Cepheid Variable Stars

Materials:

Cepheid Variable Star Special Effect
Version I 

This is the simplest option. For a portable planetarium, make a paper mask that will block all the stars except for Sirius (the brightest star) on the star projector. Sirius becomes the variable star whose brightness is controlled by the main star bulb brightness knob. For Cepheid variable star A, vary the brightness between “maximum brightness” and “very dim” in a cycle about once every 5 seconds. For Cepheid variable star B, vary the brightness between “half-maximum brightness” and “very dim” about once per second. Cepheid variable star C varies between “very dim” and “half-maximum brightness” once every 5 seconds (same brightness as B, but same pulse rate as A).

A single variable star projector can be used to simulate all three types of variable stars needed in the program. However, it is better to have the capability of showing simultaneously variable stars with different brightnesses and pulsing rates. If you do not happen to own two STARLAB projectors, the following versions are fairly easy to implement.

Cepheid Variable Star Special Effect
Version II 

This is a simple variable brightness dot projector design. You can make two or three of them very inexpensively.

At an electronics store, purchase: 

Two switches (On/off—not momentary contact)

Two potentiometers (under 20-30 ohms maximum resistance)

A meter or two of light weight electrical wire (about 24 gauge—more wire is required if you plan to put one light in the dome.)

Two integrated circuit sockets to serve as sockets for the Mini-Mag Lite® bulbs (8 or 14 pin sockets are common)

2 “D” cells and battery holder, or a  3V “battery eliminator” power supply

You also need 

Two small hand lenses (Longer focal lengths give better pinpoint appearance of star; larger diameter makes brighter star.) 

Two small cardboard boxes with removable lids (such as a box for storing slides, at least 3 cm tall), or two cardboard tubes

Two Mini-Mag Lite® bulbs  

Assemble the parts as shown in Fig. 1 (p. 6). Each projector can be manually operated (by varying the potentiometer) for the effect needed to produce Cepheid variable stars A, B, or C. 

You will need practice to make a Cepheid variable A that is brighter and slower than a Cepheid variable B (as described in version I). For Cepheid variable C, you need to operate one projector so that it is as fast as A, but as dim as B. 

The projector box or tube may point straight up at the zenith or can be mounted to point in any direction by:

a. Punching a hole in the side of the box; and 

b. Attaching it to a somewhat larger box with a paper fastener or nut and bolt (Fig. 2, p. 6).

Cepheid Variable Star Special Effect Version III

For this version you need to be able to solder and to put together a simple digital circuit on a breadboard. You will need the following parts from an electronics parts store (such as Radio Shack):

A breadboard (#350 Experimenter works well)

A meter or two of speaker wire, two-conductor, stranded, insulated, about 20 gauge (More wire is required if you plan to put one light in the dome.)

Parts for the circuit shown in Fig. 3:

(3) 555 integrated circuit chips

(3) Capacitors, electrolytic, 47 microfarad

(3) Resistors, 1000 ohm, 1/4 watt

(2) Resistors, 18 kilohms, 1/4 watt

(2) Resistors, 10 ohms, 1/4 watt

(1) Resistor, 6800 ohms, 1/4 watt

(1) Resistor, 3.9 ohm, 1/2 watt

(15) jumper wires, about an inch long, 22 gauge, solid, insulated, ends stripped

(3) Switches, single pole, single throw (On/off—not momentary contact)

(1) 5–6 volt power supply, battery eliminator, or a 4-cell battery holder and four D-cells

A soldering iron and solder

Three Mini-Mag Lite® flashlight lamps (3V; available from stores that sell Mag Lite® flashlights such as hardware or camping supply stores, or from Mag Instrument, Inc., 1635 S. Sacramento Ave., Ontario, CA 91716)

Two thin short dowels, 0.5 cm. (1/4”) thick (or less) x 15 cm. (6”) long, or two standard size pencils

One long dowel, same thickness as dowels above, 1–2 meters (3’-6’) long

Three blocks of wood or Styrofoam, about 8 cm. x 8 cm. x 3 cm.
(3” x 3” x 1”)

A drill and a drill bit the same diameter as the above dowels if you use wood blocks

A small box of cardboard or very thin wood on which to mount the circuit board and switches.

To make three Cepheid variable stars with the required brightnesses and pulsing rates, construct the three simple flasher circuits (Fig. 3). For Cepheid variable star A, that is a bright light flashing about once every two or three seconds, use the following values of resistors and capacitors: 

C1 = 47 microfarad C2 = 25,000 microfarad

R1 = 1,000 ohm R2 = 18,000 ohm

R3 = 10 ohm R4 = 10 ohm

For Cepheid variable star B, that is a dimmer light flashing about once every second, use the following values of resistors and capacitors:

C1 = 47 microfarad C2 = 5,000 microfarad

R1 = 1,000 ohm R2 = 6,800 ohm

R3 = 20 ohm R4 = 20 ohm

These two flashing lights are placed within several centimeters of each other and represent two different Cepheid variables at a standard distance for comparison of their absolute magnitudes. 

