math.duke.edubray/courses/89s-mou/2016/pap… · web viewdoes the sun’s history support the...
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THE MINDBLOWING PHYSICS OF THE SUNPRITHVIR P. JHAVERI, DUKE UNIVERSITY 2019
Abstract
This paper was written with the purpose of exposing my Professor Hubert
Bray*, and the rest of my class****, to aspects of the sun that they might
not be aware of. If bananas were to replace the hydrogen present in the
sun could the same average surface and core temperature be
maintained? Could a certain solar activity in the distant future contribute
to the destruction of the earth? Are solar minimums as predictable as we
think they are? Does the sun’s history support the theory of evolution?
How big is the sun, in reality?
Introduction
The claim that the sun would remain as hot as it is today if its hydrogen
content was replaced by bananas was explored and supported using Gay
– Lussacs’ Law. On further investigation it was noted that the nuclear
fusion reactions that take place in the sun’s core actually dispute this
claim in the long term.
The theory that the earth will, at some point in time in the distant future,
be consumed by the ever expanding sun was proved using nuclear
* Hubert Bray is a Professor of Mathematics and Physics at Duke University**** The class is a seminar on introductory astrophysics called Math 89S at Duke University
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reactions, specifically the triple alpha process in which helium is
converted to carbon.
The unpredictability of existing space and data technologies in detecting x
class solar flares was touched upon. It was concluded that no matter how
advanced our technological systems maybe, there is still a lot that is
unknown. The faint young sun paradox was dealt with in a three-fold
manner. The solution involved the greenhouse gas hypothesis, the idea of
a reduction in radiogenic activity, and the reduction in the moons distance
from the earth that lead to a decrease in tidal heating. The suns actual
volume was computed, and found to be not as large as expected. In fact,
the conclusion might be extremely surprising to most.
Could bananas work? If the sun were made of bananas it would be
probably still be as hot.
Within the core of the sun, temperatures soars at about 15000000K. While
pressures soar at about 340 billion times that on earth. It’s important to
note that the soaring temperature is actually a result of the soaring
pressure. Closed surfaces get heated when lots of fluid (in this case- gas)
is forced inside them. The pressure increases the temperature. This is a
direct application of Gay- Lussacs’ Temperature - Volume Law which
states that “At a fixed volume, the temperature and pressure of a gas are
directly proportional to each other.”
Below is the equation for Gay- Lussacs’ Law followed by a graph
demonstrating it.
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T1 = Initial Temperature (Kelvin - K)P1 = Initial Pressure (atm or mmHg)T2 = Final Temperature (Kelvin - K)P2 = Final Pressure (atm or mmHg)
Now, it’s important to note that because of this intense pressure and
temperature, nuclear reactions are constantly taking place in the sun’s
core. These nuclear reactions complete a cycle of renewing the heat and
pressure that actually cause them. The main reaction that takes place in
the sun is the fusion of hydrogen to form helium. The net result is the
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fusion of four protons into one alpha particle, with the release of two
positrons, two neutrinos (which changes two of the protons into neutrons),
and energy. The reaction is shown in the diagram below.
Furthermore, if the sun was not primarily composed of Hydrogen, the
fusion reaction that keeps it going would not get underway: so a banana
sun would would cool down rapidly from it’s initial heat.
Even if the sun were to cool down instantaneously, it would take the
people on earth 8 minutes to realize this. Light travels at a speed of 3 x
10^8 m/s and the distance between the sun and the earth is 1.5 x 10^11
m/s. Assuming there is no acceleration of the velocity of this light,
Time taken = (1.5 x 10^11) / (3 x 10^8) s
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= (0.5 x 10^3) s
~ 8 minutes 20 seconds.
It’s interesting, however, to wonder whether the high potassium content
in bananas could possibly contribute to the nuclear reaction in some way,
owing to potassium and hydrogen’s proximity in the periodic table, and
their highly similar chemical nature.
