred to a computer.

Remember the sound of old-fashioned 12-inch, vinyl LP records? Even the best of them had a hiss audible during quiet musical passages, and the worst served up more snap, crackle, and pop than a popular breakfast cereal. CDs, recorded digitally, changed all that by electronically filtering out the nonmusical noise found at high frequencies. Analogous digital computer techniques can be used to filter out the “visual noise” in an image to improve its quality. The disadvantage of current CCDs is that they are relatively small. That is, CCD chips are much smaller than a photographic plate, so that only relatively small areas of the sky can be focused on a single CCD chip.

The effect of twinkling star

Theoretically, the giant Hale telescope at Mount Palomar is capable of a spectacular angular resolution of a .02” (or 20 milliarcseconds); that would be its resolution in the absence of complicating factors like the earth’s atmosphere. In actual practice, it has a resolution of about 1”. The source of this limit is related to the reason that stars twinkle. The earth’s turbulent atmosphere stands between the telescope’s gigantic primary mirror and the stars, smearing the image just as it sometimes causes starlight viewed with the naked eye to shimmer and twinkle.

If you took a still photograph of a twinkling star through a large telescope, you would see not a pinpoint image, but one that had been smeared over a minute circle of about 1” (1 arcsecond). This smeary circle is called the seeing disk, and astronomers call the effect of atmospheric turbulence seeing. When weather fronts are moving in (even if the skies appear clear), or have just moved out, the seeing can be particularly bad.

High, dry locations generally have the best seeing. To achieve resolutions better than about 1” from the surface of the earth is possible, but it requires a few tricks.

Adaptive optics, for example, are being increasingly employed on new research telescopes. This method allows a mirror in the optical path to be slightly distorted in real time (by a series of actuators) in order to compensate for the blurring effects of the atmosphere. Of course, much higher resolutions are possible at other wavelengths. As we will see, radio interferometers regularly provide images with resolutions better than 0.001” (or 1 milliarcsecond).

The Power to Gather Light

Why this passion for size?
As we mentioned before, the bigger the bucket, the more light you can collect, so the more information you can gather. The observed brightness of an object is directly proportional to the area (yes, area; not diameter) of the primary mirror. Thus a 78-inch (2-meter) diameter mirror yields an image 4 times brighter than a 39-inch (1-meter) mirror, because area is proportional to diameter squared, and the square of 2 (2 times 2) is 4. A 197-inch (5-meter) mirror would yield images 25 times brighter (5 times 5) than a 1-meter mirror, and a 393-inch (10-meter) mirror would yield an image 100 times brighter than a 1-meter mirror.

Now, things that are farther away are always going to be more faint. It should be obvious that a 100-watt light bulb will appear more faint if it is 1 mile away versus 1 foot away. Thus, a telescope that can see more faint objects is able to see things that are farther away. So, in general, the bigger the telescope, the more distant are the objects that can be viewed. As we’ll see near the end of this book, being able to see very distant (faint) objects is important to answering some fundamental questions about the ultimate fate of the universe.

Size Does Matters

Throughout the nineteenth and well into the twentieth century, astronomers and others interested in science and the sky avidly followed news about every new telescope that was built, each one larger than the last. In 1948, the Hale telescope at Mount Palomar, California, was dedicated. Its 200-inch (5-meter) mirror was the largest in the world.
It was designed flexibly to be used as a prime-focus instrument (with the astronomer actually ensconced in a cage at the front end of the telescope), a Cassegrain-focus instrument (with the observer perched on an adjustable platform at the back of the telescope), or a coudé-focus instrument. The Hale telescope was the largest in the world until 1974, when the Soviets completed a 74-ton, 236-inch (6-meter) mirror, which was installed at the Special Astrophysical Observatory in Zelenchukskaya in the Caucasus Mountains.
In 1992, the first of two Keck telescopes, operated jointly by the California Institute of Technology and the University of California, became operational at Mauna Kea, Hawaii. A second Keck telescope was completed in 1996. Each of these instruments combines thirty-six 71-inch (1.8-meter) mirrors into the equivalent of a 393-inch (10-meter) reflector. Not only do these telescopes now have the distinction of being the largest telescopes on Earth, they are also among the highest (of those based on Earth), nestled on an extinct volcano 2.4 miles above sea level.

