SPECULATIONS ON THE SUN'S DARK STAR COMPANION, ACCORDING TO PHYSICS
by R.F.
February
14, 2015
INTRODUCTION BY LUCA SCANTAMBURLO
The following article <<Speculations
on
the Sun's Dark Star Companion, according to Physics>>
- unpublished so far - is written by R.F., an American applied
mathematician who lives in USA and is interested in
discussing Nibiru's approach and the possibile existence of a dark
star, beyond the outer planets of the Solar System. He contacted me
by e-mail a few months ago, after reading my articles in
English language published on Internet. That's why he sent me his
writings. I know his first name and surname but he kindly asked me
to spread his study only with his initials. The following study is
his second work on the subject of irregularities in the orbits of
Uranus and Neptune (after his first article <<When
Will Nibiru Get Here According to Physics?>>
hosted since last year on my website):in this study he points
out the possibile presence of a Dark Companion Star of our Sun,
called by him with the expression of
Vulcan, and he focus his attention on the Sun's angular
momentum.
Of course there is no guarantee on these speculations, above all
because we do not know all the astronomical data with enough
throughness, and everything is based on clues come out in the course
of the search for Planet X and Nemesis (a Dark Star, perhaps a
brown dwarf) carried out by NASA, by U.S Naval Observatory and by
other scientific institutions involved in the last century. The same
existence of Nibiru beyond Neptune is not sure and accepted by
modern Astronomy yet. The main idea of the author is that the Sun is
involved in a cosmic dance with its invisible dark star companion:
Vulcan (another name used after the well-known name of Nemesis). As
the Author R.F. says in his scientific article,
<<[...] One recent estimate even places the frequency
of multiply related stars in the Milky Way as high as
85%. With such a high rate of occurrence and given the
apparently low value of angular momentum observed in the solar
system today, an interesting possibility is that our own star
might be in a binary system itself, which raises the question
about whether any evidence exists that can support or conversely
rule out such a theory. A binary companion for the Sun could
answer both puzzles of the solar system's and the Sun's angular
momentum both being apparently too small>>.
The sad thing is that weeks ago I have forwarded this work to some
astronomers (in Europe and in North America): nobody has found the
time to answer, so far. But it does not matter, because if the
Author is right - about the existence of Nibiru and of the Sun's
dark star companion - sooner or later everyone will be involved in
the biggest scientific and social revolution since the times of
Galileo Galilei and Christopher Columbus. Another aspect touched by
the Author is the following: is there any threat to the Earth posed
by Vulcan?
In my opinion this point is connected to the existence of Nibiru,
the so-called Planet of Crossing. As the matter of fact, R.F. (the
Author) in his original research talks about the <<retinue
of
satellites which at perihelion could come careening through the
inner solar system to create cataclysmic havoc on a scale
difficult to imagine>>.
Please, if any astronomer at the moment is fully aware of this and
of possibile unknown comet and meteor showers which could already
got involved the Earth, contact me. Maybe we can warn the general
public, to help everyone to be ready for the survival of humankind,
and to accept the reality of Planet X and of his masters ad
inhabitants: the Anunna, the Sumerian Gods who are probably
returning.
Luca Scantamburlo
February 14, 2015, www.angelismarriti.it
[the following study has been updated by the Author R.F., and
it contains appropriate corrections in interpreting Dr.
Warmkessel's work - March 30th, 2015]
Reproduction is allowed on the Web if accompanied by
the statement
© L. Scantamburlo - www.angelismarriti.it
Reproduced by permission.

The Sun's Dark Companion
According to Physics
by R.F.
Hints of a Dark Star
Astronomers have known about the irregularities in the orbits of
Uranus and Neptune for almost two centuries now, since the time when
French astronomer Joseph J.F.
Lalande first detected, in May 1782, an anomaly on the
motion of Uranus: the new planet discovered by Wilhelm Herschel in
1781, did not respect the time schedule predicted for it,
during its motion. The responsible cause was the planet Neptune,
discovered later on in 1846. Very soon astronomers realized
that the presence of Neptune alone could not explain the
motions of Uranus: the problem of a trans-Neptunian planet was born
(the so-called Planet X, see the work by Percival Lowell). The
suspicion early on was that some large celestial body lurking in the
outer reaches of the solar system is most likely the cause, and with
the discovery of Pluto in 1930 astronomers thought they might have
found it, although at the time they had no way to determine Pluto's
size to know for sure. But with the discovery of Pluto's moon
Charon in 1978 (James W. Christy,
U.S. Naval Observatory), astronomers were finally able to compute
the mass of the two bodies, which they proved to be too small to
account for the unexplained irregularities (Christy
and R.S. Harrington). And
so the search went on. NASA and the US Naval Observatory had
already become interested in the problem in the early 70s, if
not sooner, when they began releasing information to the press about
their research plans in 1981.
