XYLENE POWER LTD.

SOLAR ENERGY

By Charles Rhodes, P. Eng., Ph.D.

INTRODUCTION:
This web page shows that fusion of solar hydrogen will provide the Earth a reliable source of energy for about another 10 billion years, but inter-stellar collisions will likely cause a mass extinctions on Earth at intervals of less than 100 million years.

ENERGY IN THE UNIVERSE:
From an energy persective the universe can be viewed as an assembly of electrons, anti-electrons (pions), protons, anti-protons, neutrinos and photons. The energy contribution of neutrinos as compared to charged particles is thought to be relatively small.

The charged particles are almost all bound into neutral atoms or neutral plasma. If a significant fraction of the charged particles were free electromagnetic radiation (photons) could not propagate long distances through the universe.

The total energy of an isolated particle can be thought of as consisting of core energy plus field energy plus kinetic energy.

ENERGY THAT CAN DO WORK IN THE SOLAR SYSTEM:
Obtaining work from particle core energy requires a matter-antimatter reaction that does not normally occur in the solar system for lack of antimatter. Hence, all energy in the solar system that can do work comes from pre-existing kinetic energy or from change in overlap of particle fields.

NEUTRINOS:
Neutrinos account for the energy and spin difference between isolated neutrons and the combination of equal numbers of isolated electrons plus isolated protons. In terms of energy this difference is less than 0.1%. Neutrinos propagate at about the speed of light. The rest energy of an isolated neutrino is believed to be zero.

PHOTONS:
A photon is a quantum of electromagnetic energy that propagates at the speed of light. The rest energy of a photon is zero. The amount of energy E conveyed by a photon is given by:
E = h F
where:
h = Plancks constant
= 6.626069 X 10^-34 J-s
and F is the electromagnetic wave frequency as seen by an inertial observer.

STABLE PARTICLE DESCRIPTIONS:
An electron is a stable particle with a charge of - 1.60217646 X 10^-19 coulombs and a rest mass of 0.00054857990946 atomic weight units. An electron has associated with it external electric, magnetic and gravitational fields. These fields contain a small portion (~ 1%) of the total electron rest mass.

An antielectron is a stable particle with a charge of + 1.60217646 X 10^-19 coulombs and a rest mass (rest energy) of 0.00054857990946 atomic weight units. An antielectron has associated with it external electric, magnetic and gravitational fields. These fields contain a small portion (~ 1%) of the total anti-electron rest mass. As compared to an electron an antielectron is believed to have a sign reversal in its gravitational field unit vector.

A proton is a stable particle with a charge of + 1.60217646 X 10^-19 coulombs and a rest mass of 1.007276466812 atomic weight units. A proton has associated with it external electric, magnetic field and gravitational fields. These fields contain a small portion (~.34%) of the total proton rest mass.

An antiproton is a stable particle with a charge of - 1.60217646 X 10^-19 coulombs and a rest mass of 1.007276466812 atomic weight units. An antiproton has associated with it electric, magnetic field and gravitational fields. These fields contain a small portion (~.34%) of the total anti-proton rest mass. As compared to a proton an antiproton is believed to have a sign reversal in its gravitational field unit vector.

CHARGED PARTICLE FORMATION AND ANNIHILATION:
In certain circumstances a sufficiently energetic photon will form a proton-antiproton pair. In certain circumstances a sufficiently energetic photon will form an electron-antielectron pair.

On contact a proton and an antiproton will spontaneously convert to a very high energy photon. On contact an electron and an antielectron will spontaneously convert to a high energy photon.

A proton and an antiproton have opposite charges. An electron and an antielectron have opposite charges. Hence for free normal-antiparticle pairs to exist at formation these particles must have sufficient kinetic energy to escape from their mutual potential energy well.

