Fall Sky 2003

Fixed Stars

If you want to know the distance to a tree somewhere down the street, one way to proceed would be to measure the diameter of a penny, in inches, and then give it to a friend who would stand next to the tree and hold up the penny. You would then measure the apparent diameter of the penny in radians. To find the distance to the tree in inches you would simply divide the diameter in inches by the apparent diameter in radians. This might not be the most convenient way to measure the distance to a tree, but it is the basis of almost every distance measurement in astronomy.

There are many examples of such measurements, but perhaps the most striking is the moving cluster parallax method. We discussed this in some detail two years ago in this column, where we pointed out that its only really successful application is to the Hyades. Readers wishing to view the Hyades during this quarter will have to stay up late, when it can be seen in the eastern sky, just to the west of Aldeberan. It is very large, but too diffuse to appear as a spectacular object. It is best viewed with the naked eye or with binoculars.

In order to measure the distance to the Hyades we need only know some real size (such as the diameter of the penny) and a corresponding apparent size. Sizes may not be easy to determine, but a real and apparent velocity will do just as well. These are readily available in the form of the velocity along the line of sight (in kilometers per second) and the proper motion (in arc seconds per year). The trick here is to relate these two quantities correctly, because they correspond to two different components of the same motion. We need to know the direction of motion of the cluster in space, but this is just the point toward which all of the stars seem to be converging in their motion across the sky. The angle between the directions to the cluster and to this convergent point is just the angle between the direction of the cluster motion and the line of sight. A little trigonometry is sufficient to solve the problem. The reader can try it for himself, using the data in the accompanying box. The weak point in the method is determining the convergent point, because the stars do not all move together, each having its own peculiar velocity. Thus they do not all move toward a single point, but rather toward a poorly determined region. Even worse, if the cluster is expanding or contracting, as it may well be, the convergent point will be shifted away from or toward, respectively, the position of the cluster. This kind of problem severely limits the usefulness of the method.

For the very nearest stars, the method of trigonometric parallax has always been preferred, in part because of its directness. In this case we use the orbit of the Earth around the Sun as our penny, but instead of having the orbit of the Earth moved out to the star (as we would carry the penny down to the tree), we would prefer to leave it where it is and travel out to the star ourselves, where we would measure the apparent size of the Earth's orbit. Since this travel is inconvenient and time-consuming, we prefer to stay on the Earth and simply measure the difference in the direction to the star from two opposite ends of the Earth's orbit. This must be a very precise measurement, and it is never easy. The greatest difficulty is establishing a fixed coordinate system in which to make the measurement. For this purpose, we use a background of stars, all of which we assume to be at a much greater distance than the star of interest. This is not always an adequate assumption, and correcting the measured parallax for the finite distance to the background stars is one of the greatest sources of uncertainty. Sometimes we even measure a negative parallax, which (formally) leads to the implausible conclusion that the star is not in front of the observer but behind his back! An additional complication is that all of the stars are moving in arbitrary ways. Fortunately these motions are constant with time, so that by extending our observations over several years, it is possible to eliminate this effect.

Data for the Hyades cluster

1) Average velocity of the stars along the line of sight = +20 km/sec.

2) Average apparent motion of the stars toward the convergent

point = 0.1 arc seconds per year.

3) Angle between the direction toward the cluster and the

direction toward the convergence point = 25 degrees.

The Hipparcos satellite, whose mission concluded 10 years ago, provided new and greatly improved trigonometric parallaxes for a large number of stars. These parallaxes have accuracies of about 0.001 arc seconds, far exceeding anything possible from the surface of the Earth. Thus the distance to a star at 100 parsec is accurate to 10 per cent, and the distance to the Hyades is more accurately known from trigonometric parallaxes than from the moving cluster method.

Two other closely related methods can be mentioned, although neither is of much practical use. We might assume that the stellar motions within a star cluster are randomly oriented, as they would be if the cluster were dynamically relaxed. Then the velocities along the line of sight, measured in km/sec, should be equal to those across the line of sight, measured in arc seconds per year. The distance calculation is then quite simple. Unfortunately, we usually cannot assume that open clusters are sufficiently relaxed for this method to give reliable results, and globular clusters are too distant for accurate measurement of the internal proper motions.

A group of closely related methods depend upon the solar peculiar motion, which is quite accurately known, in km/sec, with respect to the nearby stars. As long as the nearby stars move about randomly, we should see the solar motion reflected in their proper motions, provided we take the averages correctly. In this way we find no individual stellar distances, but we do find the average distance to a sample of stars. The method is limited, among other things, by the fact that outside a small local region, the motions of the stars are influenced by galactic rotation and are thus no longer random.

Astronomy is full of applications of the penny method of distance determination, and we shall no doubt mention some of them as we discuss various other objects in the night sky.

Planets

Mercury will be visible to northern observers in early October before sunrise and again in early December after sunset, but in both cases it will be very low in the sky and hard to find.

Venus becomes visible low in the southwestern evening sky during the second half of October. Its visibility improves slowly during the quarter, but it will remain very low in the sky.

After a magnificent opposition, at least as seen from the Oliver Observing Station, Mars will be moving into the evening sky, where it will remain very bright until almost the end of the year.

By the beginning of October Jupiter will already be visible in the eastern morning sky. Its visibility will improve during the quarter until, at the end of the year, it will rise before midnight.

Saturn, which has been visible for some time in the morning sky, will be stationary in Orion on October 26. Thereafter it will move, in retrograde motion, into Gemini and will reach opposition on December 31.

Meteor Showers

During the last few years, the Leonids have dominated the fall meteor calendar, and we have learned that predicting the strength of this shower is a very uncertain matter. The parent comet, 55P/Temple-Tuttle, is now well past perihelion, so we may expect to see the meteor rates return to normal levels. However, as we have seen, unexpected outbursts are always possible. The Leonids are best observed after midnight, but this year observations will be made difficult by the presence of a last quarter Moon in the direction of the radiant. The maximum should occur during the night of November 17-18.

The Geminids, which peak rather sharply on the night of December 13-14 and will be observable during the whole night, should be the strongest shower of the quarter. These, however, will also suffer from moonlight, the Moon being then a few days before last quarter.

The Draconids, peaking on October 8-9, will be lost in the full Moon this year. The Orionids, which show a very broad maximum around October 21, is more favorably located this year. The Taurids, which occur in two complex streams, should peak on November 5 and 12, when the Moon will be close to full. However, they may well be observable outside the period of full Moon. The alpha-Monocerotids, which peak on November 22-23, are usually quite sparse, but they do occasionally produce strong outbursts. the Moon is very favorable. Several minor showers in early December will all suffer from moonlight, but the last two showers of the year will again be well observable. These are the weak and diffuse Coma Berenicids, which peak on December 20 and last well into January, and the stronger Ursids, which peak on December

22-23. The latter show occasional bursts, which are worth looking for.

Comets

Currently almost all of the comet activity seems to be in the southern sky. The only northern comet of any promise is LINEAR (2002 T7), which is gradually brightening but still observable only with a moderate sized telescope. It will pass perihelion next spring, when it may become faintly visible to the naked eye.

Eclipses

A total solar eclipse on November 23 will be visible only from Antarctica, with the partial phase being observable from Australia and New Zealand.

Of more interest to local observers is the total lunar eclipse on the evening of November 8. This will be almost a repeat of the eclipse earlier this year, but it will be even less central, so totality will last only 25 minutes. For the same reason, there will be a strong gradient in illumination across the Moon during totality. At the time of moonrise we will almost have reached the total phase, so that twilight will seriously reduce our enjoyment of the event. In this respect the earlier eclipse was a little more favorable.