Inverse Square Law: Background

One of the hardest problems in studying the Universe is figuring out how far away things are. You can't just fly over to another galaxy with a ruler in the morning and be back for lunch. Even light takes millions and millions of years to go that far!

Light is very important to astronomers. Unlike other kinds of scientists, we cannot take the objects we are studying into a lab and poke them! We can only study the light they have given off. This is important to remember. What if there is lots of stuff out there which is not shining? Can you think of a way we might learn about it?

If a light is giving off lots of energy every second, we say it is very luminous. For example, a 100-Watt light bulb in your house is using 100 ``Joules'' of energy every second (100 Joules is enough energy to lift you up several centimeters!). But a luminous light is NOT necessarily a bright one! Why not?

You've probably noticed that if you get closer and closer to a light, it looks brighter and brighter. Think of a big fire and a small candle, both 5 feet away from you. The fire is much more luminous--it is putting out much more energy. Now move the fire farther and farther away, and it starts to look fainter and fainter, even though it is putting off just as much energy as before. Eventually, the nearby tiny candle seems brighter than the distant roaring fire! So how bright something is depends not only on how much light it is giving off, but also on how far away it is.

All this gives astronomers an idea. Suppose that we have a row of candles, all giving out the same amount of energy in a second. Now suppose someone scattered the candles all around while you weren't looking. Can you figure out how far away each candle is without using a ruler? YES! The farther away a candle is, the dimmer it is. So all you have to do is look and measure the brightness. That's just like the Universe, where we'd like to know the distance to far-away galaxies without going there. But in the real Universe it's really hard to find candles that all put out the same amount of light. We'll talk about that more later on.

For our experiment today, we will actually measure how the brightness of a light depends on how far away it is. This is the same idea some astronomers use to figure out the distance to galaxies on the edge of the known Universe!