Exactly what the responsible object is has never been pinned down,
at least officially, but in the early 80s it was suspected by
government scientists and academia to be an unknown and
larger-than-Earth-sized planet, which was called Planet X. One
of the first articles describing NASA's intent to decipher the
riddle appeared in Astronomy magazine
in December 1981 entitled ?Search
for the Tenth Planet? [1], in which a leading astronomer at
the US Naval Observatory, Dr. Tom van Flandern, described NASA's
plans to use the Pioneer satellite probes, conveniently launched in
the early 70s, to locate the object. As the article stated:
<<Beyond Pluto, in the cold,
dark regions of space, may lie an undiscovered tenth planet two to
five times the size of Earth. Astronomers at the US Naval
Observatory (USNO) are using a powerful computer to identify the
best target zones and a telescopic search will follow soon
after... Van Flandern thinks the tenth planet may be between two
and five Earth masses and lie 50 to 100 astronomical units (4.6
billion- 9.3 billion miles) from the Sun.>>
The June 28, 1982 issue of Newsweek
added more detail to the story and an alternative to the Planet X
theory with an article entitled ?Does
the
Sun Have a Dark Companion? [2], in which another solution
to a perturbing influence was first officially offered by the
writer's source, once again USNO astronomer Tom van Flandern:
<<A 'dark companion' could
produce the unforeseen force that seems to tug at Uranus and
Neptune... The best bet is a dark star orbiting at least 50
billion miles beyond Pluto. It is most likely either a brown
dwarf or a neutron star. Others suggest it is a tenth
planet...>>
That possibility of an orbiting quasi star became even more apparent
later that year with an article in the November 1982 issue of
Science Digest, written by Dr. J. Allen Hynek, professor emeritus of
astronomy at Northwestern University. The article states that
the orbital anomalies of Neptune and Uranus could be caused by
either a planetary object 4 to 7 billion miles away or a much larger
object such as a brown dwarf at a distance of about 50 billion miles
[3]. Dr. Hynek said that NASA believed that data coming from
the Pioneer 10 and 11 space probes, launched in 1972 and 1973
respectively, would allow scientists at NASA's research center in
Pasadena, Cal., the Jet Propulsion Laboratory (JPL), to determine
which of the two it is.
He also said
that a telescope on board another satellite scheduled to be
launched in January the following year would soon provide
additional search capabilities:
<<... planetary
scientists at NASA's Ames Research Center plan to use the
Infrared Astronomy Satellite (IRAS) planned for launch next
month, to try to find a brown dwarf in our solar system or
even farther out in space.>>
Interestingly, a diagram of the solar system in the article
depicts both celestial objects, Planet X and the dark star, and
the two space probes, Pioneer 10 shown as heading nominally in
the presumed direction of the two proposed objects and Pioneer
11 heading in the opposite direction. It was becoming
apparent that authorities were considering the possibility of
two large unseen objects in the solar
system.
That strategy apparently worked. IRAS was launched in
January 1983, and later that year NASA made the official
announcement that the satellite had in fact detected the
infrared signature of a large celestial body beyond the orbit of
Pluto. An article proclaiming the event appeared on the
front page of the prestigious Washington
Post in December of that year: ?Mystery
Heavenly
Body Discovered? [4]. The article begins ?A
heavenly body possibly as large as the giant planet Jupiter
and possibly so close to Earth that it would be part of this
solar system has been found in the direction of the
constellation Orion by an orbiting telescope aboard the U.S.
Infrared Astronomical Satellite (IRAS).... The mystery body
was seen twice by the infrared satellite as it scanned the
northern sky from last January to November, when the satellite
ran out of the supercold helium that allowed its telescope to
see the coldest bodies in the heavens. The second observation
took place six months after the first and suggested the
mystery body had not moved from its spot in the sky near the
western edge of the constellation Orion in that time.?
Further on the article states:
<<The most fascinating
explanation of this mystery body, which is so cold it casts no
light and has never been seen by optical telescopes on Earth
or in space, and that it is a giant gaseous planet as large as
Jupiter and as close to Earth as 50 trillion miles.>>
This number was corrected by the Post the following day to ?50
billion miles?, which is about 538 AU (astronomical unit, 1 AU
being the distance from the Earth to the Sun). The article
continues:
<<'All I can tell you is
that we don't know what it is,' Dr.
Gerry Neugebauer, IRAS
chief scientist for California's Jet Propulsion Laboratory and
director of the Palomar Observatory for the California
Institute of Technology, said in an interview.>>
The researchers apparently had some idea of how big the object
is though from the additional comments of Dr. James
Houck of Cornell University's Center for Radio Physics
and Space Research and a member of the IRAS science team, who
designed the IRAS instrumentation. In commenting on the
fact that the object hadn't appeared to move over the six months
of the two observations, he said <<This
suggests it?s not a comet because a comet would not be as
large as the one we?ve observed and a comet would probably
have moved. A planet may have moved if it were as close as 50
billion miles but it could still be a more distant planet and
not have moved in six months time.>>
Additional information on the IRAS discovery came out in the
national press the following summer. US
News and World Report published an article in its
September 10, 1984, issue entitled <<Planet
X ? Is It Really Out There?>> in which Dr. Neugebauer is
again quoted as having confirmed the previous year's
observations [5]. The article was very clear that the
astronomer believed that IRAS had detected something large
within the solar system:
<<Last year, the
infrared astronomical satellite (IRAS), circling in a polar
orbit 560 miles from the Earth, detected heat from an object
about 50 billion miles away that is now the subject of intense
speculation... Scientists are hopeful that the one-
journeys of the Pioneer 10 and 11 space probes may help to
locate the nameless body.>>
The questions raised in the article involved only what exactly
the object is, not whether it was really observed or actually
exists, which the article makes clear towards the end:
<<Some astronomers say
the heat-emitting object is an unseen collapsed star or 'brown
dwarf' - a protostar that never got hot enough to become a
star. However, a growing number of astronomers insist
that the object is a dark, gaseous mass that is slowly
evolving into a planet.>>
One week later in its next issue the magazine withdrew the
article, which was the last official mention of the object to
appear in the national media press to the best of this author's
knowledge. Something had changed.
In early 1984 a series of peer-reviewed papers by NASA and a few
universities began appearing in various science journals to
parse the IRAS findings, most of which listed both Neugebauer
and Houck as coauthors. One of the first of these indicated
that the IRAS mission had accomplished the impressive task of
surveying over 72% of the sky and imaging some 8709 infrared
sources, of which NASA had highlighted nine in particular
because they appeared in no existing catalogs of 'nonstellar
sources' [6]. No mention whatsoever was made about the much
closer object at 50 billion miles distance in the Orion
constellation that IRAS had seen twice the previous year and
splashed across the front page of the Washington
Post only a few months earlier.
