2. STELLAR POSITIONS

Stars have three properties that are visible to the naked eye: position, brightness, and color. These properties are extrinsic, i.e., they depend not only on the properties of the actual star, but also on external conditions, such as the location of the observer. To understand stars, we must find ways to infer their intrinsic properties from these extrinsic properties. Intrinsic properties are properties that describe the star itself, independently of the observer, such as radius, luminosity, surface temperature, composition, and mass.

Let's start with position: the location of a star in the sky. Position is clearly an extrinsic property. If the Earth were located a few hundred light years away from its present position, all the constellations would be different. The positions of the brightest stars relative to each other would be totally different. In fact, we can see the positions of the nearby stars change. The motion is very slight -- the constellations look almost the same today as they did thousands of years ago. But with very accurate measurements, we can see the nearby stars move relative to the more distant stars by fractions of an arcsecond (denoted ") over timescales as short as a year. These apparent motions are the result of three actual motions: (1) the Earth's orbit around the Sun; (2) actual motion of the nearby stars through space; and (3) the actual motion of the Solar system through space.

The most important and useful kind of proper motion of nearby stars is that due the Earth's motion around the Sun. This motion causes the apparent positions of nearby stars to wobble back and forth annually [in circles if the star is toward the ecliptic poles (poles of the Earth's orbit), in straight lines if the star is in the ecliptic (equator of the Earth's orbit)]. The closer the star, the greater the angle of wobble, called parallax. (Precisely, parallax is half the total angle of wobble over a period of one year.) By measuring the parallax of a star, we can infer its distance.

Actually, parallax is a phenomenon that is familiar to all of you, although you may not have heard the name. It is illustrated in the animation above. As you drive along the highway, the nearby trees and buildings seem to move backwards faster than the distant mountains. In fact, the viewing angles of the nearby objects do sweep backwards much faster than those of the distant objects. In astronomy, the car speeding along the highway is replaced by the Earth speeding around the Sun. Since the Earth travels around the Sun in a circle instead of speeding along in a straight line, the angles of the nearby stars wobble back and forth once a year. For the Earth and stars, the principle is illustrated the animation below.

Or better yet, you can play with this Parallax Java Applet by the University of Washington.

Parallax angles are very small because the radius of the Earth's orbit is very small (< 10^-5 times) compared to the distance to the nearest star. In fact, the nearest bright star, a-Cen, has a parallax of 0.753". Such an angle is no greater than the size of the blurred stellar image seen through a telescope under conditions of very good seeing. Astronomers can actually locate the position of a star more accurately by measuring the average position of the center of the blur. That will give positions of the star that are accurate to about 0.01"; but that is about the limiting accuracy that can be achieved with ground-based telescopes.

A little trigonometry, explained here, gives the simple formula d = 1/p, where d stands for the distance of the star and p stands for the parallax angle of the star (measured in arcseconds). This formula works if the distance is measured in units called parsecs (pc). One parsec is equal to 3.24 light years, or 3.08 x 10¹⁶ meters. Therefore, the nearest star a -Cen, with p = 0.753", has a distance d = 1/(0.753) = 1.33 parsecs, or (1.33 x 3.24) = 4.3 light years from the solar system.

Since astronomers can measure parallax with an accuracy of about 0.01" from the ground, they can infer the distances of stars (with decreasing accuracy) out to about 100 pc. Here's a list of the 26 nearest stars. All are within a distance of 12 light-years.

As you will learn throughout this course, it's very important for astronomers to be able to measure the distances to more distant stars, galaxies, and other objects. They took a giant step in this direction with the launch of the Hipparcos satellite, built and operated from 1989 - 1993 by the European Space Agency. Above the blurring effect of the Earth's atmosphere, Hipparcos measured parallaxes with an accuracy of 0.001". With such accuracy, Hipparcos could measure the distances of stars out to about 1000 pc (or 1 kiloparsec, 1 kpc), or about 10 times better than could be done from the ground. The Hipparcos catalog contains some 120,000 stars.

Actually, you can think of the parallax method as a kind of binocular vision. You have depth perception because nearby objects in the image on the retina of your left eye are shifted a little to the right compared with the same objects in the image on the retina of your right eye. The part of your brain devoted to processing these images makes millions of calculations every second to combine these shifted images of objects and your mind that they actually come from nearby objects. You can think of two Hipparcos images of the sky taken 6 months apart as images from the left and right eyes. But in the case of the Hipparcos images, the "left eye" and the "right eye" are separated by the diameter of the Earth's orbit, or 2 AU.

The image shown above is a part of the sky containing the Big Dipper (Ursa Major) as seen by Hipparcos. It's actually a superposition of two images, one in blue and one in red, taken 6 months apart. The red image is taken when the Earth is to the right, so the nearby stars in the red Dipper are shifted to the left (by about 1 cm in this picture) compared to those in the blue Dipper, while more distant stars are shifted less. In these images the shift (or parallax angle) is exaggerated by a large factor to make it easy to see. With red-blue ("3-d") glasses (put the red over your left eye), you can actually see the amazing depth of this field of stars. It may take a while for the 3-d effect to come in. Your brain must solve many thousands of equations to create this image in your mind. You can find a few more of these fantastic images in the Hipparcos home page.  (The Hubble Space Telescope can also measure parallaxes with comparable accuracy, but Hubble has such a narrow field of view that it would take forever to compile a catalog with as many stars as there are in the Hipparcos catalog.)

In addition to parallax, the positions of nearby stars move because the stars themselves are actually moving relative to each other. These motions, called proper motions, and can be distinguished easily from parallax motions because they do not oscillate with a one-year period. They appear as a steady drift in a straight line that is combined with the oscillatory motion due to parallax to create a kind of loopy drift. If two stars have the same transverse (sideways) velocity, the nearer one will have a greater proper motion (i.e., will have a greater drift angle in a given time). The star with the greatest known proper motion is called Barnard's star. It has a proper motion of 10.31" per year, much greater than its parallax of 0.544", which implies that it is actually moving through space with a transverse velocity of about 90 km/s.

Even if all the nearby stars were stationary, they would have proper motions due to the Sun's actual motion. If the Sun were moving to the east, the nearby stars would appear to be moving toward the west (relative to the more distant stars). We can distinguish the apparent proper motions due to the Sun's actual motion from those due to the stars' actual motions because the Sun's motion will cause all the nearby stars to appear to be moving in the same direction, whereas those motions due to the stars' actual motions will have no such correlation.

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Last modified October 12, 2002
Copyright by Richard McCray