Variations on an Optical Theme

While the two major types of optical telescopes are the refractor and the reflector, it is also useful to be aware of the basic variations in reflector design, especially when you think about choosing a telescope for yourself (see the next chapter). We have already seen that the simplest reflector (prime focus) focuses its image at the front of the telescope, introducing the possibility that the observer may block the image. The Newtonian focus instrument, as mentioned, overcomes this problem by introducing a secondary mirror to direct the focus to an eyepiece at the upper side of the instrument. This remains a popular arrangement for small reflecting telescopes used by amateur astronomers. This arrangement is unwieldy, however, for a large telescope. Imagine trying to get to the “top” of a telescope 6 feet long, perched on a 6-foot pedestal.

Some larger reflecting telescopes employ a Cassegrain focus. The image from the primary mirror is reflected to a secondary mirror, which again reflects the light rays down through an aperture (hole) in the primary mirror to an eyepiece at the back of the telescope.

Finally, a coudé-focus (coudé is French for “bent”) reflector sends light rays from the primary mirror to a secondary mirror, much like a Cassegrain. However, instead of focusing the light behind the primary mirror, another mirror is employed to direct the light away from the telescope, through an aperture and into a separate room, called the coudé-focus room. Here astronomers can house special imaging equipment that might be too heavy or cumbersome to actually mount to the barrel of the telescope. Reflecting telescopes have their problems as well. The presence of a secondary mirror (or a detector, in the case of a prime-focus reflector) means that some fraction of the incoming light is necessarily blocked.

Although reflectors do not experience “chromatic aberration” (since light does not have to pass through glass), their spherical shape does introduce spherical aberration, light being focused at different distances when reflecting from a spherical mirror. If not corrected, this aberration will produce blurred images. One common solution to spherical aberration is to use a very thin “correcting” lens at the top of the telescope. This type of telescope, which we will discuss more in the next chapter, is called a Schmidt-Cassegrain, and is a popular design for high-end amateur telescopes.

What is Reflection?

The refracting telescope was one of humankind’s great inventions, rendered even greater by the presence of a genius like Galileo to use it. However, the limitations of the refracting telescope soon became apparent:

• Even the most exquisitely crafted lens produces distortion, which can be corrected only by the introduction of other lenses, which, in turn, introduce their own distortion and loss of brightness, since a little of the energy is absorbed in all that glass. The chief distortion is chromatic aberration.
• Excellent lenses are expensive to produce, and this was even more true in the days when all lenses were painstakingly ground by hand. Lenses are particularly difficult to produce because both sides have to be precision crafted and polished. For mirrored surfaces, like those found in reflecting telescopes, only a single side must be polished.
• Generally, the larger the lens, the greater the magnification and the brighter the image; however, large lenses get heavier faster than large mirrors. Lenses have volume, and the potential for imperfections (such as bubbles in the glass) is higher in a large lens. All of this means that large lenses are much more difficult and expensive to produce than small ones. Recognizing the deficiencies of the refracting telescope, Isaac Newton developed a new design, the reflecting telescope, in 1668.

Instead of the convex lens of a refractor, the reflector uses a concave mirror (shaped like a shallow bowl) to gather, reflect, and focus incoming light. The hollow side of your breakfast spoon is a concave mirror (the other side is a convex one). This curvature means that the focal point is in front of the mirror—between the mirror and the object being viewed. Newton recognized that this was at best inconvenient—your own head could block what you are looking at—so he introduced a secondary mirror to deflect the light path at a 90-degree angle to an eyepiece mounted on the side of the telescope.

Refracting telescope design continued to develop throughout the eighteenth and nineteenth centuries, culminating in the 40-inch (that’s the diameter of the principal lens) instrument at Yerkes Observatory in Williams Bay, Wisconsin, installed in 1897.
But due to the limitations just mentioned, the biggest, most powerful telescopes have all been reflectors. In the eighteenth century, the great British astronomer Sir William Herschel persuaded the king to finance an instrument with a 47-inch (1.2-meter) mirror.

