PARALLAX

Hold your thumb at arms length in front of your face and look at it with one eye closed. Notice its placement with respect to the background. Now close that eye and open the other one, and look at the background. Notice that your thumb seems to change position against the background -- it appears to move across the background. This is because your eyes are a few centimeters apart from each other and have a different point of view. This is what gives you Stereo vision that lets you judge the distance of an object. The angle the object appears to move from eye to eye gives a measure of its distance. You are automatically triangulating its position.

Astronomers use the same principle to calculate the distances to the nearer stars. Their method is called Trigonometric Parallax.

Most stars are so far away that they never appear to move when viewed from the Earth. Astronomers use these far stars as a fixed background. Repeat the thumb experiment, but move if closer to your face. Notice that the closer your thumb is to your eyes, the farther it appears to shift in the background. Even the nearest stars are so far away that astronomers can only measure a very small shift in the closest stars.

To be able to measure the biggest angular displacement, we want to observe the star from two places that are as far from each other as possible. For us on the Earth, this is when the Earth is on opposite sides of the sun. Therefore, the measurements are taken 6 months apart, on the opposite sides of our orbit around the sun. We observe the position of the star with respect to the fixed background stars, and then again in 6 months.

The distance from the Earth to the sun is defined by astronomers as an Astronomical Unit (A.U.). So the distance between measurement is 2 A.U. in length. Half the angle the star appears to move in the sky between the two measurements (or angle shifted for one for 1 A.U.) is called the PARALLAX. We define this as the parallax because it is part of a Right triangle -- if we measure the parallax angle at the proper place in the Earth’s orbit. [See picture.] We know an angle (the parallax), and the length of one side (1 A.U.) -- thus, have enough information to solve the third angle and the other triangle lengths. The length of the hypotenuse, in this case, gives us the distance to that star.

1 A.U. = 149,597,870,000 meters = 149,597,870 kilometers = 490,830,611,500 feet = 92,960,343 miles or about 93 million miles.

A star's parallax is measured in arc seconds, where 1 arc second = 0.00027 of a degree!! The nearest star to use is Proxima Centauri, which has a parallax of about 0.75 arc seconds. This is the angle subtended by a dime at a distance of 2 kilometers! This is why astronomers can only measure the distance of very close stars, using parallax, only as far as 300 light years -- which is less than 1 percent the diameter of our galaxy, the Milky Way. Of course, very close is very, very relative!! Very close in astronomical terms.

Astronomers commonly use, as a unit of measure, a PARSEC (pc). A parsec is the distance at which 1 A.U. subtends 1 arc second -- 1 parsec = 3.26 light years or 30,970,000,000,000,000 meters. Where 1 light year is the distance light can travel in one years time or about 9,500,000,000,000 kilometers.

Close Stars

Star Parallax (arc seconds) Distance (pc)
Proxima Centauri 0.772 1.3
Barnard’s Star 0.542 1.8
Wolf 359 0.421 2.38
Sirius 0.377 2.65


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