How far away in parsecs is the star Spica if its parallax is 0.0120”? How far away is Spica in light-years and in Astronomical Units (AU)?

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Tamara K. H. | Middle School Teacher | (Level 3) Educator Emeritus

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In astronomy, a parallax refers to the angular distance between a celestial body and the observation point at earth's surface. Since we see the celestial body up in the sky, we measure the distance by noting the body's angle of inclination ("Parallax"). It's also important to note that a star travels in an ellipse, which is made up of arcs, so the distance of the star is the measure of an arc. But, since the angular distances, or parallaxes, of stars are so small, astronomers find it easier to measure arcs in seconds rather than in typical degrees. A parallax of 1 second is the equivalent of 206,265 Astronomical Units (AU). An AU is equal to 149,597,871 kilometers; so, 206,256 AU is the equivalent of 3.1 x 10^16 meters. As the School of Astronomy and Space Science of Nanjing University in China states, "astronomers call this distance [3.1 x 10^16] 1 parsec (1 pc), from 'parallax in arc seconds'" ("17.1 The Distances to the Stars"; "Astronomical Unit"). In addition, a star at a distance of 1 parsec is at a distance of about 3.3 light-years away ("17.1 The Distances to the Stars").

According to the School of Astronomy and Space Science, if we know the star's parallax, we can easily calculate the star's distance in parsecs using the following equation:

distance (in parsecs) = 1/parallax (in arc seconds)

Therefore, to find the distance of Spica in parsecs, we complete the following calculation:

parsecs = 1/0.0120" = 83 parsecs

83 parsecs certainly approximately fits our known data about Spica. Astronomers have already calculated Spica to be at a distance of 80 parsecs (eSky, "Spica").

Plus, if we know that one parsec equals 3.3 light-years, we can simply take our calculation of parsecs and multiply it by 3.3 light-years, which yields 273 light-years, which again approximately matches our known data. Astronomers have calculated the distance of Spica to be 262 light-years away.

One should also note that if our calculations of parsecs and light-years do not match astronomer's data perfectly, it's because is parallax measurement of 0.0120” is not completely accurate.

Finally, if we also know that one parsec is the same as 206,265 AU, we can also calculate the AU by multiplying 83 parsecs by 206,265, which yields 17,119,995 AU.

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