The Death of the Earth: There are many theories floating around that
speak of the ultimate destruction of the earth. Most of these stem, in
some way or another, from the activities of the sun. The most popular
theory is that at some point in the distant future, the sun will consume the
earth. The sun is believed to have been burning for about 5 billion years.
It is supposed to be “middle aged”. I.e. it has burnt up half the hydrogen
present in its core. Therefore, its life expectancy is postulated to be
around 5 billion more years. When all the hydrogen in the core is used up,
nuclear reactions will stop there, but they will continue in a shell around
the core. The core will contract (since it is not generating energy) and as it
contracts it will heat up. Eventually it will get hot enough to start burning
helium into carbon.
This is called the triple- alpha process. Here, three Helium- 4 nuclei (alpha
particles) are converted to carbon.
4He2 + 4He2 8Be4 (-91.8 KeV)
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8Be4 + 4He2 12C6 (+7.367 MeV)
While the core is contracting, the helium burning around it in the outer
layers will heat up and then expand, and then cool. The Sun, as a whole,
will gradually expand. At some point in time it will become what is called
a Red Giant* and its radius will be large enough to envelop the Earth.
Unpredictability of solar minimums
Approximately every 10 years, solar activity increases to a maximum.
Sunspots (temporary phenomena on the photosphere of the sun that
** a very large star of high luminosity and low surface temperature. Red giants are thought to be in a late stage of evolution when no hydrogen remains in the core to fuel nuclear fusion.
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appear visibly as dark spots compared to surrounding regions that
correspond to concentrations of magnetic field flux that inhibit convection
and result in reduced surface temperature compared to the surrounding
photosphere) appear at different locations all over the sun, and
unsystematically explode. Large clouds of gas known as “Coronary Mass
Ejections” (large bursts of gas and magnetic field arising from the solar
corona*) spread throughout the solar system. These CMEs actually
contribute to the Auroras seen in northern countries like Greenland and
Iceland etc. In fact, in a solar maximum between 2000 and 2001, people
as far south as Mexico and Florida claimed to witness auroras. As
dangerous as these solar maximums are to radio and electrical activity on
earth, they are predictable. We know when to expect them and thus take
the necessary precautions to deal with them.
Recently, there has been discussion that solar minimums are a whole
different ball game. Solar Physicist David Hathaway of the NASA Marshall
Space Flight Center believes that solar activity never stops. “Not even
during a solar minimum.” Hathaway counted the number of X- class solar
flares each month during the last three solar cycles of the 20th century as
seen in the diagram below. An X-class solar flare is the most powerful
solar flare with Peak Flux Range at 100-800 picometre of > 10-4
Watts/metre2. The result was that there was at least one X class flare in
each of the last three solar minima.
** A corona (Latin, 'crown') is an aura of plasma that surrounds the sun and other celestial bodies. The Sun's corona extends millions of kilometers into space and is most easily seen during a total solar eclipse
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What this tells
us is that no matter how advanced our space technology detecting
systems are1, we still have a long way to go. Space travel is still
extraordinarily dangerous. Astronauts have to always be on the look out
for X- Class solar flares, even in periods of so called solar minima. Space
travel is planned in ways that reduce the amount of predicted interaction
between the travel path and CMEs. However, there will always be that
sense of unpredictability.
Faint young sun paradox
During the Archean period (3.8 – 2.5 billion years ago), the sun was
supposed to be only 75% as bright as it is today. Given the radius of the 11 Here’s an example of how advanced our space detecting systems can be http://www.solarmonitor.org/forecast.php
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earth’s orbit around the sun, there is no way that the sun would’ve been
able to provide the same energy to maintain a temperature conducive to
liquid water on earth. The temperature would’ve been way too low and
water would be frozen. Obviously, life would not have been able to
develop the way that it did. There is no way that that temperature would
be able to support of the theory of evolution.
Here lies the contradiction. Geologists believe that the earth has remained
at a constant temperature throughout its development. Furthermore, the
primary species prevalent during this period, the Archaea, are not just
extremophilic microbes. Many of them cannot survive in harsh conditions.