The next telling paper came out a year later, in which NASA
identified eight of the nine uncatalogued objects listed earlier
as galaxies [7]. The ninth source was later declared to be
a galaxy as well. Two astronomers from the University of
Arizona's Steward Observatory took a bit longer to get the
message and published contrary papers in the mid 1980s
based on their detection of radio signals from some of the nine
sources, but they too soon came around to the official view that
all nine of the sources had to be galaxies and there were no
others in question. None of the NASA papers or those of the
Steward Observatory ever mentioned the object announced on the
front page of the Washington
Post that December day in late
1983.
That this object actually exists and that NASA has been analyzing it
now for over 30 years appears to be close to certain. In official
circles the object has been called a "hypothetical" gas giant living in
the far reaches of the Oort cloud, which astrophysicists and NASA call Tyche,
but NASA now claims in a more recent infrared satellite search
for it they couldn't find it so therefore it must not
exist. Other names being used run the range of Planet
X, Nibiru, Nemesis, and Vulcan. We'll
use the less common name Vulcan
to clearly distinguish the Sun's
distant
companion from other conceptual possibilities such as
Planet X or something else in the Kuiper Belt or Oort
cloud. The following analysis explores some of the
implications of this discovery from the standpoint of physics,
but doesn't really depend on whether NASA spotted Vulcan or
not.
Solar System Formation
Whether a massive unseen object is looming in the outer reaches
of the Sun's gravitational dominion or not, something about the
solar system's configuration is a bit odd in any case. The
mass of the Sun contains over 99% of the mass of the entire
known solar system and yet less than 4% of its angular
momentum. From classical physics we know that angular
momentum is always conserved in a "closed system", so how can
there be such a skewed imbalance between how much the Sun has
versus how much the planets have? Jupiter has over 60% of
the system's angular momentum by itself. The great minds of
astronomy have never reached a consensus on why this is so or
why an even larger disparity discussed below is also
glaring. There's a deep puzzle about the solar system's
arrangement, and this paper will attempt to unravel
it.
The most widely accepted model of the solar system's origin,
believed to be at work throughout the galaxy, is called the
nebular hypothesis, first proposed in the mid 18th century by
the Swedish scientist-mystic Emanuel
Swedenborg, followed shortly by philosopher Immanuel
Kant and the French polymath Simon
La Place. According to this model stellar
planetary systems begin as a massive cloud of matter, mostly
dust particles and molecular hydrogen, that coalesces into
clumps under gravitational attraction, which causes them to
collapse into a swirling mass that forms stars and
planets. A refinement of this theory called the solar
nebular disk model (SNDM) says that the evolving nebula also
tends to form a flat protostellar accretion disk with thickness
much less than its radius that rotates in the same direction and
roughly in the same plane. This rotating mass has massive
angular momentum, which earlier in the system's formation can be
partially lost due to passing stars, stellar winds and various
other dissipation processes, aided by the structure's weak
gravitational field, but at some point the structure becomes
stable. At this point the angular momentum of the system
remains approximately constant as long as the stellar system's
mass stays intact and large external influences are
minor. Angular momentum is always preserved in closed
systems, so our own solar system would normally be expected to
have most of its later stage angular momentum still intact.
The collapse of a molecular cloud into a protostellar disk goes
through several stages which astronomers label Class 0 through
Class III. Our focus and the research being leveraged involves
the Class I stage, which begins at the end of Class 0, about
100,000 years after the start of collapse. At this point
the accretion disk is formed, although a hazy envelope of mass
still surrounds the disk and protostar. At the end of Class I
the disk's surrounding envelope is largely dispersed, at least
80% of the mass of the future star is accreted into the newly
formed protostar, and the disk itself has reached a certain
dynamic stability. From this point on the greater part of
the disk's angular moment should be conserved in the evolving
stellar system. For stars of relatively low mass such as
the Sun, the loss of angular momentum from the protostar / disk
system due to stellar winds and other sources is normally small
from this point on. In any case the system's angular
momentum has to be at least as great as the amount that the
solar system has today, an obvious premise we use
throughout.
One key goal of the following discussion is to come up with an
approximate lower bound for the angular momentum of the Sun's
disk at a representative point in its early development, which
specifically does not encompass attempting to develop a model of
the protostellar disk's dynamic behavior and evolution over
time. To this end we opt to consider the protostellar disk
at the end of the Class I stage and take the most conservative
estimates available for each parameter used in our analysis,
where ?conservative? is taken to mean that value which implies a
low or lowest associated value for the disk's angular momentum
among all accepted values. The approach draws heavily from
data given in a recent survey paper by Williams
and Cieza published in
the 2011 issue of Annual Review of Astronomy and Astrophysics
[8] in which the findings of a number of astronomical
observational studies are described. With the approach
given herein some interesting inconsistencies with the current
state of the solar system emerge, and the implications of these
are used to assess a possible
solution.
The motion of material in a protostellar accretion disk is
believed to closely follow a Keplerian rotation in which a
subtle outwardly directed influence is embedded. If G is
Newton's constant of gravity, then at a distance r from the
accreting protosolar mass M, the angular velocity w of a thin
ring of matter around the disk at that radius is described by
the rule [9, 10]:
w
= √G M / r3.
(1)
<<... planetary scientists at NASA's Ames Research Center plan to use the Infrared Astronomy Satellite (IRAS) planned for launch next month, to try to find a brown dwarf in our solar system or even farther out in space.>>
Interestingly, a diagram of the solar system in the article depicts both celestial objects, Planet X and the dark star, and the two space probes, Pioneer 10 shown as heading nominally in the presumed direction of the two proposed objects and Pioneer 11 heading in the opposite direction. It was becoming apparent that authorities were considering the possibility of two large unseen objects in the solar system.
