Roanoke Times
Copyright (c) 1995, Landmark Communications, Inc.
DATE: THURSDAY, October 20, 1994 TAG: 9410210019
SECTION: EXTRA PAGE: 1 EDITION: METRO
SOURCE: JOEL ACHENBACH
DATELINE: LENGTH: Long
A: The other day the sun set fat and bloody. We knew it was 93 million miles away, roughly, but it didn't look 93 million miles away. Something that is 93 million miles away ought to be a speck, even if it is a star.
On the other hand, we couldn't honestly say how far away it appeared. It was just ... there. Kind of godlike. Apollonian.
Why is it so hard, indeed impossible, to perceive the distance to the sun and moon?
You probably think that's a dumb question. You are thinking we are doodoo-brains for not realizing that it's all because of the vacuum of space. There's nothing but clear stuff between us and the sun and the moon, is what you think the explanation is. If there was a haze between the Earth and the sun, maybe you could tell how far away it was, right?
Nah, it's just geometry.
The way we perceive depth in everyday life is through stereoscopic vision. Hold up a finger in front of you, look at it first with one eye, then with the other. The eyes have slightly different angles on the finger, so the finger seems to shift against the background. This is a simple example of what is called parallax. Our brain combines the two images into a single perception with depth of field.
This trick only works for things within a few yards of us. As we write this column, we easily perceive the three spatial dimensions around our desk, but as we look across the Why bunker, toward the tennis courts and the putting green, objects and shapes tend to become flattened out.
Fortunately a second clue kicks in, which is that we know how tall people are, how high the ceiling, etc., and we know that if we see a very small but normally proportioned human being it is probably someone far across the room and not a midget right in front of us.
But you see the problem with the sun and moon: They are not close, nor is their size obvious. So basically there's no way to tell where they are or even what they are (spheres? disks?).
Did ancient people think they could build a tower tall enough to reach the moon or sun? Did they shoot arrows at them and wonder why they never got there?
Actually it was always obvious that the sun and moon were far away. They didn't get larger when you climbed a tree or a mountain.
A couple of thousand years ago, the Greek astronomer Eratosthenes came up with an essential piece of cosmological information: The size of the Earth. He dug a well in what is now the Egyptian city of Aswan. One day a year, at the summer solstice, the sun would be directly overhead and shine on the water at the bottom of the well. That same day, Eratosthenes would measure the angle of the sun's rays on a stick far to the north in the city of Alexandria. Because he knew how far it was between Alexandria and Aswan, and because he knew geometry, he was able to calculate that the Earth was about 29,000 miles in circumference, which was a bit high but not a bad estimate.
If you know the size of the Earth, then it's possible to estimate the distance to the moon. The secret is to let the Earth's rotation assist your observation of the moon.
``You look at the moon when it's on the horizon and then you look at the moon when it's straight overhead, and you see that it's displaced by a degree with respect to the fixed stars,'' say Al Van Helden, author of ``Measuring The Universe.''
The moon, in other words, has parallax just like the finger held up in front of your face. You just have to wait a few hours (in 6 hours you will move a distance equal to one Earth radius) and do some fancy equations. The ancients were able to calculate that the moon was roughly 60 Earth radii away.
The sun's distance was much harder to figure. Ptolemy, the Alexandrian astronomer of the second century A.D. who created a cosmology that lasted until the Copernican revolution 13 centuries later, figured the sun was 1,200 Earth radii away. But that's only about 5 million miles. (What a dunce!)
In 1672, when astronomers were finally figuring out once and for all which objects orbited around which, an important experiment helped clear up matters. An astronomer in Paris recorded the position of Mars, as did an astronomer on the coast of South America. They compared notes, and spent years crunching the numbers. There was enough parallax to give them a sense of the distance to Mars.
Since the relative positions of the sun and planets were well understood by then (they correctly supposed that Mars was about 1.5 times as far from the sun as Earth), the astronomers were eventually able to extrapolate their data and come up with a pretty good estimate of the distance between the Earth and the sun.
Nowadays if you want to know precisely how far it is to the moon you can bounce a laser beam off a reflector left on the surface of the moon by the Apollo 11 astronauts. The speed of light is constant, so we can use light to calculate distance.
Better yet you could just look up the number in an encyclopedia.
Washington Post Writers Group
by CNB