# Far Out, Man: Measuring Astronomical Distances

Centuries ago the stars were believed to reside just beyond the planets of our solar system.It never fails to astound me how big the Universe is—how far away even the nearest stars are, let alone other galaxies scattered from here to near infinity….

How do we know how far away celestial objects are? This shouldn’t be taken for granted, as it’s not as straightforward as sounding the depth of the ocean floor with sonar, or determining the range to an object by bouncing radio waves off it and timing the reflection.

In fact, we have “pinged” the nearest celestial objects with radar to determine their distances very accurately. Examples are the Moon and Venus, where round-trip lightspeed travel is measured in seconds or minutes.

Before radar, the scale of the Solar System had to be determined geometrically, by observing events like Venus or Mercury transiting the face of the Sun from different locations on Earth and triangulating. Even this technique requires telescopes, which we’ve had only four hundred years. Before that, figuring out distances to just about everything except the Moon was mostly guesswork. In fact, it wasn’t too many centuries ago that the entire Universe was believed to be not much larger than the Solar System—the Sun and it’s nine…excuse me…eight planets—as we know it today.

Once the distance from Earth to the Sun was figured out, that length (the “Astronomical Unit”) in effect became a basic measuring rod for working out distances to everything else, by one means or another.

As Earth orbits the Sun, the direction from which we see stars shifts minutely, and we can observe a small change in a star’s position compared to the more distant “background” stars. You can see the same effect by holding a finger in front of your face and looking at it alternately with one eye, then the other.

The geometry of this observation is a simple triangle, whose base is the distance between your eyeballs and whose legs are the lines from each eyeball to your finger. By knowing the length of the base, and observing the change in viewing angle against the background, the length of the legs (distance from your eyeballs) can be calculated.

In the case of Earth and a nearby star, the “eyeballs” are the Earth at two ends of its orbit around the Sun (six months apart) and the “finger” is the star.

But this measuring of distance by “trigonometric parallax,” as it’s called, only works for the nearest stars, as the minute shift in the star’s apparent position diminishes with distance.

As astronomers learned more about the distance to nearby stars, they determined how to relate their temperature and mass to their actual brightness, and it became possible to estimate the distance of many stars by measuring their apparent brightness, with an understanding of how the brightness of light weakens with distance.

To measure the depths of space between us and galaxies far, far away, in which individual stars are indistinguishable from the overall galactic glow, we can turn to certain types of supernovae: individual stars that temporarily shine brightly enough to be observed and measured. Like the flare of a match struck in the dark night, the brilliance of the flash reveals how far away the striker stands.

We have built up our knowledge of the Universe’s vastness over the past couple centuries, working out the problem from the near to the far. Even as science and technology have made the world on which we live smaller, it has done exactly the opposite to the Universe….

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Far Out, Man: Measuring Astronomical Distances 12 June,2013

• Ken Sanderson

Two questions:
First, what is the source–and the name, if it has one–of the image of the man breaking through the celestial sphere to see what lies outside it? (My wife found it by Googling “celestial spheres,” but unaccompanied by any information.)

And second: how have people developed “an understanding of how the brightness of light weakens with distance”? I can guess a little: light scattering as objects get in the way, for example. But what’s the full, real explanation?

A very interesting blog you have. Thanks.

• Answer to question 1: Apparently it was a woodcut made by astronomer Camille Flammarion in 1888.

Answer to question 2: Certainly the strength of light can be weakened as it passes through intervening material–dust, gas, etc. But even in the absense of such impeding materials, the strength of light weakens as it spreads out in space. A source of light like a star or a candle, which sends out light in all directions, weakens with distance since, the greater the distance it travels, the more space it is spread out in. Even a laser beam, whose rays are “coherent,” or all traveling in the same direction and so not spreading out, weakens with distance because–well, it’s not a perfect universe and even a laser beam spread out with distance. (A pencil thin laser beam fired at the Moon will have spread out to cover a few square kilometers by the time it gets there.)

## Author

### Ben Burress

Benjamin Burress has been a staff astronomer at Chabot Space & Science Center since July 1999. He graduated from Sonoma State University in 1985 with a bachelor’s degree in physics (and minor in astronomy), after which he signed on for a two-year stint in the Peace Corps, where he taught physics and mathematics in the African nation of Cameroon. From 1989-96 he served on the crew of NASA’s Kuiper Airborne Observatory at Ames Research Center in Mountain View, CA. From 1996-99, he was Head Observer at the Naval Prototype Optical Interferometer program at Lowell Observatory in Flagstaff, AZ.

Read his previous contributions to QUEST, a project dedicated to exploring the Science of Sustainability.