Chapter 15--Our Sun - Geological Sciences

Figure 15.9 Vibrations on the surface of
the Sun can be detected by Doppler shifts.
In this schematic representation, red indicates
falling gas, and blue indicates rising gas.
The speckled region indicates the convection
zone. The vibration pattern illustrated
here is just one of many possible patterns.
The overall vibration pattern of the Sun is a
complex combination of patterns similar to
this one.
In principle, we can deduce a great deal about the
solar interior by carefully analyzing these vibrations. (By
analogy to seismology on Earth, this type of study of the
Sun is called helioseismology—helios means “sun.”) Results
to date confirm that our mathematical models of the
solar interior are on the right track (Figure 15.10). At the
same time, they provide data that can be used to improve
the models further.
Mathematical Insight 15.1 Mass-Energy Conversion in the Sun
We can calculate how much mass the Sun loses through nuclear
fusion by comparing the input and output masses of the proton–
proton chain. A single proton has a mass of 1.6726 10 27 kg,
so four protons have a mass of 6.690 10 27 kg.
A helium-4 nucleus has a mass of only 6.643 10 27 kg,
slightly less than the mass of the four protons. The difference is:
6.690 10 27 kg 6.643 10 27 kg 4.7 10 29 kg
which is 0.7%, or 0.007, of the original mass. Thus, for example,
when 1 kilogram of hydrogen fuses, the resulting helium weighs
only 993 grams, while 7 grams of mass turns into energy.
To calculate the total amount of mass converted to energy
in the Sun each second, we use Einstein’s equation E mc 2 .The
total energy produced by the Sun each second is 3.8 10 26 joules,
so we can solve for the total mass converted to energy each second:
E mc 2 E
⇒ m c 2
3.8 10 26 joules
3.0 10 8 m s 2
4.2 10 9 kg
The Sun loses about 4 billion kilograms of mass every second,
which is roughly equivalent to the combined mass of nearly
100 million people.
Example: How much hydrogen is converted to helium each
second in the Sun?
Solution: We have already calculated that the Sun loses 4.2 10 9 kg
of mass each second and that this is only 0.7% of the mass of hydrogen
that is fused:
4.2 10 9 kg 0.007 mass of hydrogen fused
We now solve for the mass of hydrogen fused:
mass of
hydrogen fused 4.2 10
9 kg
0.007
6.0 10 11 kg 1m etric
ton
103
kg
6.0 10 8 metric tons
The Sun fuses 600 million metric tons of hydrogen each second,
of which about 4 million tons becomes energy. The remaining
596 million tons becomes helium.
chapter 15 • Our Star 505