Labs from YSI 95:
How Bright are the Stars?

This is the staff copy of the lab and other brainstorming/reflections.

Teacher's Guide:

Materials:

• small telescope (we used a Celestron 8 inch)
• photoelectric photometer (optional--the activity can be done using only visual photometry to measure apparent brightnesses of the stars)
• pens or pencils
• flashlights with red filters
• Finder charts and data sheets (included in this file)
• cardboard with various sized pin holes (in case of cloudy weather)
• "pointer" flashlight (very bright, well-focused flashlight that can be used to point to stars in the night sky)

Outline of Class

• We'll start the activity indoors, during twilight. Ask the students to recall what they noticed in looking at the sky on previous nights: Do all the stars look to be about the same brightness? (If necessary, remind them that the sun is also a star!) Encourage them to think about what happens at your eye, to make one star look brighter than another. Lead into understanding that something looks brighter if more light is hitting the surface of your eye. (The cloudy weather demo, where it's obvious that the larger hole appears brighter because more light is getting through the larger hole, is a good way to illustrate this). Introduce concept of apparent brightness as a measure of how much light hits a detector (in this case your eye) of a certain surface area in a certain amount of time. Discuss importance of referring to a fixed surface area. Point out that if the collector is made bigger, more light is gathered, so the object will appear brighter. (This is why bigger telescopes are generally better: they can collect more light.) This is also a good point to challenge students to use what they've learned so far to come up with an explanation of the inverse square law for apparent brightness. (The same amount of light is spread out over a larger area as you go farther away, so less of it hits the fixed area of your eye)

  Summarize: the apparent brightness is amount of light received per unit area per unit time.

  (now hand out student packets)

• Make connection with daytime activity on the solar constant. What did we learn earlier today that light is a form of? (energy) And what were the units of the energy flux we measured? (the "solar constant": energy/time/area). Lead them to see connection that apparent brightness is also a measure of an energy flux. So measuring the apparent brightness of stars is another way to measure the amount of energy we receive from them, just as the experiment we did this afternoon was a way to measure this energy from the sun. We now have 2 different methods for measuring the same thing: the flux of energy carried by starlight.

• Introduce magnitude system: Ancient astronomers classified stars on the basis of their apparent brightness. The "magnitude" system in use today originated around the 4th century BC. They grouped the brightest stars together as stars of the "first magnitude," the next brightest as stars of the "second magnitude", etc., on down to "6th magnitude", the faintest you can see with the unaided eye, under a very clear, dark sky. Note that the brightest stars were given the smallest number, in the same way that we talk about "first class" as the best (brightest), then "second class" and "third class." In order to make the system more accurate and to accomodate the fainter stars we can see with modern telescopes, the system has been extended and standardized. Each star is assigned a precise magnitude value. The history of this system has made it very confusing, because the brightest stars have the smallest magnitude values (some are even negative!) while the biggest numbers are assigned to the very dimmest stars.

  The system is also confusing because our eyes register ratios of brightness rather than differences in brightness. Every time you increase by one magnitude on the scale, the brightness is multiplied by 2.512. Increasing by 2 magnitudes means the brightness increases by 2.512 x 2.512 = 6.3, etc. Here's an example to help understand this system better:

  Vega is one of the brightest stars you can see in the sky tonight. On the magnitude scale we've just been talking about, it has an apparent magnitude of + 0.04. By comparison, the sun has an apparent magnitude of -26.7. This means that the sun is about 27 magnitudes brighter than Vega. So to figure out how many times brighter then sun appears than Vega, we have to take 2.512 multiplied by itself 27 times, or 2.512 to the 27th power, which is about 6 x 10^10. In other words, the sun is about 60 billion times brighter than Vega, as viewed from the earth! If there were 60 billion stars in the sky as bright as Vega, then the nighttime sky would be just as bright as the daytime sky. So based on our results from earlier today, we can figure out how much the temperature of our water would have been raised, if we had used only the energy of the light from Vega.

  (Have the students work through this, using their own data, to see what the temperature change would be. Might also figure out how large the collector area would have to be (for the same amount of water), to raise the water temperature by the same amount; this would help get across idea that it's energy per unit area that you get when measuring brightness)

• Visual photometry (outside): First just have the students rank order the stars by brightness using visual comparison. They might find it helpful to use the telescope and de-focus the images of the stars. Here are the standard V magnitudes for the stars (this choice of stars, and the V magnitudes for them, were obtained from "Introductory Astronomy Exercises," by Dale C. Ferguson, p. 167):

  alpha Cygni:        1.26
  
  pi Herculis:         3.15
  
  gamma Aquilae:     2.62
  
  alpha Aquilae:      0.77
  
  alpha Lyrae:        0.04
  
  theta Lyrae:        4.35
  

  Photoelectric photometer: just as your eyes convert amount of light hitting them into some kind of signal in your brain, photometer converts to current, which we read out. This makes it more objective and generally much more accurate for comparing brightnesses of stars than our eyes.

• Take readings of each star with the photometer, have students record the values on their worksheets. Experiment with best exposure time, aperture size, etc.

• Go back inside, check whether order of brightness matches with what they found visually. If there is time, convert readings to magnitude scale, using 1 star with known brightness as reference.

• Discuss possible sources of error, go back and do photometry with background measurements if time.

Student Worksheet

The apparent brightness of a star is just how bright that star appears to be. Our eyes can do a pretty good job of ordering stars by brightness. Early sky-watchers developed a system for classifying stars on the basis of how bright they looked. The brightest stars were referred to as stars of the "first magnitude," the next brightest were "second magnitude," and so on down the line. This classification system has evolved into the very precise magnitude system that astronomers use today. It assigns a specific magnitude number to each star, indicating how bright it is. The smaller the magnitude, the brighter the star. For example, the sun is very bright at magnitude -26.7, while the bright star Vega is +0.04.

Using what we've talked about in class, and your results from the daytime lab, how much would the light from Vega have raised the temperature of your calorimeter?

Observing procedure:

On the next page, you have a chart with several stars on it. Find each of these stars in the sky, and rank them in order of brightness (1 for the star you think is brightest, down through 6 for the one you think is faintest).

alpha Cygni     _________

pi Herculis       _________

gamma Aquilae  ________

alpha Aquilae     ________

alpha Lyrae     __________

theta Lyrae      __________

Now we're going to try the same thing with a device called a photoelectric photometer. It does essentially what your eyes do: measures brightness. But it does this by converting the light that hits it into a current we can read out: the more light that hits it, the more current, and the bigger the number on the readout. For this part of the lab, record the readout you obtain on the photometer when you point it at each star:

alpha Cygni     _________

pi Herculis       _________

gamma Aquilae  ________

alpha Aquilae     ________

alpha Lyrae     __________

theta Lyrae      __________

Does the order of brightness match with what you found using your eyes as the detectors?

If we have time, we'll also convert the photometer measurements into magnitudes, and see how closely they match with "standard" values.

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