A Lunar Occultation

On the night of Sunday, March 9th, 2003, the Moon will pass in front of the star kappa¹ Tau. Observing this event will yield information useful in determining the Moon's distance; it will also provide some dramatic, if indirect, evidence on the distances of stars.


An occultation occurs when a nearby celestial object passes in front of a more distant one and completely hides it from view. In a lunar occultation, the Moon passes in front of a star or planet. Lunar occultations of faint stars occur all the time, but such events are hard to observe because the Moon's light swamps fainter objects. On March 9th, 2003, between 22:25 (10:25 pm) and 22:30 (10:30 pm), observers in Hawaii will see the Moon occult kappa¹ Tau, a 4th magnitude star in the constellation of Taurus. This is the best and most easily observed occultation visible from Hawaii this semester.

Shown below are simulated images of the Moon and stars in Taurus on March 9th, 2003. At that time, the Moon is still a few days short of first quarter, but already bright enough to obscure all but the brightest stars. In these images, kappa¹ Tau appears just above the Moon; it will not be visible to the unaided eye, but you should have no trouble seeing it with binoculars.

Simulated views of the Moon and stars in Taurus on 03/09/03, 22:00, produced using Celestia. kappa¹ Tau is the star just above the moon. Left: wide-field view including the Hyades and the Pleiades; the faintest stars are 5th magnitude. Right: view through 10×50 binoculars; the faintest stars are 6th magnitude.

THE OBSERVATION

To watch this occultation, you need an observing site with a good view toward the West. Find a site where you can watch comfortably until at least 22:30 (10:30 pm). You will need binoculars to see kappa¹ Tau with the Moon so close in the sky. Also bring a watch, set as accurately as possible, and the chart included with this handout.

IMPORTANT: If you are going to be on another island on Sunday night, please let me know. Predicted times differ by a few minutes on the neighbor islands.

If possible, begin looking at about 21:30 (9:30 pm). At that time you should see kappa¹ Tau above the Moon; the angular separation between them will be about equal to the Moon's angular diameter, which is 0.5°. (Note: the angular diameter of an object is just the angular separation between opposite sides of the object; thus the angle from your eye to the left and right sides of the Moon is 0.5°.) As the Moon moves eastward in its orbit, its dark side will advance toward kappa¹ Tau and eventually pass in front of the star. When this happens, the star's light will be cut off in an instant. Your main objective is to be looking at the star at that moment!

Depending on conditions, you may be able to see a fainter star just to the left of kappa¹ Tau. This fainter star is kappa² Tau. Together, these two stars form an optical double: a pair of stars which appear close together but are not actually orbiting each other. Both of these stars are outlying members of the Hyades star cluster. If kappa² Tau is visible, you will see it disappear behind the Moon a few minutes before kappa¹ Tau does.

There are two different measurements we want you to make:

  1. At about 22:15 (10:15 pm), draw the Moon on the chart included with this handout. Try to show the Moon's position with respect to kappa¹ Tau and other stars as accurately as possible. The Moon's angular diameter of 0.5° corresponds to 1 cm on the scale of this chart, so draw the entire disk of the Moon as a circle 1 cm in diameter, and shade in the illuminated part to indicate the direction of sunlight.

  2. When you see kappa¹ Tau disappear behind the Moon, start counting seconds, and look at your watch as soon as you are sure the star is really gone. Subtract the number of seconds you counted from the reading on your watch to get an accurate time for the star's disappearance. (If you can see kappa² Tau, try to measure its time of disappearance as well.)

Please be sure to record your observing location along with the times you measure. Observers in different places will see the star disappear at different times as the Moon's shadow sweeps across the island. If enough people can make accurate timings, we can estimate the speed of the Moon's shadow. To set your watch accurately, call 983-3211.

Advanced options

If you have a camcorder with high-sensitivity chip, you may be able to make a video of the occultation. Put the camcorder on a tripod or rest it against something to hold it steady, and zoom in as close as you can. Remember that the Moon will be setting, so start with the Moon towards the top of the frame; it will slowly drift down the frame, but you won't have to interrupt your observations to track the camcorder. Begin shooting at around 22:20 (10:20 pm), or just after you complete your plot of the Moon's position. If everything works, you'll have a permanent record of the occultation.

In timing occultations, accuracy is the name of the game. As emphasized above, you should be sure to set your watch as accurately as possible. If you have a stopwatch, you can start it at 22:25:00 (10:25 pm exactly), and stop it the instant you see the star disappear. For even more accurate timings, you could use a short-wave radio tuned to WWV (2.5, 5, 10, 15, or 20 MHz).

If the sky is clear to the West and you don't have to get up early on Monday (yeah, sure), you can watch kappa¹ Tau reappear after the Moon passes. This will happen almost exactly one hour after the star disappears; it won't be as dramatic since the star reappears from behind the bright side of the Moon.

INSTANTANEOUS DISAPPEARANCE?

Just how fast is kappa¹ Tau's light cut off by the edge of the Moon? If the star was close enough to appear as a disk, and not just a point of light, you'd see it fade out gradually as the Moon drifts across. In fact, the star will wink out extremely fast - you will not be able to notice any gradual dimming.

We can use this fact to make a very rough estimate of the distance to kappa¹ Tau. Let's say the star takes 0.1 seconds to fade out (this is about the shortest time human beings can perceive). Let's also say that kappa¹ Tau has the same diameter as our Sun, which is 1.4×106 km. These are the only assumptions used in this estimate; neither is very accurate, but they are OK for a very rough answer. In particular, they will serve to find the smallest distance the star could possibly have.

As seen from Earth, the Moon moves with respect to the stars at a rate of 0.00015° per second (360° per 27.3 days); in other words, each second it's position changes by 0.00015°. So if kappa¹ Tau takes 0.1 seconds to fade out it must have an angular diameter which is one-tenth of this angle, or just 0.000015°. (This is about 20 times smaller than anything we can expect to see as a disk with our telescopes; in fact, even the most powerful telescopes have trouble seeing detail that small!) Now we know how big the star really is, and we know how big it appears to be, so we should be able to work out its distance. The equation required is the same one we used for parallax distances:

Here we use our estimate of kappa¹ Tau's actual diameter (1.4×106 km) for the baseline b, and our estimate of the star's angular diameter (0.000015°) for the angle . The result for the star's distance D is about 5.3×1012 km, or 0.55 l.y. (light-years); remember that this is the smallest possible distance, and the actual distance can be much greater. In fact, the actual distance to kappa¹ Tau is about 153 l.y., so our simple estimate is about 300 times too small. Still, this is at least a rough figure for the distance to a star; it's pretty good for an estimate made using nothing more than a pair of binoculars!

WEB RESOURCES

REVIEW QUESTIONS

REPORT: A LUNAR OCCULTATION

Make the observations described above, and write a report on your work. This report should include, in order,

  1. a general motivation for the observations,
  2. a description of the observing site and equipment you used,
  3. a summary of your observations, and
  4. the conclusions you have reached.

In more detail, here are several things you should be sure to do in your lab report:

This report is due in class on March 18. If you have a previous commitment and are unable to observe, please talk to me about an alternate assignment.


Joshua E. Barnes (barnes@ifa.hawaii.edu)

Last modified: March 4, 2003
http://www.ifa.hawaii.edu/~barnes/ASTR110L_S03/lunaroccultation.html