That strategy apparently worked. IRAS was launched in January 1983, and later that year NASA made the official announcement that the satellite had in fact detected the infrared signature of a large celestial body beyond the orbit of Pluto. An article proclaiming the event appeared on the front page of the prestigious Washington Post in December of that year: ?Mystery Heavenly Body Discovered? [4]. The article begins ?A heavenly body possibly as large as the giant planet Jupiter and possibly so close to Earth that it would be part of this solar system has been found in the direction of the constellation Orion by an orbiting telescope aboard the U.S. Infrared Astronomical Satellite (IRAS).... The mystery body was seen twice by the infrared satellite as it scanned the northern sky from last January to November, when the satellite ran out of the supercold helium that allowed its telescope to see the coldest bodies in the heavens. The second observation took place six months after the first and suggested the mystery body had not moved from its spot in the sky near the western edge of the constellation Orion in that time.?
Further on the article states:
<<The most fascinating explanation of this mystery body, which is so cold it casts no light and has never been seen by optical telescopes on Earth or in space, and that it is a giant gaseous planet as large as Jupiter and as close to Earth as 50 trillion miles.>>
This number was corrected by the Post the following day to ?50 billion miles?, which is about 538 AU (astronomical unit, 1 AU being the distance from the Earth to the Sun). The article continues:
<<'All I can tell you is that we don't know what it is,' Dr. Gerry Neugebauer, IRAS chief scientist for California's Jet Propulsion Laboratory and director of the Palomar Observatory for the California Institute of Technology, said in an interview.>>
The researchers apparently had some idea of how big the object is though from the additional comments of Dr. James Houck of Cornell University's Center for Radio Physics and Space Research and a member of the IRAS science team, who designed the IRAS instrumentation. In commenting on the fact that the object hadn't appeared to move over the six months of the two observations, he said <<This suggests it?s not a comet because a comet would not be as large as the one we?ve observed and a comet would probably have moved. A planet may have moved if it were as close as 50 billion miles but it could still be a more distant planet and not have moved in six months time.>>
Additional information on the IRAS discovery came out in the national press the following summer. US News and World Report published an article in its September 10, 1984, issue entitled <<Planet X ? Is It Really Out There?>> in which Dr. Neugebauer is again quoted as having confirmed the previous year's observations [5]. The article was very clear that the astronomer believed that IRAS had detected something large within the solar system:
<<Last year, the infrared astronomical satellite (IRAS), circling in a polar orbit 560 miles from the Earth, detected heat from an object about 50 billion miles away that is now the subject of intense speculation... Scientists are hopeful that the one- journeys of the Pioneer 10 and 11 space probes may help to locate the nameless body.>>
The questions raised in the article involved only what exactly the object is, not whether it was really observed or actually exists, which the article makes clear towards the end:
<<Some astronomers say the heat-emitting object is an unseen collapsed star or 'brown dwarf' - a protostar that never got hot enough to become a star. However, a growing number of astronomers insist that the object is a dark, gaseous mass that is slowly evolving into a planet.>>
One week later in its next issue the magazine withdrew the article, which was the last official mention of the object to appear in the national media press to the best of this author's knowledge. Something had changed.
In early 1984 a series of peer-reviewed papers by NASA and a few universities began appearing in various science journals to parse the IRAS findings, most of which listed both Neugebauer and Houck as coauthors. One of the first of these indicated that the IRAS mission had accomplished the impressive task of surveying over 72% of the sky and imaging some 8709 infrared sources, of which NASA had highlighted nine in particular because they appeared in no existing catalogs of 'nonstellar sources' [6]. No mention whatsoever was made about the much closer object at 50 billion miles distance in the Orion constellation that IRAS had seen twice the previous year and splashed across the front page of the Washington Post only a few months earlier.
The next telling paper came out a year later, in which NASA identified eight of the nine uncatalogued objects listed earlier as galaxies [7]. The ninth source was later declared to be a galaxy as well. Two astronomers from the University of Arizona's Steward Observatory took a bit longer to get the message and published contrary papers in the mid 1980s based on their detection of radio signals from some of the nine sources, but they too soon came around to the official view that all nine of the sources had to be galaxies and there were no others in question. None of the NASA papers or those of the Steward Observatory ever mentioned the object announced on the front page of the Washington Post that December day in late 1983.
That this object actually exists and that NASA has been analyzing it now for over 30 years appears to be close to certain. In official circles the object has been called a "hypothetical" gas giant living in the far reaches of the Oort cloud, which astrophysicists and NASA call Tyche, but NASA now claims in a more recent infrared satellite search for it they couldn't find it so therefore it must not exist. Other names being used run the range of Planet X, Nibiru, Nemesis, and Vulcan. We'll use the less common name Vulcan to clearly distinguish the Sun's distant companion from other conceptual possibilities such as Planet X or something else in the Kuiper Belt or Oort cloud. The following analysis explores some of the implications of this discovery from the standpoint of physics, but doesn't really depend on whether NASA spotted Vulcan or not.
Solar System Formation
Whether a massive unseen object is looming in the outer reaches of the Sun's gravitational dominion or not, something about the solar system's configuration is a bit odd in any case. The mass of the Sun contains over 99% of the mass of the entire known solar system and yet less than 4% of its angular momentum. From classical physics we know that angular momentum is always conserved in a "closed system", so how can there be such a skewed imbalance between how much the Sun has versus how much the planets have? Jupiter has over 60% of the system's angular momentum by itself. The great minds of astronomy have never reached a consensus on why this is so or why an even larger disparity discussed below is also glaring. There's a deep puzzle about the solar system's arrangement, and this paper will attempt to unravel it.
The most widely accepted model of the solar system's origin, believed to be at work throughout the galaxy, is called the nebular hypothesis, first proposed in the mid 18th century by the Swedish scientist-mystic Emanuel Swedenborg, followed shortly by philosopher Immanuel Kant and the French polymath Simon La Place. According to this model stellar planetary systems begin as a massive cloud of matter, mostly dust particles and molecular hydrogen, that coalesces into clumps under gravitational attraction, which causes them to collapse into a swirling mass that forms stars and planets. A refinement of this theory called the solar nebular disk model (SNDM) says that the evolving nebula also tends to form a flat protostellar accretion disk with thickness much less than its radius that rotates in the same direction and roughly in the same plane. This rotating mass has massive angular momentum, which earlier in the system's formation can be partially lost due to passing stars, stellar winds and various other dissipation processes, aided by the structure's weak gravitational field, but at some point the structure becomes stable. At this point the angular momentum of the system remains approximately constant as long as the stellar system's mass stays intact and large external influences are minor. Angular momentum is always preserved in closed systems, so our own solar system would normally be expected to have most of its later stage angular momentum still intact.