The origin of free electrons and free protons in interstellar space is the subject of speculative theorys that are beyond the scope of this web site. Somehow, by processes that are not fully understood, free electrons and free protons formed in interstellar space. The free electrons and free protons aggregated to form hydrogen. Possibly at the same time antihydrogen also formed in interstellar space, but the antimatter was gravitationally repelled away from the solar system by the normal matter.

On Earth we do not observe antielectrons or antiprotons except as products of high energy nuclear collisions. In the solar system the numbers of normal electrons and normal protons vastly outweigh the numbers of antielectrons and antiprotons. Any antimatter that is formed is quickly destroyed by contact with normal matter.

PHOTON GENERATION AND EMISSION:
Free charged particles are the primary source of energy in the universe. Free electrons and free protons are in a high rest energy state. When the vector fields of particles with opposite charges overlap the total field energy decreases. Hence, the law of conservation of energy forces the particles' kinetic energy to increase. This mechanism manifests itself as electric or magnetic attraction.

When the vector fields of particles with like charges overlap the total field energy increases. Hence, the law of conservation of energy forces the particles' kinetic energy to decrease. This mechanism manifests itself as electric or magnetic repulsion.

Randomly moving charged particles in matter gradually lose their acquired kinetic energy by emitting photons of electromagnetic radiation. Charged particles can gain energy by capturing photons of electromagnetic radiation. At steady state conditions the rate of photon energy capture equals the rate of photon energy emission. The photon emission is known as black body radiation.

INTER-STELLAR MATTER:
In interstellar space electrons and protons aggregate to form hydrogen. This hydrogen emits photons with the spectral distribution of black body radiation. The experimentally measured cosmic background radiation has a peak at 160.2 GHz, and has slight variations with respect to direction, indicating that inter-stellar space contains a low concentration of matter (dust, gas) at a temperature of about 2.725 degrees K. It is believed that the stars formed by gravitational aggregation of this inter-stellar matter.

The Earth emits thermal radiation with characteristic temperatures in the range 220 degrees K to 285 degrees K. The low temperature matter in inter-stellar space acts as a heat sink for thermal radiation from the Earth. This heat sink action enables work on Earth.

STELLAR MATTER:
Spectral analysis of star light indicates that stellar matter is mostly hydrogen (or antihydrogen).

In stars hydrogen fuses first into deuterium, then into light elements, then into common elements and finally into heavy elements. The Earth, which contains an abundance of common and heavy elements, is believed to be a remnant from another star, not a product of our sun, because the sun has not advanced far enough along its fusion cycle to form the heavier elements.

STELLAR IGNITION:
Matter in interstellar space is gravitationally attracted to star formation sites. The kinetic energy that the matter acquires while falling into a star's gravitational potential well provides the heat necessary to initiate hydrogen fusion in the star. Note that some of the acquired thermal energy is radiated away before fusion reactions commence.

PRE-FUSION HEATING:
From Newton's law of gravitation, the kinetic energy Ek acquired by a hydrogen atom with mass Mh falling into the sun's gravitational potential well and impacting the sun at radius Rs from the center of the sun is given by:
Ek = (G Ms Mh) / Rs
where:
G = 6.674 X 10^-11 m^3 kg^-1 s^-2 = gravitational constant
Ms = 1.98892 X 10^30 kg = solar mass
Mh = 1.008 X 10^-3 kg / 6.023 X 10^23 = mass of one hydrogen atom
Rs = 6.955 X 10^8 m = solar radius

Numerical substitution gives:
Ek = (6.674 X 10^-11 m^3 kg^-1 s^-2 X 1.98892 X 10^30 kg X 1.008 X 10^-26 kg) / (6.023 X 6.955 X 10^8 m)
= [(6.674 X 1.98892 X 1.008) / (6.023 X 6.995)] X 10^-15 m^2 kg s^-2
= 0.3176 X 10^-15 J
= 0.3176 X 10^-15 J X 1 eV / 1.602 X 10^-19 J
= 0.1982 X 10^4 eV
= 1982 eV

