# How do astronomers know how far away stars and galaxies are from earth?

It sounds like a simple question, but in many ways it’s not. How can we know how far away something is if we can’t touch it?

By comparing the way it appears to us with the appearances of things whose distances we know. If we assume that the same physical laws apply everywhere, we can use reasoning to find our way from things we measure with our hand out to the farthest stars in the universe. For mankind, the first link in the chain stretching to the stars was finding the distance from Earth to Mars.

By observing the paths of the stars and planets as they moved across the sky over the centuries, Western astronomers came up with an accurate model of how the solar system was constructed, with the sun at its center and the planets making elliptical orbits around it.

By counting the months or years it took for each wandering planet to return to its original position in the sky, astronomers could tell which planets were more and less distant from the sun, those that took the longest to go around were farthest from the center. But they had no idea of the actual distances in miles. In 1671 two Frenchmen, using a measuring technique common in surveying called trigonometric parallax, found the distance in miles to Mars, and from that they figured all the distances in the solar system.

A ship carrying one astronomer, Jean Richer, set out for the port of Cayenne in French Guiana, which is in the Western Hemisphere. Richer’s colleague, Giovanni Domenico Cassini, stayed behind in Paris, which is in the earth’s Eastern Hemisphere.

On the same night (which they had agreed upon before Richer left France), at nearly the same moment, both astronomers thousands of miles apart pointed their telescopes toward Mars and took down its position relative to the stars around it. Each man saw Mars in a slightly different position; the difference was caused by a phenomenon called parallax.

If you look at something from two different places, it appears to move in relation to its background. You can demonstrate parallax yourself: hold one finger up about a foot from your face, against the background of objects in a room. Look at your finger with your left eye alone, and then with your right eye alone. The finger will seem to move; through one eye it might be next to the lamp, and through the other it may line up with the chair leg. This happens because you’re looking through eyes 2 to 3 inches apart; it’s only 12 inches out to your finger, so the change in vantage point makes a big difference. If you look at the avocado plant 20 feet away through each eye, however, it won’t seem to move. The parallax you observe with your eyes gives you depth perception for nearby objects; the use of parallax on a larger scale in astronomy gives us depth perception to find the distance of relatively near objects in space.

In Richer and Cassini’s experiment, Paris and Cayenne are the two eyes, and Mars is the finger. To Richer in Cayenne, Mars’s perimeter lined up in front of one set of stars, and to Cassini it seemed to lie slightly east of that position. When they were able to get back together and compare readings, they measured the amount of the discrepancy in degrees of arc.

Surveyors and astronomers use degrees to measure how much of their field of vision an object takes up, each degree is 1/460 of the circle you see turning completely around while watching the horizon. Richer and Cassini were able then to draw an imaginary triangle in space, between Paris, Cayenne, and Mars. They knew the length of the base of the triangle: 4,000 miles; that was the distance between Paris and Cayenne, which had been measured by sailing ships, minus a calculated amount to allow for the earth’s curvature. They could find the angles of the triangle from the degree measurement they had made: the triangle’s top angle equaled the number of degrees’ parallax shift in Mars’s position. Using trigonometry, they could then find the height of the triangle: the distance to Mars from Earth, about 49 million miles.

Parallax measurement has also been used to find the distance of some of the nearer stars, such as Alpha Centauri and Sirius. Since stars are so much farther away than the planets, sightings taken from different points on Earth are not far enough from each other to show a measurable parallax. Astronomers instead take down the position of the star twice from the same spot, six months apart. The second sighting is thus made when Earth is on the other side of its orbit of the sun. So when sighting a star trillions of miles away, instead of trying to measure the minute parallax shift from vantage points only 4,000 miles apart, we can use points separated by twice the distance from Earth to the sun: 2 x 93 million miles, or 186 million miles. With a triangle base of that size, we can find by parallax that the distance to Alpha Centauri, the nearest visible star to our solar system, is about 24 trillion miles (4.3 light years) away, and to Sirius about 52 trillion miles (8.8 light years).

The universe is unimaginably vast. Stars are so far apart just within one galaxy that if the sun were the size of an orange, the nearest star would be represented by another orange 1,000 miles away. A journey from our solar system to neighboring Alpha Centauri in the fastest rocket known to man would take 1 million years. Thus, parallax sightings taken from the far points of Earth’s orbit are useful only for finding the distance to stars 100 light years away or less. Most of the galaxy is much farther from us than that, and we must use other methods of reckoning. There are many, and they draw on a wide assortment of facts scientists know about the stars.