The collapse of a molecular cloud into a protostellar disk goes through several stages which astronomers label Class 0 through Class III. Our focus and the research being leveraged involves the Class I stage, which begins at the end of Class 0, about 100,000 years after the start of collapse. At this point the accretion disk is formed, although a hazy envelope of mass still surrounds the disk and protostar. At the end of Class I the disk's surrounding envelope is largely dispersed, at least 80% of the mass of the future star is accreted into the newly formed protostar, and the disk itself has reached a certain dynamic stability. From this point on the greater part of the disk's angular moment should be conserved in the evolving stellar system. For stars of relatively low mass such as the Sun, the loss of angular momentum from the protostar / disk system due to stellar winds and other sources is normally small from this point on. In any case the system's angular momentum has to be at least as great as the amount that the solar system has today, an obvious premise we use throughout.
One key goal of the following discussion is to come up with an approximate lower bound for the angular momentum of the Sun's disk at a representative point in its early development, which specifically does not encompass attempting to develop a model of the protostellar disk's dynamic behavior and evolution over time. To this end we opt to consider the protostellar disk at the end of the Class I stage and take the most conservative estimates available for each parameter used in our analysis, where ?conservative? is taken to mean that value which implies a low or lowest associated value for the disk's angular momentum among all accepted values. The approach draws heavily from data given in a recent survey paper by Williams and Cieza published in the 2011 issue of Annual Review of Astronomy and Astrophysics [8] in which the findings of a number of astronomical observational studies are described. With the approach given herein some interesting inconsistencies with the current state of the solar system emerge, and the implications of these are used to assess a possible solution.
The motion of material in a protostellar accretion disk is believed to closely follow a Keplerian rotation in which a subtle outwardly directed influence is embedded. If G is Newton's constant of gravity, then at a distance r from the accreting protosolar mass M, the angular velocity w of a thin ring of matter around the disk at that radius is described by the rule [9, 10]:
The rotation is circularized by gravity around the accreting mass
and increases in speed with decreasing radius, producing an inwardly
swirling flow of matter that rotates ever faster as it spirals in
towards the protoSun. The accretion disk's angular momentum
under the influence of the Keplerian rotation in general is fairly
complex. As matter swirls into the Sun it brings angular
momentum with it which would normally increase the planetary
system's angular momentum. But angular momentum is always conserved
in a closed system, so the accretion disk has to do something else
to reduce it somehow, which it does by 'transporting' it
outwards. This process occurs because adjacent rings of
material in the disk rotate at slightly different rates, which
produces an outwardly-directed torque in the material of the
disk. The torque generates heat and also transports matter away
from the center of rotation, which increases the disk's angular
momentum at the expense of the protostar's angular
momentum. This effect accounts for at least part of the reason
why the Sun's angular momentum accounts for only about 4% of that of
the entire solar system, since the Sun can lose it to the transport
process. The evolution of the accretion disk is a constant
struggle between these two opposing effects, but amazingly at some
point in time this conflict settles down and the ensemble angular
momentum of the disk remains constant over time.
The following table provides a summary of the angular momentum of
each primary body in the solar system, together with other relevant
parameters, where the angular momentum of the Sun provided is due
solely to its rotation and those of the planets are due strictly to
their orbital motion. Specifically, the Sun is presumed to have
no orbital angular momentum by conventional astronomy. Although
countless smaller bodies are also members of the solar system, these
listed in the table are believed to represent over 99.99% of the
mass and angular momentum of the known solar system. As can be
seen, Jupiter, Saturn and Neptune all have angular momenta much
greater than the Sun's, and in fact Jupiter alone has over 60% of
the angular momentum of the entire solar system. From this
summary the total current angular momentum of the planetary solar
system is found to be a little over 3.1 x 1043 kg-m2/sec,
which is almost 30 times that of the Sun alone.
Table 1.0 Angular Momentum in the Solar System
The angular momentum of the solar system's accretion disk can best
be understood by considering a thin band around the Sun made up of a
circular cross-sectional increment of the disk's material. The
band's angular momentum is simply the expression from classical
physics, mr r2
w,
where mr is
the
mass of the band, r is the distance from the center of rotation and
w is the band's angular rate of rotation. Because w is simply
the rate from equation (1) above, the band's angular momentum
Jr can be written by combining the two equations; the term with
the radical is known as the specific angular momentum, the angular
momentum per unit mass.
Jr = mr r2 w = mr (G M r)1/2 . (2)
But mr also varies with
radius because the density of the bands drops off with distance and
also because the bands get larger as their distance from the Sun
increases. Density is believed to vary as r to the power -p
where p according to Williams and Cieza is always less than 1.5,
which we take here as the most conservative density profile that
drops off the fastest, thereby producing the least angular momentum
for our model. That said a small increment dm of the disk's
total mass m is computed by taking the disk's density to use the
above density rule times its height y, assumed to be roughly
constant, its length 2?r and thickness dr, where all
constants in the calculation are collected together in the single
constant K:
dm
= k r-3/2
2 p r y dr = K r-1/2
dr
The total mass of the disk is then computed by integration:
m R
m = ∫ dm = ∫ K r-1/2 dr = 2 K √R - 2 K √Ro ≈ 2 K √R
mo Ro
The second term is omitted as insignificant due to the
relatively small size of Ro and therefore the mass of the disk
is found to increase as the square root of the disk's radius for
this model.