With this telescope, Herschel had a big enough light bucket to explore galaxies beyond our own Milky Way (though he did not know that’s what they were). By the middle of the nineteenth century, William Parsons, third Earl of Rosse, explored new nebulae (fuzzy patches of light in the sky, some of which are galaxies) and star clusters with a 73-inch (1.85-meter) instrument constructed in 1845. It ranked as the largest telescope in the world well into the twentieth century, until the 100-inch reflector was installed at the Mount Wilson Observatory (near Pasadena, California) early in the century.

What is Refraction?

Galileo’s instrument, like all of the earliest telescopes, was a refracting telescope, which uses a glass lens to focus the incoming light. For all practical purposes, astronomical objects are so far away from us that we can consider that light rays come to us parallel to one another—that is, unfocused. Refraction is the bending of these parallel rays. The convex (bowed outward) piece of glass we call a lens bends the incoming rays such that they all converge at a point called the focus, which is behind the lens directly along its axis. The distance from the cross-sectional center of the lens to the focus is called the focal length of the lens. Positioned behind the focus is the eyepiece lens, which magnifies the focused image for the viewer’s eye.

Modern refracting telescopes consist of more than two simple lenses. At both ends of the telescope tube, compound (multiple) lenses are used, consisting of assemblies of individual lenses (called elements) designed to correct for various distortions simple lenses produce. For example, the exact degree to which light bends or refracts in a piece of glass depends on its wavelength. Since light consists of many different wavelengths, a single lens will produce a distortion called “chromatic aberration.” The compound eyepiece of many modern telescopes also corrects the image, which a simple eyepiece would see upside down and reversed left to right.

The Telescope Is Born

In 1608, lens makers in the Netherlands discovered that if they mounted one lens at either end of a tube and adjusted the distance between the lenses, the lens that you put to your eye would magnify an image focused by the lens at the far end of the tube. In effect, the lens at the far end of the tube gathered and concentrated (focused) more light energy than the eye could do on its own. The lens near the eye enlarged to various degrees that concentrated image. This world-changing invention was dubbed a telescope.

The word telescope comes from Greek roots meaning “far-seeing.” Optical telescopes are arrangements of lenses and/or mirrors designed to gather visible light efficiently enough to enhance observation of distant objects and phenomena. Many, perhaps most, inventions take time to gain acceptance. Typically, there is a lapse of more than a few years between the invention and its practical application. Not so with the telescope.

By 1609, within a year after the first telescopes appeared, the Italian astronomer Galileo Galilei demonstrated their significance in military matters (seeing a distant naval foe), and was soon using them to explore the heavens. The largest of his instruments was quite small, with only modest magnifying power, but, as we’ve seen in the preceding chapter, Galileo was able to use this tool to describe the valleys and mountains on the Moon, to observe the phases of Venus, and to identify the four largest moons of Jupiter.

Buckets of Light

Of course, the fraction of the emitted energy we receive from a very distant star—or even a whole galaxy, like far-off Andromeda—is very small, having been diminished by the square of the distance (but never reaching zero). Imagine a sphere centered on a distant star. As the sphere becomes larger and larger (that is, as we get farther and farther from the star), the same amount of energy will pass through ever larger spheres.

Your eye (or your telescope) can be thought of as a very tiny fraction of the sphere centered on that distant star. You are collecting as much light from the distant source as falls into your “light bucket.” If your eye is a tiny “bucket,” then a 4-inch amateur telescope is a slightly larger bucket, and the Hubble Space Telescope is an even larger bucket. The larger the bucket, the more light you can “collect.” And if we collect more light in our bucket, we get more information.
One early question among astronomers (and others) was, “How can we build a better bucket than the two little ones we have in our head?” The answer came in the early seventeenth century.

Understanding Electromagnetic Spectrum

Electromagnetic radiation travels though the vacuum of space in waves. A wave—think of a water wave—is not a physical object, but a pattern of up-and-down or back-and-forth motion created by a disturbance. Waves are familiar to anyone who has thrown a rock in a pond of still water or watched raindrops striking a puddle. The wave pattern in the water, a series of concentric circles, radiates from the source of the energy, the impact of the rock or the rain drop. If anything happens to be floating on the surface of the water—say a leaf—the waves will transfer some of the energy of the splash to the leaf and cause it to oscillate up and down.