One way of finding the distance to a star more than 100 light years away is by spectroscopic parallax, analyzing the color of the light that reaches us from the star with a spectroscope, a device that very precisely spreads out the spectrum from a beam of light the way a prism does, arranging the frequencies the beam contains from highest to lowest. The brighter the “blue” or high frequency end of the spectral band, the hotter the star. Heat is the motion of particles; the faster the atoms of a star vibrate, the more frequently (per second) they emit waves of energy in the form of light, and the more high frequency waves show on the spectrum.

Astronomers have noticed among the near stars, whose distances they can measure by trigonometric parallax, that the hotter stars have the most mass and the greatest luminosity, they send out the most total light. They conclude that the trend applies to all stars, that temperature always has the same relation to luminosity.

Thus from the bright blue spectrum of Epsilon Orionis in the constellation Orion (the Hunter), which shows it to be burning at the fierce temperature of 24,800 Kelvins (about 44,000 degrees Fahrenheit), scientists estimate that it must have a radiating power 470,000 times that of the sun, the sun’s temperature is only 5,800 Kelvins. If we can accept the estimate of Epsilon Orionis’s true brightness and compare it to how bright it appears to us on Earth, we can then figure its distance, since light always dissipates at the same rate the farther it gets from its source.

A photometer, analogous to a photographer’s light meter, attached to a telescope measures the apparent brightness of a star by counting the light particles that reach us from it per second; the formula for apparent brightness is luminosity 4.7r (distance)2. From the color of Epsilon Orionis, which indicates its temperature, which in turn tells its radiating power, we conclude that it is 1,600 light years away.

Spectroscopic parallax, however, is useful only out to the edge of our own galaxy, 100,000 light years away. The Milky Way, which contains 100 billion stars like the sun, is only one of 10 billion or so galaxies in the universe. As wide as the void is between stars in the Milky Way 5 light years, the distance between galaxies is an even more staggering 2 million light years. The light we see coming from our closest neighboring galaxy, Andromeda, was emitted 2 million years ago, when mankind’s prehistoric ancestor Australopithecus was busy chasing gazelles near the Olduvai Gorge in East Africa.

To judge the distance to another galaxy, astronomers scan its stars for a type known as a Cepheid variable. The brightness of a Cepheid varies regularly; some give off twice as much light in the bright phase as in the dim. Polaris, the North Star, is one of the Cepheid variables in our own galaxy. By measuring the distance to the nearer Cepheids by spectroscopic parallax and other short range methods, astronomers have found that the length of a variable star’s period of pulsation, its complete cycle of bright and dim, is related to its mass and luminosity. The longer the period, the greater the peak luminosity. Polaris has a four day cycle and is 2,500 times as bright as the sun.

Applying the principle to a Cepheid in another galaxy, we can tell its luminosity from the length of its period and compare the star’s apparent brightness with its luminosity to get the distance, as with spectroscopic parallax.

Beyond 10 million light years things get more approximate: we know the luminosity of the entire Milky Way Galaxy; when we sight a distant galaxy, we assume it is about as intrinsically bright as our own and again estimate distance from apparent brightness.

But how about galaxies near the far ends of the universe 2 billion to 20 billion light years away? The only way now known to determine how far it is to a galaxy so distant is to measure the amount of its red shift; those with the greatest red shift are receding the fastest. Their trajectories suggest that the universe consists of the fragments of a cosmic explosion scattering into space.

In an explosion, the fastest moving particles fly the farthest from the blast; that is what astronomers see happening in the universe. Among stars whose distances can be measured by Cepheid or galactic luminosity, it seems the farther away they are, the faster they are receding from us, and the more pronounced is their red shift. Thus for the very farthest galaxies more than 3 billion light years away, for which we can barely pick up a spectrum, we must figure that the distance is proportional to how fast a galaxy is flying from us, as shown by its red shift.

The extreme shift of a galaxy in the constellation Hydra shows it to be receding at 38,000 miles per second, which is more than 20 percent of the speed of light. That would indicate that the galaxy is 3.6 billion light years away.