To compute the angular momentum J of the accretion disk with
mass m, we integrate the angular momenta of all the incremental
bands that make up the disk from the surface of the protostar to
the outer edge of the protostellar disk
m R
J = ∫ √G M r dm = ∫√ G M r K r-1/2 dr (4)
mo Ro
= ˝ 2K √R √G M R - ˝ 2 K √Ro √G M Ro ≈ ˝ m √G M R (5)
This last expression follows from collecting together the parameters
for the disk's total mass m from equation (3), excluding that
within the protoSun's radius, and from the fact that the lower limit
Ro is the radius of the protoSun and again can be ignored in the
following analysis since its value is several orders of magnitude
smaller than the outermost radius of the solar system R. The
solution of interest becomes only the first term of the
integration. It's interesting that even though the angular
velocity of the disk decreases with increasing R from equation (1),
the corresponding angular momentum increases linearly when we take
the variation of mass into account. To be very clear, the above
equation represents the instantaneous angular momentum of the non
solar mass contained in the protostellar accretion disk once the
Class I stage has ended.
The most controversial part of the calculation is picking realistic
values for the constants used in the computations, in particular
that of the early solar system's effective radius. To do this
we use the research of Williams and Cieza again. To make the
numbers easier to work with we use "solar coordinates" to express
the various quantities with most of the time, where S is the unit of
mass expressed as multiples of solar mass, yr is the integer number
of years and AU is astronomical units, one AU being the distance
from the Earth to the Sun.
The mass of a Class I protostellar disk in theory can be as high as
20% of the mass of the protostar's mass and even
greater. Williams and Cieza quote an astronomical study of 20
Class 0 and 1 protostars, however, in which the mass was seen to
vary from 0.02 to 0.10 solar masses with a median value of 0.04,
although the masses of the stars were not provided. The lower
value is the more conservative, and this is the one selected for the
study. A lower value of disk mass is not all that unreasonable
in any case because the researchers site another study that
indicates the protostar typically gains half its mass from the
accretion disk in only about 7% of the 500,000 years of its Class 0
and I lifetime.
The radius of a protostellar disk varies considerably and is
difficult for astronomers to assess reliably in any case because of
the disk's tenuous structure in its outer regions that causes it to
emit only very weakly. Several studies have been performed of
protostellar disks in the Orion constellation, however, one of which
had a sample of 125 disks for which the researchers inferred a
median radius of 75 AU. Another study of Orion protoplanetary
disks found that radii varied from 50 to 194 AU, so because 50 AU
was the smallest identified, in the interest of angular momentum
conservatism we'll use 50 AU.
So, with these numbers we estimate a lower bound for the angular
momentum Jp of the protostellar accretion disk corresponding to the
values for mass and disk radius indication, and using the
interesting fact that in the units being used GM equals (2p)2:
Jp = ˝ ( .02 S ) (6.28 )? 50 = 0.444 S-AU 2 / yr. (6)
In comparison, the known angular momentum of the solar system's
0.14% non solar mass is known to be
J = 3.1 x 10 43 kg-m2/sec = .0219 S-AU 2 / yr. (7)
Adding in the Sun's angular momentum due to rotation, the angular
momentum of the entire known solar system is therefore not much
larger:
JT = 3.21 x 10 43 kg-m2/sec = .0227 S-AU 2 / yr. (8)
This value is an order of magnitude smaller than the above
theoretical ?minimum? value Jp, which in a nutshell is the problem
at hand. Over 95% of the solar system's minimal protostellar
angular momentum is now missing. In a study cited by Williams
and Cieza that was performed in 2009 on eleven protostellar disks,
the researchers found that the specific angular momentum, i.e. the
angular momentum per unit mass, of all of them fell in the range of 1015.4 m2/ s to 1016.9 m2/ s. Using the specific angular
momentum is nice on the one hand in that it removes the relative
effect of mass which serves to make comparisons easier. But it
also adds a degree of subtlety that warrants a note of caution,
because it tends to compress differences. The specific angular
moment of Jupiter for example is 1.02x1016 , but that of all the
planets taken together is 1.11x1016. Even though Jupiter has
62% of the planetary angular momentum, it has over 98% of the
planetary specific angular momentum. Similarly, the lower bound for
the specific angular momentum corresponding to Jp computed in
equation (6) is 1.57 x 1016, only 40% larger than that of all the
planets taken together even though Jp is 20 times larger than J, the
angular momentum of all the planets together. The main message to
note here is that although Jp falls in the middle of the range
found in the study, so does the specific angular momentum of the
planetary solar system. Both numbers are ?reasonable? in the
sense of falling in the range of actual observations. From this
sample alone we cannot conclude that the solar system's angular
momentum looks odd.
Whatever subtle dynamics the solar system may have gone through
during its evolution that caused it to lose more than 95% of its
angular momentum, perhaps much more, however, this massive loss has
no explanation in conventional astronomy, the above study
notwithstanding. The loss is excessive by any measure, but in
all likelihood is probably considerably larger yet, because of the
extremely conservative approach used to estimate the lower bound
derived for the solar system's protostellar angular momentum at the
end of its Class I stage. But could it be that the original
angular momentum didn't get lost at all and is still somehow hiding
in the solar system? A body of sufficient mass in a long-period
orbit could possibly account for the apparent
loss.
A Binary Alternative
The galaxy's organization is now known to be very different in some
ways than astronomers had long presumed. Of the stars nearest
our Sun over half have been shown to be in binary or higher multiple
systems, a fact which is apparently true throughout the
galaxy. One recent estimate even places the frequency of
multiply related stars in the Milky Way as high as 85%. With
such a high rate of occurrence and given the apparently low value of
angular momentum observed in the solar system today, an interesting
possibility is that our own star might be in a binary system itself,
which raises the question about whether any evidence exists that can
support or conversely rule out such a theory.
