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 Name___________________________________________ Elementary Astronomy
Activity 3
The Sun
Background
In this lab we consider sunspots, which are regions on the Sun that are cooler than the
surrounding photosphere. Sunspots are effects of the Sun’s strong magnetic field, and occur
when magnetic field lines pass through the photosphere. We will be approximating a sunspot
as a circle, so we need to recall how to find the area of a circle. Using d for diameter, the area
of a circle is
(1)
𝐴=𝜋
!!
!
We will also want to find the amount of power emitted from the sunspot, that is the
luminosity of the sunspot. Luminosity can be found from the Stefan-Boltzmann equation:
(2)
𝑃 = 𝑒𝜎𝐴𝑇 !
P is power, e is the emissivity (take to be 1), σ=5.67x10-8 W/(m2*K4)is the Stefan-Boltzmann
constant, A is the surface area of the emitter and T is the temperature.
We know that the Sun shines because of nuclear reactions in its core. We refer to these nuclear
reactions as nuclear fusion because 4 hydrogen nuclei are fused to one helium nucleus. The
resulting mass of the helium is slightly less than the mass of the original 4 hydrogen nuclei.
The “missing” mass has been converted to energy which is much later emitted from the Sun.
The relation between mass and energy is described by the famous Einstein equation:
(3)
𝐸 = 𝑚𝑐 !
Experiment
Show all work!
1. Take the image of the Sun from this week that has been provided to you.
2. Measure the width of the circle of the Sun on your paper in millimeters. Now measure the
approximate diameter of one of the sunspots in millimeters.
3. What is the ratio of the sunspot diameter to the Sun diameter?
Name___________________________________________ _______________________________________________
4. The diameter of the Sun is 1.38x109 meters. What is the actual diameter of the sunspot?
________________________________ m
5. The diameter of the Earth is 1.28x107 meters. Find the ratio of sunspot diameter to Earth
diameter:
___________________________________
6. Calculate the area of the sunspot using the result from 4 and Eq. 1.
________________________________m2
7. Using Eq. 2, what is the approximate luminosity of this sunspot? Take the average
temperature of a sunspot as about 4000 K (compared with the rest of the photosphere at 5800
K).
Name___________________________________________ ___________________________________ W
8. Find the ratio of this to the total luminosity of the Sun, 4x1026 W.
_________________________
9. A Watt is a Joule per second. Using the result of 7 and Eq. 3, find how much mass would
have been converted to energy to supply the energy emitted in one second by the sunspot.
__________________________kg
10. A 150 pound person has a mass of about 70 kg. How many 70 kg persons would it take to
equal the mass found in 9?
__________________________ persons
Questions
1. Would an area of the photosphere of equal size to our sunspot but at the normal
photosphere temperature have a higher or lower luminosity than the sunspot? Explain.
Name___________________________________________ 2. If the Sun is converting mass to energy on a regular basis, why does the Sun not get
progressively smaller in our sky?
3. The Sun is mostly made of hydrogen. Hydrogen can also be found in the Earth’s
atmosphere. Why does the hydrogen in the Earth’s atmosphere not fuse into helium?