Harvard University Astronomy Lab and Clay Telescope

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Luminosity and Temperature of the Sun

How much energy does the Sun put out every second? You should be able to determine this surprisingly accurately - for example, well enough to use in combination with your measure of the solar radius to derive the surface temperature of the Sun (and compare with the true value). We will use a paraffin photometer, which is simply 2 paraffin blocks optically separated by aluminum foil and held together with a rubber band, to measure the apparent brightness of the Sun.

What you'll need:

• 200 or 300 Watt lightbulb
• measuring stick
• paraffin photometer (two paraffin blocks separated by foil)

Procedure:

• The idea is to measure the apparent brightness of the Sun, by measuring the distance that your photometer has to be from your lightbulb to give the same apparent brightness of the sunlit paraffin block vs. the light bulb lit block.
• You first need to set up the heliostat so that sunlight is being directed into the lab on the bench. The sunlight will illuminate one side of the paraffin photometer and the lightbulb should illuminate the other side.
• Then you will need to move the lightbulb to the distance where the two sides of the photometer are of equal apparent brightness. The interesting difficulty is that the two sides of the photometer will appear to have slightly different colors, because the color of the much hotter Sun is whiter than that of the relatively cooler lightbulb. Do your best to compare the brightness, not color, and note the effect.
• Once you have the lightbulb at a distance that both sides of the photometer have the same apparent brightness, you will take a measurement from the center of the photometer to the lightbulb filament. Repeat this 3-5 times! Enter these measurements into the table (pdf or docx).

Analysis:

• The ratio of the output of the Sun (in Watts) to that of the lightbulb is easily calculated by the Inverse Square Law describing the drop-off of apparent brightness with distance. That law states that if you have the same apparent brightness of two objects than the luminosities compare
  • L_Sun/D²_Sun = L_Lightbulb/D²_Lightbulb
  • D_Sun is the distance from your measuring device to the Sun (namely 1 AU, or 1.5 x 10⁸ km), and D_Lightbulb is the distance from your measuring device to the lightbulb.
• We can now combine the measured solar energy output, L_Sun, with the diameter of the Sun result from either the Pinhole Experiment or the Timing the Motion of the Sun Experiment to calculate the temperature of the Sun using the blackbody equation (Stefan-Boltzmann Law).
  • L = 4πR²σT⁴
  • L is the luminosity of the Sun in Watts, R is the radius of the Sun in meters, σ is a constant of physics known as the Stefan-Boltzmann constant (σ = 5.67 x 10^-8 watt/m²/degree⁴), and T is the surface temperature of the Sun in degrees Kelvin (degrees above absolute zero).
  • Using this equation you can determine the surface temperature of the Sun and determine whether the material of the Sun is solid, liquid, or gaseous. The highest temperature which any solid or liquid vaporizes is a few thousand degrees K.
• Make sure to consider your errors.
  • Note the color difference between the Sun and the lightbulb and relate its cause to Wien's Law. How did this effect your measurements?
  • What other errors were there? Were there any clouds at the time of observation? Dust in the Earth's atmosphere? Reflectivity of the heliostat mirrors? Do you think a 200-Watt bulb really emits 200-Watts of visible light?