The present solar volume Vs is given by:
Vs = (4 / 3) Pi Rs^3
= 1.333 X 3.14159 X (6.955 X 10^8 m)^3
= 1409 X 10^24 m^3

Hence the present average density of the sun is given by:
Ms / Vs = 1.98892 X 10^30 kg / 1409 X 10^24 m^3
= 1412 kg / m^3

By comparison the density of liquid hydrogen is:
67.8 kg / m^3

These calculations indicate the the hydrogen in the sun, in addition to being very hot is highly compressed. Once hydrogen fusion started the temperature within the sun rose. Meanwhile mass accumulation from gravitational aggregation of inter-stellar matter continued.

STELLAR NUCLEAR PROCESSES:
Fusion of hydrogen reduces its total electron and proton field energies. There is a corresponding increase in particle kinetic energy (temperature) that causes release of energy into space by emission of thermal photons.

In a star hydrogen atoms at high temperature and under high pressure slowly combine to form deuterium. This process is very slow because free electrons and free protons generally do not directly combine via a two body reaction to form free neutrons. Direct free neuton formation does not occur because a free neutron contains more energy than the sum of the energies of a free electron and a free proton.

The initial deuterium formation process requires three body interactions (2 protons + 1 electron). Statistically three body interactions occur much less frequently than two body interactions and hence are very slow.

During the star's early life hydrogen gradually converts to deuterium. Later, after the deuterium concentration in the star is significant, deuterium atoms combine with each other to form tritium and helium-3. The tritium and helium-3 then readily combine with more deuterium to form helium-4. These processes release free neutrons which when captured by hydrogen increase the deuterium formation rate.

Tritium and helium-3 can also combine with helium-4 to form lithium-6. The lithium-6 will then combine with tritium or helium-3 to form more helium-4. These processes release energetic free protons and free neutrons which further increase the deuterium formation rate.

Thus deuterium, tritium, helium-3 and lithium-6 are transition elements in the conversion of hydrogen into helium-4. However, formation of tritium, helium-3 and lithium-6 does not occur until there is a significant deuterium concentration. Hence in the early life of a star the dominant energy production reaction is fusion of hydrogen into deuterium whereas in the later life of the star energy production reactions involving deuterium to produce helium-4 become more important.

At each reaction stage energy is released and the average energy per nucleon decreases. The surplus kinetic energy converts to photons that radiate into outer space. Once the deuterium-deuterium reactions start the sun's thermal output increases.

TABLE OF RELATIVE ENERGIES PER NUCLEON AS COMPARED TO CARBON-12
Neutron = 1.00866491600

Free electron plus free proton:
Proton 1.007276466812
+
Electron 0.00054857990946
= 1.007825046721

Hydrogen = 1.00782503207

Hydrogen plus neutron:
Hydrogen 1.00782503207 / 2
+
Neutron 1.00866491600 / 2
= 2.01648994807 / 2
= 1.00824497403

Deuterium 2.0141017778 / 2
= 1.0070508889

Tritium 3.0160492777 / 3
= 1.0053497592

Helium-3 3.0160293191 / 3
= 1.0053431063

Lithium-6 6.015122795 / 6
= 1.002520466

Helium-4 4.00260325415 / 4
= 1.00065081354

Carbon-12 12.0000000 / 12
= 1.0000000

SOLAR RADIATION:
The solar irradiance at the Earth's orbit measured via satelite borne instruments is:
1.361 kW / m^2.