A binary companion for the Sun could answer both puzzles of the
solar system's and the Sun's angular momentum both being apparently
too small. Binary systems of low mass stars can have orbital
angular momenta three orders of magnitude larger that of the solar
system and five orders greater than the spin angular momentum
of the Sun, which rotates at a rate typical of low-mass
stars. If we assume that a hidden solar twin does exist, then
its additional angular momentum may be able to explain why the Sun's
and solar system's is so small. Maybe the solar system's
angular momentum didn't really go away, it was just transferred to
something we can't see. The following analysis sheds light on
just how big such a hidden twin might be.
Orbital Analysis
If we know the approximate orbital period and eccentricity of a body
in orbit around the Sun, Vulcan if you will, and we ignore minor
perturbations induced by the planets, then we can compute its
Vulcan's orbital semi major axis and mass uniquely, provided that we
have some idea of the solar system's ?original? angular momentum,
which we now have in the form of our lower bound estimate. The
particular period and eccentricity to use comes from various
sources, but there are not many that have been proposed, and so we
examine a few of these. To begin with, we describe the
methodology to be used.
We need to know how to calculate key attributes about the binary
system's orbit including the semi-major axis of its orbital ellipse,
its angular momentum and the mass of the Sun's dark twin. For
the semi-major axis, using Kepler's third law we know that the
period T of two objects in orbit around one another satisfies the
following relationship:
T 2 = 4 p2 a3 / G (M + m) (9)
T is the orbital period of the orbiting body around the Sun,
M is the mass of the larger, central body, here taken to be the Sun
m is the mass of the second object
G is the Newton's gravitational constant and,
a is the semi-major axis of the orbital ellipse.
If a is expressed in astronomical units (AU's), M and m are in
multiples of solar mass and T is in years, then M is unity, m is a
fraction (of the Sun's mass), the other constants can be suppressed
and we can recast the above equation to calculate the semi-major
axis as
a = ( T2 (M + m) )1/3 (10)
Another key expression we need is called the specific relative
angular momentum h, which is the total orbital angular momentum per
unit mass of two orbiting bodies. In a closed system this
quantity is constant, a direct consequence of Kepler's second law,
which says that a line joining a planet and the Sun sweeps out equal
areas in equal time intervals. For h, this statement is basically
another way of saying that angular momentum is conserved. There are
a number of equivalent ways to express h, but the one most useful
for us is given as:
h = ( 2p / T ) a2 √ 1 - e2 (11)
Using h and standard astrophysics the total orbital angular momentum
J of the two bodies relative to their center of mass is then h times
the ?reduced mass? of the bodies. Note that this is the total
orbital angular of the dark companion and the Sun, since the Sun now
has an orbit around its companion as well. Because at least 95%
and most likely much more of the solar system's orbital angular
momentum is unaccounted for, the analysis ignores the relatively
small planetary angular momentum and for convenience of calculation
assigns that of the entire accretion disk to the Sun's dark
companion. The primordial disk not only produced a small dark
star with angular momentum, but in the process induced orbital
angular momentum in the Sun as well in its role as the larger member
of a binary system. Accordingly, J is then the combined
orbital angular momentum of both bodies, and is given by:
Jp = h M m / (M + m ). (12)
For a given period and eccentricity the above equations can be used
to solve for the mass and semi major axis of the dark companion
uniquely. By fixing the eccentricity, orbital period and
angular momentum of the solar system, the orbital semi major axis
and mass of the hidden companion form a unique matched set defined
by equations (10), (11) and (12). Specifically, when a star
with known mass has an object in orbit around it with known period
and eccentricity, then that object's mass and semi major axis are
determined uniquely. To compute these parameters from the
equations directly is a bit messy, however, but fortunately there is
a simpler way. If we solve for m in equation (12), we can
create a recursive algorithm to determine both quantities using a
simple bootstrap scheme. The desired expression for m is
m = Jp M / (M h - Jp ) (13)
By setting m to zero initially and using equations (10), (11)
and (13) in that order recursively, both parameters can be readily
calculated. Once the initial value for m is computed in equation
(13) the next iteration simply uses that value of the dark object's
mass in equation (10) in the next iteration. Notice that each
iteration also produces an updated version of the semi-major axis a,
which is used for other calculations within that iteration. The
algorithm converges quickly; two iterations are normally sufficient
to compute both parameters of interest, m and a, to three or more
decimal places.
The following table provides the calculated value of m using this
methodology for a range of orbital scenarios of interest. The
values m and a computed for each scenario completely compensates for
the "missing" angular momentum defined as the difference between the
known and presumed theoretical value used in the computations given
in column four of the table. The measure of Vulcan's mass in
terms of Jovian masses in column nine, Jupiter's mass being
0.0009546 S, is interesting, and gives maybe a clearer idea of the
range of possible sizes of the Sun's dark companion.
The scenarios examined center around four particular orbital
periods. The first of these is 3661 years proposed for Planet X
by historian Zecharia Sitchin and examined by a number of
researchers including me. The period of 5000 years is the
approximate period proposed by physicist Barry
Warmkessel [11] based on his analysis of comets and other
phenomena. The mass for the dark star he proposes to be less
than 0.0005 solar masses. The third period derives from NASA's
announced detection of an object in 1983 at a distance of some 50
billion miles (537 AU). We don't really have any way to know
where the object was in its orbit since NASA only published the one
number, but if we assume arbitrarily that the distance away then was
about half the length of its orbit which equals the length of its
semi-major axis, then the resulting period turns out to be a little
under 12500 years. The last period of interest is 26000 years
proposed by researcher Walter
Cruttenden [12], which matches the time the Earth's
precession takes to complete a full 360° cycle. Cruttenden
proposes that the Sun's dark companion contributes to the precession
and that its orbit might be synchronized with the precession, which
interestingly enough seems to be slowing down. (This writer
strongly disagrees with this view, by the way.) The mass for the
dark star he proposes as .06 solar masses. The eccentricities
of .54 and .90 were selected because one researcher is pushing very
hard for the former, and the latter induces a cometary orbit for
comparison. Also, visual binary stars have been found to have
eccentricities of about .50 on average anyway, so the former number
is close to one we might expect anyway. Other values can
readily be evaluated using the computational methodology provided
above.
