## Distances To Nearby Stars

The huge, fiery stars are really trillions of kilometers beyond our atmosphere. The difficult problem of ascertaining the actual distances to the stars has challenged astronomers for centuries.

The method of parallax is used in measuring the distances to nearby stars. The position of a star is carefully determined relative to other stars. Six months later, when Earth's revolution has carried telescopes halfway around the Sun, the star's position is measured again.

Nearby stars appear to shift back and forth relative to more distant stars as Earth revolves around the Sun. The apparent change in a star's position observed when the star is sighted from opposite sides of Earth's orbit is called stellar parallax. The distance to the star is calculated from its parallax angle, which is one half of the apparent change in the star's angular position (Figure 3.1).

Stellar parallaxes are very small and are measured in seconds of arc ("), where 1" = 1/3600°. An aspirin tablet would appear to have a diameter of 1" if it were viewed from a distance of about 2 km (a mile)! The parallaxes of even the nearest stars are less than 1" (Appendix 5).

One parsec (pc), is the distance to an imaginary star whose parallax is 1 second of arc (1"). One parsec equals about 31 trillion km (19 trillion miles), or 3.26 light-years.

To calculate the distance to any star from its measured parallax, use the formula:

Star's distance (in pc)

parallax (")

Parallax Apparent

angle change @ star first

• distant stars

Figure 3.1. Stellar parallax. A nearby star that is sighted from opposite sides of Earth's orbit appears to shift its position from 1 to 2 against a background of distant stars. (The actual parallax angle is extremely tiny.)

Stellar parallax decreases with the distance of a star. Stellar parallaxes can be measured down to about 0".01, corresponding to a distance of 100 pc. Only a small fraction of the stars are within this distance or have accurately measured parallaxes.

The European High Precision Parallax Collecting Satellite, or Hipparcos, an astrometry spacecraft (1989-1993) measured the positions, parallaxes and motions of 118,000 stars precisely and of another 2 million stars less exactly. Its name honors Hipparchus (Section 1.7), who calculated the Moon's distance from Earth in 120 b.c. by measuring the Moon's parallax. The Hipparcos Star Catalog of star data and subsequent Tycho-2 catalog list voluminous data.

Other indirect methods must be used to determine the distances to the great majority of stars beyond 100 pc.

Would you like to know what "close" means for a star? Refer to Figure 3.2. If the measured parallax for Alpha Centauri is 0".74, then its distance from Earth is 1.35 pc, or 4.4 light-years, which is about 40 trillion km (25 trillion miles). (Alpha Centauri is actually a double star and, with faint Proxima Centauri—the night star closest to us—a member of a triple star system.)

If the measured parallax of Sirius is 0".38, what is its distance from Earth in (a)

parsecs?_(b) light-years?_(c) kilometers or miles

(approximate)?_

Answer: (a) 2.6 pc; (b) 8.6 ly; (c) 81 trillion km or 50 trillion miles.

Solution:

km pc miles

(a) 0".38 ; (b) (2.6 pc) x 3.26 pc (c) (2.6 pc) x 31 trillion pc

June 21

Alpha Centauri (Closest visible star, southern hemisphere)

Sirius

(Closest star seen from mldlatltudes of nothern hemisphere)

June 21

Alpha Centauri (Closest visible star, southern hemisphere)

December 21

Figure 3.2. Using the parallax method to determine the distances to our closest bright neighbor stars.

December 21

Figure 3.2. Using the parallax method to determine the distances to our closest bright neighbor stars.