# 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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### 1 Answer

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:

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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