Parallax Angles are Small

The parallax angle is so small that it is difficult to measure, except in the closest stars. As an example, the nearby star 61 Cyg was the first star to have its parallax measured (in 1838). It has a parallax angle of only 0.286 seconds of arc. This is about as large as the apparent size of your thumbnail seen from a distance of 15 kilometers! Most other stars have much smaller parallax angles.

The Parallax Method

Measuring distances is one of the most important, and often most difficult, tasks in astronomy. Several methods can be used, but only a few yield the distance in a relatively simple way. We shall discuss the most reliable method where it can be used, that of parallax, in this section. Other less direct methods will be discussed later.

The Parallax Angle
The parallax method requires determining a very small angle called the parallax angle. The parallax angle p is illustrated in the following figure (which is not drawn to scale; realistic parallax angles are far too small to be shown in a diagram like this because the stars are so far away compared with the size of Earth's orbit).

The angle p corresponds to a small shift in apparent position on the celestial sphere because of the differing vantage points as the Earth moves around its orbit.

From Parallax Angle to Distance
If the parallax angle can be measured reliably, the distance can then be determined from simple trigonometry. This animation illustrates the parallax method for determining distances and here is a parallax-distance calculator that permits you to determine distances from parallax angles in a simple way.

Parallax Limitations
The parallax angle is small because stars are far away. Only for the more nearby stars can it be measured reliably. Ground-based telescopes can measure parallax for stars within a few hundred light years. The best ground resolution is about 0.5", and even averaging over many measurements only reduces it to about 0.01". This corresponds to a distance of about 300 light years (a light year being the distance light travels in a year). Telescopes above the atmosphere can measure smaller parallax shifts and hence larger distances. But even then the most distant objects for which distance can be determined by parallax are a few thousand light years away.

Precision

Sometimes science advances on the basis of qualitatively new ideas, but sometimes it advances because previously known quantities are measured with unprecedented precision. The distance of the nearest stars is now known with an uncertainty of only about 0.2-0.3 percent because of Hipparcos parallax measurements. As noted in the main text, this higher precision has a number of implications for our understanding of the Universe.

The Hipparcos Satellite
The European Space Agency's Hipparcos satellite, which was launched in 1989 and operated until 1993, gave greatly improved stellar parallax measurements. This satellite was an orbiting telescope with a relatively small 29 cm diameter mirror. It measured position, stellar motion, and parallax for over 120,000 stars (the "main mission"), as well as providing less precise information on over a million additional stars (the extended "Tycho experiment"), and identified many new variable stars and binary star systems. To set this in perspective, the parallax angles were known well for fewer than 1000 stars before the Hipparcos mission.

Precise Astrometry
Since parallax angles are so small, it is the precision of the Hipparcos measurements that makes them so useful. Uncertainties in Hipparcos stellar parallax measurements are as small as 0.001 arc seconds, which is comparable to the angular size of a golf ball viewed across the Atlantic Ocean! The part of astronomy that deals with making precise measurements of quantities such as distance, motion, and light output of the stars is called astrometry. The importance of such precision astrometry to our understanding is discussed in the box and below.

Implications of the Hipparcos Mission
The impact of the precise new Hipparcos data is continuing, but we may summarize several implications that have already become apparent.

  • Precise measurement of local distances serves as a calibration of all distance scales in astronomy. Hipparcos measurements led to a recalibration of the distance scale set by Cepheid variables (see the later chapter on variable stars). This has led in turn to a firmer foundation for the entire distance scale of astronomy, not just the part measured directly by Hipparcos.
  • As a result of the recalibration of distance scales, some distances in astronomy have changed significantly from their previously accepted values. For example, the distance to the Large Magellanic Cloud, a small galaxy very near our own, is now thought to be 10 percent larger than it was thought to be before Hipparcos. On the other hand, the distance to the Pleiades star cluster has been revised downward by 10 percent based on Hipparcos observations. These distance changes have in turn had an impact on our theoretical understanding. For example, if the Pleiades cluster is 10 percent closer than previously thought, the luminosity of stars in the cluster is 20 percent lower than previously thought. Theories of stellar evolution (how stars evolve over time) are presently having difficulty explaining the luminosity of stars in the Pleiades as revised by the Hipparcos data.
  • Based on the new data, the observable Universe appears to be somewhat larger than previously thought. This has in turn increased the estimated age of the Universe by about a billion years (about a 10 percent increase).
  • The Hipparcos data have been used to revise the colors (which are related to surface temperatures) and the luminosities of many relatively nearby stars. This has in turn suggested that the oldest stars are not as old as previously thought by as much as 4 billion years (see the later discussion of the Hertzsprung-Russell diagram and stellar evolution). One important implication of this, and the larger age for the Universe noted above, is that it helps to resolve an earlier puzzle that some stars were estimated to be older than the Universe itself (an obvious logical contradiction). Although it is not yet certain that the problem is completely resolved, the Hipparcos data have certainly removed a significant part of the discrepancy.

    • We shall discuss some of these issues in more detail later, but this list gives a sample of the implications that precise distance measurements can have in astronomy.