How Fast the Stars

Copyright © Karl Dahlke, 2023

For a million years, we viewed gravity is a force that pulls everything toward the ground. We didn't try to explain it, or understand it, it was just there.

Even the animals develop a working model of gravity. A dog or a cat knows how far he can fall without injury. Higher than that, and he won't jump. In You're a Good Man Charlie Brown, Snoopy is about to pounce down on a cat, when he says, “Gee, I never quite realized it was so far down to the ground from here. Hmmm.”

The Greeks accepted the reality of gravity, but wondered, why don't the stars and planets come crashing down to earth? The explanation was simple. The stars are points of light affixed to a sphere that rotates around the earth, and the planets, moving against the backdrop of stars, are carried about by gods, which keep them aloft. These explanations are somewhat untestable, but that was the hypothesis of the day.

Newton was the first to provide an explanation for gravity, or at least a mathematical model that could be tested. Everything doesn't fall to earth; any two objects fall toward each other. We never noticed, because the earth is trillions of times heavier than we are. When an apple falls, the earth pulls the apple down to the ground, yes, but the apple also pulls the earth up, in proportion to their masses. The earth may only come up a trillionth of the width of a proton, but it does come up to meet the falling apple. This he understood, in an epiphany, when he saw the apple fall. (It almost certainly did not fall on his head, that was added later.)

The earth is heavier than we are, but the sun is heavier still, and so, the planets all fall toward the sun. They don't crash into the sun, because they are in orbit. The force of gravity toward the sun balances the outward pull as the planets spin around the sun. Newton calculated those orbits from first principles, using the calculus that he invented, and it matched what we saw in the sky. Orbits that had baffled astronomers for 2,000 years were now explained, with mathematical precision. That was the proof that Newton was right.

But it didn't explain the stars. They weren't really points of light on a sphere, but suns far away. Why then didn't they fall toward us, i.e. toward our sun, or more accurately, why didn't all the stars in the sky, including our sun, fall toward each other? We knew that the universe was very old, perhaps millions of years old. Even if the stars were far apart, whence the gravitational tug was weak, it was still there, and over millions of years, surely the stars would fall together. But they don't. They appear fixed in the sky, unmoving, eternal. This was called a "steady state".

This was such a profound mystery, that even Einstein wrestled with it. He finally came up with an unsatisfying constant, a fudge factor, that keeps them apart.

In the 1920's we found the answer. Stars and galaxies are flying apart, as though they had been blasted apart by an unseen force in the past. We express this in the succinct phrase, “The universe is expanding.”

How do we know that? It turns out, the starlight changes when the star moves toward or away from us. This is a form of the Doppler shift. When a fire engine comes up behind you, and passes you at high speed, its siren is higher when it is moving toward you, and lower when it is racing away. The pitch changes fairly quickly as it passes by. The same effect is heard at the race track, when cars whizz by at 200 mph. This is of course more pronounced than the fire engine travelling at 90 mph. Something similar happens to light as well. A specialized telescope can measure the shift in starlight, and thus, determine the speed of the star, towards or away from us.

With a few notable exceptions, all the stars are moving away. Furthermore, the farther away the star is, the faster it is moving away from us. This is consistent with the theory of a big bang in the past, that sent all the galaxies flying apart.

What we still don't know, a century later, is whether the universe will expand forever, or whether it will stop and collapse back onto itself. To illustrate, take a rubber ball and throw it up in the air. It flies away from your hand, and from the earth, for a while, but eventually gravity wins the day, and it comes back down. If you could throw it hard enough, and fast enough, it would not come back down. It would escape earth's gravity and fly off into space forever. Are the stars flying apart fast enough that they will spread out forever, or is that temporary, and some day, a trillion years from now, the stars will slow down and start to fall back together under their own gravity? We don't know.

There is a third theory, called dark energy. Some force, every bit as mysterious as gravity, pushes the stars apart. At the present time, it only works across great distances, but as the universe expands, this force becomes ever more powerful. At the end of time, the force will be so strong it will tear everything apart, including human beings, and even the atoms we are made of. This is called the big rip. There is some evidence for this idea, though it remains highly speculative.