The important thing to remember about waves is that they convey both energy and information. Even if we didn’t actually see the rock or the raindrop hit the water, we would be able to surmise from the action of the waves that something had disturbed the surface of the water at a particular point. The type of energy and information created and conveyed by electromagnetic radiation is more complex than that created and conveyed by the waves generated by a splash in the water. Do take a moment now to make sure that you understand two properties of waves: wavelength and frequency.
Wavelength is the distance between two adjacent wave crests (high points) or troughs (low points), measured in meters. Frequency is the number of wave crests that pass a given point per unit of time (and has units of 1/second).

We think of the light from our reading lamp as very different from the x-rays our dentist uses to diagnose an ailing tooth, but both are types of electromagnetic waves, and the only difference between them is their wavelengths. Frequency and wavelength of a wave are inversely proportional to one another, meaning that if one of them gets bigger, the other one must get smaller. The particular wavelength produced by a given energy source (a star’s photosphere, a planetary atmosphere) determines whether the electromagnetic radiation produced by that source is detected at radio, infrared, visible, ultraviolet, x-ray, or gamma ray wavelengths.

The waves that produce what we perceive as visible light have wavelengths of between 400 and 700 nanometers (a nanometer is 0.000000001 meter, or 1 X10–9 m) and frequencies of somewhat less than 1015 Hz. Light waves, like the other forms of electromagnetic radiation, are produced by the change in the energy state of an atom or molecule. These waves, in turn, transmit energy from one place in the universe to another. The special nerves in the retinas of our eyes, the emulsion on photographic film, and the pixels of a CCD (Charge Coupled Device) electronic detector are all stimulated (energized) by the energy transmitted by waves of what we call visible light. That is why we “see.”

The outer layers of a star consist of extremely hot gas. This gas is radiating away some fraction of the huge amounts of energy that a star generates in its core through nuclear fusion. That energy is emitted at some level in all portions of the electromagnetic spectrum, so that when we look at a distant or nearby star (the sun) with our eyes, we are receiving a small portion of that energy.

A Slice of Light

The universe is ruled by the tyranny of distance. That is, the universe is so vast, that we are able to see many things that we will never be able to visit. Light is able to travel at extraordinary speeds (about 984,000,000 feet, or 300,000,000 meters, every second), but the light that we now see from many objects in the sky left those sources thousands, millions, or even billions of years ago. It is possible, for example, to see the Andromeda galaxy, even with the naked eye, but will we ever travel there?

Well, Andromeda is about two million light-years away, and a light-year is the distance light travels in one year—about 9,461,000,000,000,000 meters (some 6 trillion miles). Now, light can travel that far every year, so to get the distance to Andromeda, you multiply the velocity of light (6 trillion miles in a year) by the amount of time it took the light to get here (2 million years), and you get a lot of miles—approximately a 1 with 19 zeroes after it. Another way to think about these unbelievable distances: If you could travel at the speed of light (an impossibility, according to Einstein’s theory of relativity), it would still take you two million years to reach Andromeda.

But we can’t travel at anywhere near the speed of light. Right now, the fastest rockets are capable of doing 30,000 miles per hour (48,000 km/h). Maybe—someday—technology will enable us at least to approach the speed of light, but that still means a trip of two million years up and two million back. All of recorded history consumes no more than 5,500 years, and civilization, perhaps 10,000 years.

Why not go faster than the speed of light? We’ll see that, according to our understanding of space and time, the speed of light is an absolute speed limit, which cannot be exceeded. So revel in the fact that, on a clear night, you are able to gaze at the Andromeda galaxy, an object so distant that no human being will likely ever visit it.
Space ships may be severely limited as to how fast they can travel, but as we’ve said, the information conveyed by electromagnetic radiation can travel at the speed of light. The information from Andromeda, it is true, is not exactly recent news by the time we get it.

In fact, the photons that we are receiving from Andromeda left that galaxy long before Homo sapiens walked the earth. But everything we know about Andromeda and almost all other celestial bodies (aside from the few solar system objects we have visited with probes or landers), we know by analyzing their electromagnetic radiation: radio, infrared, and ultraviolet radiation, as well as x-rays and gamma rays and what we call light.

Newton’s Law is not just a good idea

In Principia, Newton proposed that the force of gravity exerted by objects upon one another is proportional to the mass of the two objects, and weakens as the square of the distance between those objects.

