100 YEARSINTERNACIONALASTRONOMICAL
UNION
1919-2019

The Power of the Sun and how to measure it
Introduction: Bunsen photometer
To measure the power of the stars, the Astronomers use the photometer, aninstrument that measures the amount of light in a given location and It permits
determine the amount of energy per unit of time (the Power) from an unknown
source compared to a well characterized source. Historically, there are several
photometers proposed for comparing light sources. In this work we will focus onthat of Robert Bunsen (figure 1), a German chemist and physicist from 19 thcentury. He built many of the devices he needed in his experiments. Perhaps thebest known is the lighter that bears his name, but he also invented the oil spot
photometer.

Fig. 1 Robert Wilhelm Bunsen and his oil spot photometer

The photometer invented by Bunsen allowed to compare the intensity of two lightsources, one known and one not.
To do so, just place both sources on the ends of a tape measure. A plain white
paper with a small oil stain is placed between the sources. In the stained area, thepaper becomes semi-transparent. When moving the paper between the twosources of light, there comes a time when the stain is barely visible. In thisposition, the illuminance that reaches both sides of the paper is the same.
Illuminance is the flow that arrives per unit area. As the luminous flux that comesout of a bulb is distributed radially between the surface of a sphere of radius d and2
area = 4 π d , the further away, the less illuminance. If both sources are bulbs of
the same type, the number of lumens that come out per watt is similar, and in thecalculations, we can substitute the luminous flux for the electrical power.

That is, if P1 and P2 are the electric powers of the two lamps, and d1 and d 2 are
the distances from the paper to each of the light sources, the following must be
fulfilledP1
P2
PP==¿ 12 = 22224 π d 1 4 π d2
d1 d2
If, for example, the lamps are 100 W and 60 W halogen lamps (figure 2), theposition where the oil stain is not visible will occur:
100 60=d12 d22Fig. 2. As the stain looks dark, there is little light behind it and you should approach the bulb on
the right until the stain disappears.

We can do a classroom experience to check the functionality of the oil spot
photometer. We will compare a 60W standard bulb with two other sample bulbs,
40W and 100W. To do this, we prepare a chart (see Table 1), so that the student
can record the data accurately, including whether the lamp is transparent or theglass is painted and what colour the light it produces is. As always in Science,
we must register the results.
Table 1. Power estimation experiment: results
Lamp used as a pattern
Type of bulb

Indicated
power
(W)

Lamp used as a sample

Distance
Indicatedbulb-paper Type of bulb power(m)(W)

Distance
Calculatedbulb-paper Power(m)(W)

Experiment 1: Determination of the power of the Sun with the oilspot photometer
However, the most interesting use of the Bunsen photometer is the determinationof the power or luminosity of the Sun. Using the oil spot photometer, we willcalculate the power of the Sun comparing it with, for example, a 100 W bulb
(figure 3).

Fig. 3: Comparing the power of the Sun with a 100W lamp

On a sunny day, the photometer and a halogen bulb of at least 100 W are
installed outdoors (the more the better). The photometer is placed between theSun and the bulb, at a distance that the spot almost disappears. The distanced 1 is measured in meters, from the photometer to the filament of the lamp
(figure 4).

Fig. 4. When the stain is not visible, the distance from the paper to the filament is measured.

Knowing that the distance of the Sun from the Earth is approximately
d2=150.000.000 000 m (1 astronomical unit), the power of the Sun PSun can becalculated with the same formula as the previous activity, known as the inverse
law of squares:
100W P Sun= 2d 12d2
Note that the luminous efficiency of the Sun and the halogen bulb are not thesame, but the result obtained should not differ much from the actual luminosity ofthe Sun, which is 3,83·1026 W.

Experiment 2: Determination of the Sun's power for inclusion
We can perform another experiment (figure 5) to estimate the solar luminosity,
replacing the paper with the oil stain by our face. On a sunny summer day, it ispossible to compare the heat that comes from the Sun on one of the cheeks ofthe face and the heat that comes from a 100 W bulb in the other. The distance ofthe bulb to the face should be changed until the student (with closed eyes orblind) has exactly the same feeling of heat in the skin of both cheeks. Measuring
the distance d of the bulb to the face and the known distance R to our Sun (150x 109 m), we can estimate the luminosity of the Sun with the same formula.

Fig. 5. Application of the relationship PSun / R 2 = P / d2

The 'same sensation' means the same intensity of heat from the Sun and fromthe lamp. Assuming that the efficiency of the Sun and the light bulb were similar
at these wavelengths, the mentioned law of the inverse of the squares can beapplied.
The value of the distance d will be about 10 cm. With this value, the result of theSun's Luminosity comes out around 2.2x1026 W, a little lower than the real one.
The reason is that the atmosphere is not transparent to infrared radiation, andthen, the Sun appears at these wavelengths weaker than it really is. But thesimplicity of the method compensates for the lower precision in the result.

Autors:Alexandre de Costa, Beatriz García, Ricardo Moreno, Rosa M. Ros, NASEmembers.

Bibliography:
J. A. Belmonte, F. Berthomieu, A. Costa, H. Deeg, S. Deustua, J. Fierro, B. García, M.K.
Hemenway, R. Moreno, J.M. Pasachoff, J. Percy, R.M. Ros, M. Stavinschi, 14 steps to theUniverse, Rosa M. Ros y Beatriz García edi., Barcelona, 2018.

A. Costa & A. L. Gonçalves, Solar Physics. Theory and applications, Astronomy at ourSchools, EAAE-IAU Course on Astronomy Education, EAAE Summer School, Alexandre
Costa and Rosa M. Ros Ed., Portugal, Loulé, 2016.

B. García, R. Moreno, The meaning of the Sun and the distance to the stars: The power ofphotometry in Astronomy, Barcelona 2018.

Finally, send this sheet with the results and two or three photos of eachExperience to newsletter.nase@gmail.com

100 YEARSINTERNACIONAL
ASTRONOMICAL
UNION
1919-2019

The power of the Sun and how to measure it
ACTIVITIES TO MAKE AND SEND
Perform the Experience 1 (with oil spot), the Experience 2 (with face cheek) orboth, obtain the value for the Sun Power and record the results of eachExperience in the following Results Table:
Table of Solar Power experiments results
Teacher’s name
School, Country
Day and hour
Type ofMeasurement
Experiment 1:

PatronResults

Type of bulb

Indicated power(W)

Distancebulb-paper (m)Calculated
Solar Power(W)Type of bulb

Indicated power(W)

Distancebulb-cheek (m)Calculated
Solar Power(W)Oil spot

Experiment 2:
Cheek of the face

Project launch: March 20, 2019 (equinox)
The activity will be open until: June 21, 2019 (solstice)
The results will be disseminated worldwide under the initiative
IAU100