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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