For Variable star C, that is as dim as B, but flashing at the rate of A, using the following values:

C1 = 47 microfarad C2 = 25,000 microfarad

R1 = 1,000 ohm R2 = 18,000 ohm

R3 = 20 ohm R4 = 20 ohm

 Cepheid variable C is placed in the dome much higher than the other two lights. This represents a Cepheid variable that the audience can conclude has absolute brightness the same as that of A (since it flashes at the same rate as A), but has a fainter apparent brightness, indicating it must be farther away
than A.

To build the projectors, 

a. Construct the three circuits (Figure 3) using the component values given above. All three circuits can be built using only one breadboard
(Figure 2).

b. Cut three lengths of speaker wire. Two of them should be about 10 cm longer than the short dowels and the third should be about 10 cm longer than the long dowel.

c. Strip the ends of speaker wires and solder a Mini-Mag Lite® onto one end of each wire. Solder jumper wires to the other ends (6 jumper wires total) to allow easy insertion into the breadboard. 

d. Tie each speaker wire onto its respective dowel and connect the jumper wire ends to the appropriate points in the circuit.

e. Stick the dowels into the blocks of Styrofoam. If you use wood blocks, which are sturdier, drill a hole in each block that the dowels can fit into snugly.

f. Attach the circuit and the three switches to the box. 

Figure 2 shows what the result might look like. Of course, your construction will bear your own personal touches.

7. Slides

A complete list of the slides is on page 8.

8. Slide Projector(s)

Image 12, Zenith Angle Circles must be projected at the zenith. This can be accomplished by putting a mirror (about 8 cm x 14 cm) at a 45° angle in front of the slide projector lens. The image must also be adjusted so that it measures degrees. Adjustment can be by changing the projection distance or with a zoom lens. Compare with a meridian scale to adjust properly. 

Images 1-9 and 13-22 are best projected at the zenith, while images 10-12 have a “right-side-up” orientation to them which makes it best to project them nearer the horizon. You may have separate projector(s) for those slides, or keep all slides in one projector and remove the zenith mirror when you want to project near the horizon.







Presenter's Script:



We can measure apparent brightness of a star and still not know how far away the star is. Remember that the farther away a star is, the dimmer it looks. If we had a set of “standard 20 watt light bulbs” scattered around the universe, we could tell how far away they were by seeing how dim they appeared. The dimmest would be farthest away.
But how do we know if a star is bright because it is close, or bright because it really is a “40 watt star?” Some stars are inherently brighter than others. The inherent brightness of a star is called its absolute brightness (or absolute magnitude).
The absolute brightness of a star is what its brightness would be if it was viewed at a standard distance.
Of course stars, like the Sun, are much brighter than 20 watt light bulbs. But it just so happens that there are certain kinds of stars that are especially useful in determining brightness in an absolute sense. There are many stars that pulsate in brightness over periods of time. They are called variable stars.
In the early part of this century, astronomer Henrietta Swan Leavitt discovered a characteristic of a very special kind of variable star that has become a crucial “yardstick” for measuring distances to very distant stars. The type of variable star whose behavior she studied is called a Cepheid variable star, because the first one was found in the constellation Cepheus. It is a kind of star that tells us how much light it puts out (sort of like how many watts it is).
Optional: point out Cepheus.
Let’s look at two Cepheid variable stars to see how they are special. To make things simpler, let’s say that these two Cepheid variable stars are very nearby, and exactly the same distance away from us.
Create the effect of Cepheid variable A and Cepheid variable B, preferably going side by side. A should appear at least twice as bright and twice as slow as B.
Cepheid A should peak at magnitude 1,  about the brightness of Vega..
What is the difference between these two Cepheid variable stars? [Call the brighter one Cepheid variable A and the dimmer one Cepheid variable B. The  dimmer one is pulsing faster than the other.]


Background
The standard distance of a star to see its absolute magnitude is 32.5 light-years = 10 parsecs.  The unit, parsec, derives from the idea of parallax measurements: a parsec is the distance at which a star would exhibit one arc-second of parallax.


Optional: for Older Students
Quantitative Measurements of Cepheid Variables
Let’s measure the pulsing rate of Cepheid variable A. Its period is how long it takes to go from maximum brightness to maximum brightness. We are observing the variable star in accelerated time: each second in our planetarium is about 10 days of real time.
Please count silently how many pulses occur while I time 100 days of real time. Ready? Set. Count.
Wait until the fifth flash.
Stop! How many pulses were there? [5.] If there were five pulses in 100 days, how long did each pulse last? [20 days.]
So the period of this Cepheid variable star is 20 days.
Now let’s look at Cepheid variable star B.
Please count how many pulses occur while I again time 100 days of real time. Ready? Set. Count.
Wait until the tenth flash.
Stop! How many pulses were there? [10.] If there were ten pulses in 100 days, how long did each pulse last? [10 days.]
So the period of this Cepheid variable star is 10 days. As you can see, the period is related to the brightness.
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