Caroline Grant, age 15, of Kingston,. Ontario, Canada, for her question:

What does parallax mean?

The parallax originated in geometry, progressed to land surveying and graduated to astronomy. It is a conundrum that starts with the base of a triangle and divulges where its two sides meet to form a parallax angle at the top. Surveyors use it to measure the curved surface of the earth. Astronomers use it to measure the earth's distance from a star.

We can measure an inch worm with a ruler and the trail of a snail with a tape measure. But the scope of the sky is boundless and ordinary earth units cannot cope with its cosmic dimensions. For this, we use large units and clever devices. One of these devices is parallax. This angle at the apex of an enormous celestial triangle can reveal the distance of a star.

A triangle, naturally, has three sides with an angle at each corner. When we know the length of its base line and its two angles, we can figure the rest of the triangle. After all, its two sides must slope up at those angles and at a certain distance meet at a certain point, the apex. If a triangle is short and stubby, the parallax angle at the tip is wide. A tall skinny triangle has a narrow angle at the apex. So the size of the paxallax angle reveals the distance from the base to the top of the triangle.

Let's select a likely star to be measured and construct our immense celestial triangle. The base line is the earth's distance from the sun, known to be about 93 million miles. To get the rest of the picture we photograph the star near a more remote star in the background. Now we wait six months and photograph the same scene again. Meantime the earth has swung around to the far side of its orbit. Our viewpoint has changed and created a slight change in the relative positions of the two stars.

You can see how this works with the help of a wall, two stamps and a pointing finger at the end of a stiff arm. Stick a stamp on the wall, the other on your pointing finger and step back. Close one eye and line up the two stamps, one in front of the other. Repeat, using the other eye. Now the stamp on the wall seems to have moved to one side, because your viewpoint has changed from one eye to the other eye.

This happens when our two stars are seen from two sides of the earth's orbit. To complete our celestial triangle, we use the first picture to construct a line from the earth through the first star to the second star. Then we do the same thing for the second picture, in which the relative positions of the stars is slightly different.

The two lines, angling from different viewpoints, converge on the first star and cross over to the second star. They meet at the first star and give us the parallax angle at the top of our celestial triangle. The size of the parallax angle reveals the distance of the star.

These celestial triangles are extremely tall and thin. No star is close enough to have a parallax angle of one degree. However, for mini angles, the degree is divided into 60 minute units and there are 60 second units in each minute. Alpha Centauri, the sun's closest neighbor, has a parallax of 0.760 seconds. This translates to a distance of 4.29 light years, which is roughly 27 million million earth miles. No wonder we needed such a big triangle.