The radius of the Earth's nearly circular orbit around the sun is about 150 X 10^6 km. Hence the surface area of a sphere with the radius of the Earth's orbit is:
4 Pi R^2 = 4 X 3.14 X (150)^2 X 10^12 km^2 X 10^6 m^2 / km^2
= 28.26 X 10^22 m^2

The power of the present total photon radiation from the sun is:
1.361 kw / m^2 X 28.26 X 10^22 m^2
= 38.462 X 10^22 kW
= 3.8462 X 10^26 J / s

From Einstein's relationship of:
E = M C^2,
the corresponding rate of solar mass loss due to nuclear reactions is:
(3.8462 X 10^26 J / s) / C^2
= (3.8462 X 10^26 J / s) / (9 X 10^16 m^2 / s^2)
= .4274 X 10^10 kg / s

If the sun is in the early part of its life, when the dominant source of solar heat is fusion of hydrogen into deuterium, the corresponding rate of solar hydrogen mass loss is:
(.4274 X 10^10 kg / s) / [(1.00782503207 - 1.0070508889) / 1.00782503207]
= (.430744 X 10^10 kg / s) / (.00077414317)
= 556.414 X 10^10 kg / s

If the sun is in the later part of its life, when the dominant source of solar heat is fusion of hydrogen into helium-4, the corresponding rate of solar hydrogen mass loss is:
(.4274 X 10^10 kg / s) / [(1.00782503207 - 1.00065081354) / 1.00782503207]
= (.4307 X 10^10 kg / s) / .00717422
= 60.034 X 10^10 kg / s

SOLAR PARTICLE EMISSION:
Measurements of the solar wind indicate that the solar particle emission rate is about:
1.3 X 10^36 particles / second. The solar wind contains both electrons and protons. The particle velocity is about 750 km / s. For hydrogen the approximate mass per particle is given by:
(1.00782 gms) / (6.023 X 10^23 atoms)
= 0.167 X 10^-23 gm / atom.

Hence the kinetic energy carried away by the solar wind is:
(1.3 X 10^36 particles / second) X (1 atom / 2 particles) X (0.167 X 10^-26 kg / atom) X (750,000 m / s)^2 X 0.5
= (1.3 X 0.167 X 7.5^2 X 0.25) X 10^20 J / s
= 3.053 X 10^20 J / s
This figure is six orders of magnitude below the photon radiation power and hence does not affect the calculated solar mass loss rate via nuclear reactions.

As indicated by solar spectra, the sun consists of 73.4% hydrogen by mass. The rate of solar hydrogen mass loss via the solar wind is given by:
(1.3 X 10^36 particles / second) X (1 atom / 2 particles) X (0.167 X 10^-26 kg / atom) X .734
= .0797 X 10^10 kg / s
This mass loss rate is small as compared to the hydrogen mass loss rates due to nuclear reactions.

PRESENT SOLAR HYDROGEN MASS:
The present solar mass is: 1.98892 X 10^30 kg.
As indicated by solar spectra, 73.4% of the solar mass is hydrogen.
Hence the present solar hydrogen mass is:
.734 x 1.98892 X 10^30 kg
= 1.4598 X 10^30 kg

SOLAR LIFETIME:
Assume that both the solar hydrogen fusion rate and the solar hydrogen emission rate continue unchanged. Then the solar lifetime is given by:
Lifetime = (present solar hydrogen mass) / (present hydrogen mass loss rate)

If the sun is in its early life the projected solar lifetime is given by:
= (1.4598 X 10^30 kg) / (556.414 X 10^10 kg / s)
= .00262 X 10^20 s
= .00262 X 10^20 s X 1 h / 3600s X 1 day / 24 h X 1 year / 365.25 day
= 2.62 / (3.6 X 2.4 X 3.6525) X 10^11 years
= .0831 X 10^11 years
= 8.31 billion years

If the sun is in its later life the projected solar lifetime is given by:
= (1.4598 X 10^30 kg) / (60.114 X 10^10 kg / s)
= .02427 X 10^20 s
= .02427 X 10^20 s X 1 h / 3600s X 1 day / 24 h X 1 year / 365.25 day
= 2.427 / (3.6 X 2.4 X 3.6525) X 10^12 years
= .0769 X 10^12 years
= 76.9 billion years

COMMENT ABOUT THE SOLAR LIFETIME CALCULATION:
The calculated solar lifetime strongly depends on which fusion reactions are presently dominant in the sun. More sophisticated solar models indicate that the sun is relatively young and that the projected solar lifetime is about 10 billion years. Regardless of the limitations of the simple solar lifetime calculation methodology used herein, the actual solar lifetime is several orders of magnitude longer than humans have existed on Earth. We are not going to run out of solar energy any time soon.

