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Astrophysics. Aim: To determine the luminosity of the Sun using calculations.

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Introduction

Brionna Wilson

HL Physics

12/11/2009

Determining the Luminosity of the Sun

Aim:

To determine the luminosity of the Sun using calculations.

Diagram:

Equations Used:

b  apparent brightness

L  luminosity (of the sun)

d  =

BUT:  

                                          AND  

SO:

   ∴

Initial Information:

Mass of Water (m) = 0.937810 kg ±1 x 10-6 kg

Specific Heat Capacity (C) = 4200 J Kg-1 K-1

Change in Temperature (∆T) = 319.5 – 298.5

                                   = 21.0 K ±1 K

Distance between Sun and Earth (d2) = (1.496 x 1011)2

   = 2.238 x 1022 m

Radius of Beaker (r2) = (0.0525)2

                         = 0.00276 m ±0.002 m

Time Taken for 21.

...read more.

Middle

=    4.707 x 1026Watts

Uncertainty:

±image00.png= (1 x 10-6) + 1 + 0.002 + 600

= 601.002001 ≈ ±601

Luminosity of Sun = 4.707 x 1026 ±601 W


Conclusion & Evaluation:

Based on the results and my calculations, the luminosity of the Sun is 4.707 x 1026 ±601 Watts. The accepted value for the luminosity of the Sun is 3.846×1026 W[1], so, therefore, the value I deduced is 18.3% higher than the accepted value. Although my obtained value may be considered similar enough to the accepted value, my calculated uncertainty does not include the acknowledged value. This means that there must either be an error in the collection of data, or in the interpretation of it.

There were many assumptions made in order to conduct this experiment:

Assumption

Effect on Result if Not Correct

Possible Improvements

  1. Beaker was always in Sun

(for 1hr 35mins)

  • If partially shaded, the temperature change would not be accurate for the time taken
  • This would produce an deflated value of luminosity of the Sun
  • Shorter length of time left out in the Sun
  • Continual observance of the beaker whilst in use
  1. Sunlight fell directly perpendicular to surface of water
  • The Earth rotates, so the Sun will only be in a position to convey it’s light perpendicularly for a small amount of time in the day
  • This would produce an deflated value of luminosity of the Sun
  • Shorter length of time left out in the Sun
  • Investigation timed for midday, when the Sun would be directly overhead
  1. Value of temperature change would not vary between seasons
  • As the Earth orbits the Sun ecliptically, the distance between the two heavenly beings will vary depending on the time of year
...read more.

Conclusion

  • Close all doors & windows, & turn off all air conditioners when weighing mass of water, to prevent flow of air around the room
  1. Lack of repetitions

(Random)

  • Time limitations
  • Lack of resources
  • Repeat experiment & take an average in order to increase preciseness of resulting value and decrease random errors

The error and uncertainty that I obtained for this investigation are both relatively small; therefore I consider my results to be reasonably precise. However, I cannot judge them to be exactly accurate, as the accepted value lies out of the bounds of my calculated value, even with the range of my uncertainties. More precise equipment and timing should be ensured, along with repetitions of the experiment, in order to assume that the value obtained is correct.


[1] http://en.wikipedia.org/wiki/Sun - 3.46pm, 08/03/09

...read more.

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