In fact, the Archeans that are present in our gut today are similar to the
ones that were present in that period- they needed salinity, oxygen
levels, and temperature akin to what is present today. With the given
amount of resources and knowledge available, scientists attempt to
understand and solve the paradox. There are three basic hypotheses.
1. The Greenhouse Hypothesis: the general consensus is that the
young earth contained larger amounts of greenhouse gases in the
atmosphere than that are present today. The atmosphere was able
to trap enough heat to compensate for the smaller quantity of solar
heat energy reaching it. Carbon dioxide concentrations may have
been higher because there was no bacterial photosynthesis to
reduce the gas to carbon and oxygen. Methane, a very active
greenhouse gas that reacts with oxygen to produce carbon dioxide
and water vapor, may have been more prevalent as well. Most
importantly, it was proposed that Carbonyl Sulfide (OCS) was
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present in the Archean atmosphere. Carbonyl sulfide is an efficient
greenhouse gas and the scientists estimate that the additional
greenhouse effect would have been sufficient to prevent Earth from
freezing over.
2. The Radiogenic Hypothesis: There is mass belief that any attempts
to explain the faint young sun paradox must take into account the
radiogenic contributions. Whenever radioactive isotopes
spontaneously decay, heat energy is released as a byproduct. In the
past, the geothermal release of decay heat, emitted from the decay
of the isotopes potassium-40, uranium-235 and uranium-238, and
thorium-232 was believed to be considerably greater than it is
today. As shown in the diagram below.
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3. Tidal Heating: (also known as tidal working) occurs through the tidal
friction processes- orbital and rotational energy are dissipated as
heat in either the surface ocean or interior of a planet or satellite.
We calculate the quantity of tidal heating using this formula:
Where = mean density of the satellite. I.e. the moon;
- the fifth power of the average angular speed of the satellite;
- the fourth power of the radius of the orbit of satellite around
the planet whose tidal heating we’re calculating;
- the eccentricity of the orbit;
- the shear modulus;
Q - a dimensionless dissipation factor;
The Moon was much closer to the Earth billions of years ago. Since
the fourth power of the radius of the satellites orbit is directly
proportional to the tidal heating, one would assume that the tidal
heating was less. However, reduction in the radius also implies
greater angular velocity. And, since tidal heating is proportional to
the fifth power of the angular velocity*, tidal heating was actually
greater in the Archean period, which offset the lack of heat from the
sun and thus enabled life to develop on earth.
** angular velocity (w) = linear velocity(v) / radius of circular path (r)
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How big is the sun actually?
The sun weighs about 1.989 × 10^30 kg. The entire solar system has a
combined mass of 1.993 x 10^30 kg. This means that the sun contributes
1.989/ 1.993 or 99.8 % of the entire solar system. Furthermore, the sun
occupies 1.41×10^18 km3 of space, which is 1,300,000 times that of the
Earth.
In fact, its shape is possibly the closest perfect natural sphere known to
man.
The truth is that these are known facts, and most people interested in the
study of the universe could tell you this.
However, what people forget is that atoms are 99.9999999999999 per
cent empty space. If you forced all the atoms together, removing the
space between them, crushing them down so the all those vast empty
spaces were compressed, a single teaspoon or sugar cube of the resulting
mass would weigh five billion tons; about ten times the weight of all the
humans who are currently alive.
In the same way, the sun would have a volume of:
= 1.41 * 10^18 - (99.9999999999999 / 100 * 1.41 * 10^18)
~ 1410 km3.
In theory, if we could some how squeeze together all the atoms that
contribute the sun, we could fit all these atoms inside less than half the
volume of Lake Michigan (the 5th largest lake in the world) with a volume
of 4918 km3.
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In conclusion, the sun is truly a mind-blowing natural phenomenon. And,
we need to understand and accept the fact that despite all that we know
so far about the universe, there is still a long, long way to go.
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