Over millions of years the sun's thermal output will gradually increase due to an increasing deuterium concentration in the sun. The increased flux of thermal photons will raise the Earths surface temperature. As the Earth's surface temperature increases the polar ice caps will melt causing a permanent major increase in sea level.

AGGREGATION RADIUS:
Newton's law of gravitation gives:
Ek = G Ms Mh / R
where R is the radius from the center of the sun to the hydrogen atom.

For speeds much less than the speed of light:
Ek = (Mh / 2) (dR / dT)^2
where:
T = time.

Combining these two equations gives:
G Ms / R = (1 / 2) (dR / dT)^2
or
dR / dT = - (2 G Ms / R)^0.5
or
- (R / 2 G Ms)^0.5 dR = dT
and integrating from state a to state b gives:
- [(Rb^1.5 - Ra^1.5) 2] / [3 (2 G Ms)^0.5] = (Tb - Ta)

In this case Rb = Rs. We want to find Ra for Ra >> Rb. Hence this equation simplifies to:
[Ra^1.5) 2] / [3 (2 G Ms)^0.5] = (Tb - Ta)
or
Ra = {(Tb - Ta)[3 (2 G Ms)^0.5] / 2}^.666

Numerical solution of this equation for (Tb - Ta) = 100 million years (1% of estimated hydrogen life of sun) gives:
Ra = {10^8 years X 3 X (2 X 6.674 X 10^-11 m^3 kg^-1 s^-2 X 1.98892 X 10^30 kg)^0.5 / 2}^0.666
= {1.5 X 10^8 years X (26.548 X 10^19 m^3 s^-2)^0.5}^0.666
= {1.5 X 10^8 years X (1.629 X 10^10 m^1.5 s^-1)}^0.666
= {1.5 X 10^8 years X 8760 h / year X 3600 s / h X 1.629 X 10^10 m^1.5 s^-1}^0.666
= {77.075 x 10^24 m^1.5}^0.666
= {77.075}^0.666 X 10^16 m
= 18.11 X 10^16 m

By comparison, a light year is:
1 light year = 3 X 10^8 m / s X 8760 h / year X 3600 s/ h X 1 year
= 94.608 X 10^14 m

Hence over 100 million years the sun will gravitationally sweep matter out of a spherical volume with a radius of:
18.11 X 10^16 m / (94.608 X 10^14 m / light year)
= 19.1 light years

There are 51 known stellar systems within 16.3 light years from the Earth. By extrapolation the approximate number of stellar systems within 19.1 light years is given by:
(19.1 / 16.3)^3 X 51 = 82

Hence the average time between stellar near collisions with the sun is given by:
(100 X 10^6 years / 82) = 1.2 million years

Inter-stellar near collisions explain the varying composition of the planets and their moons within the present solar system.

Inter-stellar near collisons explain many of the mass extinctions in the Earth's geological record. Human life on Earth will likely be driven to near extinction within a few million years due to an inter-stellar near collision. A direct inter-stellar collision is not necessary for a mass extinction. All that is necessary for a mass extinction is a transient gravitational disruption that causes ocean tides which sweep right across the Earth's continents. Such a transient gravitational disruption would likely be accompanied by a transient increase in the Earth's received radiation and a corresponding transient increase in ambient surface temperature. Life forms located in high elevation mountain caves or in suitably constructed ships might survive, but their crops and livestock would be wiped out.

The astronomical and geological evidence supports the general theme of the biblical story of Noah and his Arc.

This web page last updated April 13, 2012.