Parallax

:This article is about parallax, the perspective shift. For the DC comic book character see Parallax (comics).

Stellar parallax

On an interstellar scale, parallax created by the different orbital positions of the Earth causes nearby stars to appear to move relative to the more distant stars. However, this effect is so small it is undetectable without extremely precise measurements.

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The annual parallax is defined as the difference in position of a star as seen from the Earth and Sun, i.e. the angle subtended at a star by the mean radius of the Earth's orbit around the Sun. Given two points on opposite ends of the orbit, the parallax is half the maximum parallactic shift evident from the star viewed from the two points. The parsec is the distance for which the annual parallax is 1 arcsecond. A parsec equals 3.26 light years.

Related Topics:
Parsec - Arcsecond

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The distance of an object (in parsecs) can be computed as the reciprocal of the parallax. For instance, the Hipparcos satellite measured the parallax of the nearest star, Proxima Centauri, as .77233 seconds of arc (±.00242"). Therefore, the distance is 1/0.772=1.29 parsecs or about 4.22 light years (±.01 ly).

Related Topics:
Reciprocal - Hipparcos - Proxima Centauri - Parsecs - Light years

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The angles involved in these calculations are very small. For example, .772 arcseconds is roughly the angle subtended by an object about 2 centimeters in diameter (roughly the size of a U.S. Penny) located about 5.3 kilometers away.

Related Topics:
Subtended - U.S. Penny

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Computation

The parallax p = rac {au} {d} cdot 180 cdot rac {3600} {pi} in arc seconds

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where

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: au = astronomical unit = Average distance from sun to earth = 1.4959 · 1011 m

Related Topics:
Astronomical unit - Sun - Earth

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: d = distance to the star

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Picking a good unit of measure will cancel the constants.

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Derivation:

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: right triangle

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: sin p = rac {au} {d}

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: small angle approximation

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: sin x ~= x extrm{ radians} = x cdot rac {180} {pi} extrm{ degrees} = x cdot 180 cdot rac {3600} {pi} arcseconds

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: parallax p ~= rac {au} {d} cdot 180 cdot rac{3600} {pi}

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: If the parallax is 1", then the distance is d = au cdot 180 cdot rac {3600} {pi} = 206264 au = 3.2616 lyr = 1 parsec (This defines the parsec)

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: The parallax p = rac {1} {d} arcseconds, when the distance is given in parsecs

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The fact that stellar parallax was so small that it was unobservable at the time was used as the main scientific argument against heliocentrism during the early modern age. It is clear from Euclid's geometry that the effect would be undetectable if the stars were far enough away; but for various reasons such a gigantic size seemed entirely implausible.

Related Topics:
Heliocentrism - Euclid's - Geometry

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Measurements of the annual parallax as the earth goes through its orbit was the first reliable way to determine the distances to the closest stars. This method was first successfully used by Friedrich Wilhelm Bessel in 1838 when he measured the distance to 61 Cygni, and it remains the standard for calibrating other measurement methods (after the size of the orbit of the earth is measured by radar reflection on other planets).

Related Topics:
Stars - Radar

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In 1989, a satellite called "Hipparcos" was launched with the main

Related Topics:
1989 - Hipparcos

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purpose of obtaining parallaxes and proper motions of nearby stars, increasing the reach of the method ten-fold. Even so, Hipparcos is only able to measure parallax angles for stars up to about 1,600 light-years away?a little bit more than one tenth the diameter of our galaxy.

Related Topics:
Proper motions - Our galaxy

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