Specifically, he postulated that the gravitational force between two objects is directly proportional to the product of their masses (mass of object A times mass of object B). So two objects, one very massive and the other with very little mass, will “feel” the same mutual attraction. In addition, he claimed that the force between two objects will decrease in proportion to the square of the distance. This “inverse-square law” means that the force of gravity mutually exerted by two objects, say 10 units of distance apart, is 100 times (102) weaker than that exerted by objects only 1 unit apart—yet this force never reaches zero.

The most distant galaxies in the universe exert a gravitational pull on one another. These relations between mass, distance, and force comprise what we call Newton’s Law of Universal Gravitation. Consider the solar system, with the planets moving in elliptical orbits around the sun. Newton’s Principia explained not only what holds the planets in their elliptical orbits (an “inverse-square” force called gravity), but also predicted that the planets themselves (massive Jupiter in particular) would have a small but measurable effect on each other’s orbits.

Like any good scientific theory, Newton’s laws not only explained what was already observed (the motion of the planets), but was able to make testable predictions. The orbit of Saturn, for example, was known to deviate slightly from what one would expect if it were simply in orbit around the sun (with no other planets present). The mass of Jupiter has a small, but measurable, effect on its orbital path. Newton noted with a sense of humor that the effect of Jupiter on Saturn’s orbit made so much sense (according to his theory) that “astronomers are puzzled with it.” For the first time, a scientist had claimed that the rules of motion on the earth were no different from the rules of motion in the heavens.

The moon was just a big apple, much farther away, falling to the earth in its own way. The planets orbit the sun following the same rules as a baseball thrown up into the air, and the pocket watch of the earth is held in its orbit by a chain called gravity. Did Newton bring the celestial sphere down to Earth, or elevate us all to the status of planets? Whatever you think, we have never looked at the solar system or the universe in the same way since.

The Weighty Matters

Throw a ball up into the air, and you will observe that it travels in a familiar curved (parabolic) trajectory: first up, up, up, leveling off, then down, down, down. Common sense tells us that the force of gravity pulls the ball back to Earth.

Newton’s brilliance was in postulating not only that there is a force, gravity, that pulls the ball (or apple) back to the earth, but that such a force applies to everything in the universe that has mass. The gravitational force due to the mass of the earth also pulls on the moon, holding in its orbit, and pulls on each of us, keeping us in contact with the ground. Finally there was an answer to those who thought the earth could not be spinning and orbiting the sun. What was there to keep us firmly footed on the earth? Newton had the answer: the force of gravity.

Newton’s Three Laws of Motion

Newton’s first law of motion states that, unless acted upon by some external force, a body at rest remains at rest and a moving object continues to move forever in a straight line and at a constant speed. This property is known as inertia. The measure of an object’s inertia is its mass (in effect, the amount of matter the object contains). The more massive an object, the greater its inertia.
Newton’s first law explains why the planets move in nearly circular orbits—essentially because an external force (gravity) acts on each planet. Without gravity, the planets would all fly off in straight lines, like so many pocket watches.

Newton’s second law states that the acceleration of an object is directly proportional to the force applied to the object and inversely proportional to the mass of the object. Pull two objects with the same force, and the more massive object will accelerate more slowly than the less massive one. We all know this intuitively. Your subcompact car’s engine would have a much harder time accelerating than an 18-wheel truck!
Newton’s third law of motion states that forces do not act in isolation. If object A exerts a force on object B, object B exerts an equal but opposite force on object A. A hammer, for example, exerts a force on the nail, driving it into the wall. The nail exerts an equal and opposite force on the hammer, stopping its motion.

What Hold The Universe Together?

One of us knew a young man who owned a pocket watch, which he would habitually twirl, holding the end of the chain and allowing it to orbit around the focus of his finger. One day, the chain broke, sending the costly timepiece flying off into space—and against a wall, with predictably catastrophic results.

Why don’t the planets suffer the same fate?
Despite his brilliant explanation of planetary motion, Kepler had not explained how the planets orbited the sun without flying off into space, and why they traveled in ellipses.
The answer came in the late seventeenth century when an Englishman, Isaac Newton (1642–1727), one of the most brilliant mathematicians who ever lived, formulated three laws of motion and the law of universal gravitation in a great work, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), better known simply as Principia.