Free printable SSAT practice test for Grade 8

On a clear night, the stars seem to hang in a single moment, as if the sky were a photograph taken just now. In fact, it is something stranger: a collage assembled from many different pasts. Every point of light you see left its source long ago, and each has been traveling for a different length of time.

The reason is that light, though astonishingly fast, is not instantaneous. In empty space it covers about 186,000 miles every second. That speed is so great that for much of history people assumed light arrived the instant it was given off. One of the first serious challenges to that idea came in the 1670s, when the Danish astronomer Ole Romer noticed that the eclipses of Jupiter's moon Io came earlier or later than predicted, depending on whether Earth was moving toward Jupiter or away from it. The most reasonable explanation was that light needed extra time to cross the extra distance. Light, in other words, had a finite speed, and that speed could be measured.

Once that was established, distance and time became two ways of describing the same thing. Sunlight takes a little more than eight minutes to reach Earth, so we always see the Sun as it was about eight minutes earlier. For greater distances, astronomers use the light-year, a unit that sounds like a measure of time but is actually a measure of length: the distance light travels in one year, nearly six trillion miles.

Finding out how far away a particular star is proved far harder. The method that finally worked is called parallax. Hold a finger at arm's length and look at it first with one eye and then with the other; the finger appears to jump against the background. Astronomers do the same thing on an enormous scale, observing a nearby star from opposite sides of Earth's orbit, six months apart, and measuring how much it seems to shift against far more distant stars. The shift is tiny, much smaller than the unaided eye can detect, and it was not measured successfully until 1838, when Friedrich Bessel reported the distance to a star called 61 Cygni.

The results were humbling. The nearest star beyond the Sun, Proxima Centauri, is a little more than four light-years away, so its light is over four years old when it arrives. The Andromeda Galaxy, often described as the most distant object visible without a telescope, is about 2.5 million light-years away. The faint smudge it makes on a dark autumn night is light that set out before modern humans existed.

This delay is not merely a curiosity; it is one of astronomy's most powerful tools. Because light from remote objects is old, telescopes that gather extremely faint light are, in effect, looking into the past. By studying galaxies at greater and greater distances, astronomers can observe the universe at earlier stages of its history, much as a geologist reads older rock in deeper layers. The night sky, it turns out, is less a picture than an archive.

Suppose a friend gives you a free ticket to a concert on Saturday night. The ticket cost you nothing, so going seems to cost nothing as well. An economist would disagree. If attending means giving up a shift at a part-time job that would have paid sixty dollars, or an evening you had planned to spend finishing a project, then the concert has a real cost after all. It is simply a cost that does not appear on any receipt.

Economists call this opportunity cost: the value of the best alternative you give up when you make a choice. The idea rests on a plain observation about scarcity. Time, money and attention are limited, so every decision to use them one way is also a decision not to use them another way. The old saying that there is no such thing as a free lunch makes the same point. Even when someone else pays for the meal, the hour you spend eating it is an hour you cannot spend on anything else.

Opportunity cost is easy to state and surprisingly easy to forget. A price tag is visible and specific; the alternative a purchase rules out is usually vague and unspoken. As a result, people tend to weigh what they can see. A shopper choosing between two phones may spend an hour comparing features while never asking what else the extra two hundred dollars could have bought. Researchers who study decision making have found that simply reminding people of what else they could do with their money can make them noticeably more cautious about spending it.

The concept also explains choices that look puzzling at first. Consider the full cost of attending college. Tuition and books are the obvious expenses, but economists add another: the wages a student could have earned by working full time during those years. For most students, the investment still pays off over a lifetime. For a rare few with an unusually valuable opportunity, such as a promising young athlete, the income given up may be large enough that delaying college makes sense.

It is worth separating opportunity cost from a related idea that often causes confusion. A sunk cost is money or effort already spent that cannot be recovered. Because it is gone whichever way you decide, it should not influence what you do next. The person who sits through a dull movie only because the ticket was expensive is letting a sunk cost steer the decision, while ignoring the opportunity cost of the next two hours.

None of this means every choice requires a spreadsheet. The value of the concept lies in a single habit of mind: asking, before committing, "Compared with what?" That question turns invisible costs into visible ones, and visible costs are far easier to weigh.