Table 2.0 Characteristics of the Dark Companion
To close the gap between the solar system's currently presumed
angular momentum and an associated ?original? value computed from
data based on astronomical observations of protostellar disks in the
Milky Way, Table 2.0 indicates that an object of several Jovian
masses is required. Orbits with larger periods clearly reduce
the required size of the object as expected. It's interesting
that if such an object is several thousand AU distance and emits
primarily in the infrared, it could indeed be very difficult to
observe and its effect on the solar system is apparent primarily
through its angular momentum. The above argument is interesting
and credible, but is it really true? There may be a way to
determine its validity by direct measurement, however. If an
object of several Jovian masses is adding angular momentum to the
solar system, then the Sun can tell us.
Perturbing the Sun
Knowing roughly what Vulcan's orbit looks like, we can now probe the
question regarding to what extent if any the Sun is being influenced
by Vulcan's presence. According to the laws of celestial
mechanics two bodies orbiting each other are really both orbiting a
fixed point in space between them, the location of their common
center of mass. Letting M and m be the mass of the Sun and
Vulcan respectively and rM and rm be the two distances from the
center of each body to the common center of mass, then the following
classical relationship holds:
M rM = m rm (14)
Both rM and rm certainly vary as the two bodies orbit
each other, but the variation occurs in a way such that equation
(14) is always satisfied. If we solve for rM in the above
expression we get the distance from the Sun's center of mass to the
center of its orbit:
rM = rm m / M. (15)
At aphelion, the point that the two bodies are farthest apart,
rM and rm are both at their maximal values and at
that point have the following relationship to the semi major axis of
Vulcan's orbit:
a (1 + e ) = rM + rm (16)
Combining equations (15) and (16) appropriately, we arrive at
rM = a ( 1 + e ) m / ( M + m
).
(17)
To get some idea of how the Sun is moving about in its dance with
Vulcan, we can assume for the sake of discussion that Vulcan is
orbiting somewhat like the orbit we guessed at to model NASA's IRAS
observation of 1983. To do this we assumed an eccentricity of
.54, an orbital period of 12500 years and a semi major axis a of 538
AU. If we consider the corresponding value of Vulcan's mass
from Table 2.0 computed as 0.0036 S and the other numbers as
indicated immediately above, then on applying equation (17) rM is
found to be about 2.97 AU for this case. This implies that the
Sun would have an orbit about the common center of mass with a
maximum radius three times Earth's orbital radius around the
Sun. With longer periods and / or a larger mass for Vulcan, the
Sun's orbital radius would be appropriately larger. Presuming
Cruttenden's 26000 yr period, the eccentricity also at 0.54 (he
actually proposed 0.038), the orbit's semi major axis of 879 AU and
a computed mass for Vulcan of 0.0063 S, then rM becomes 8.47
AU, which is larger than the orbital radius of Jupiter! An
interesting thing to note is that as with this case, the orbits of
the Sun and Vulcan never intersect. Vulcan appears to have the
orbital character of a very out-sized planet.
These equations also allow us to take a closer look at some of the
earlier proposed orbits for
Vulcan in a different light. For Dr. Warmkessel's proposed
configuration of Vulcan with period of 5000 years, eccentricity
0.54, semi-major axis of 292 AU and mass of 0.0005 S, then rM is
only 0.22 AU using equation (17), well within the orbit of Mercury.
The problem with this scenario is that the mass is too small to
account for the solar system's missing angular momentum. If the mass
figure is actually close to being correct then either the
eccentricity has to be significantly smaller, the period
considerably larger or both.
For Dr. Cruttenden's proposed Vulcan characteristics with period of
26000 years, eccentricity 0.038, semi-major axis 878 AU, and mass of
0.06 S, the value of rM becomes an astonishing 51.58 AU! The
orbit of the Sun is comparable to the orbit of Pluto, and the nearly
circular orbit implies that for his scenario Vulcan's perihelion is
845 AU. If we take the angular momentum into account and solve
the orbital equations for a, h and m accordingly, then again Dr.
Cruttenden's mass for Vulcan seems excessibely high. But again, we
don't really know how large the missing angular momentum actually
is, just its minimum size. In any case Cruttenden's orbital scenario
appears to be very
unlikely.
A crucial implication of this portion of the analysis is that it
uncovers the Sun's missing angular momentum. That portion of
the Sun's angular momentum due to its orbital dance with Vulcan is
actually embedded in equation (12), which represents the sum of both
bodies' orbital angular momentum about the pair's common center of
mass. The portion due strictly to the Sun's orbiting motion is
the counterpart to Vulcan's orbital angular momentum. The
angular momentum of the two bodies individually in the following two
equations produce equation (12) when summed together [13]:
Jsun = h M m2 / ( M + m )2 = Jp m / ( M + m ) (18)
Jvul = h m M2 / ( M + m )2 = Jp M / ( M + m ) (19)
An interesting aspect of these equations is that the angular momenta
of the Sun and Vulcan can both be calculated without knowing
anything about the orbit! All we need are Jp and the mass of each
body. Using these two equations another interesting
relationship is now apparent:
Jsun
= Jvul
m / M
(20)
The value of Jsun is entirely determined by knowledge of Jp , M and
m, which depend on the overall arguments used in the
discussion. Even though we can't know the exact size of Jsun
because Jp is only approximated and the calculation of m depends on
an assumed orbit, we can get a rough idea about the range of
Jsun from the various cases examined in Table 2.
For comparison purposes, the Sun's rotational angular momentum given
in Table 1.0 is equivalent to .0007771 S-AU2/yr in the
solar-based units we're using. In the table the lowest and
highest estimates of Jsun are .0013 and .0047 S-AU2/yr , which are
respectively 1.7 and 6.1 times more than the known value of
the Sun's rotational angular momentum. If a large body is
orbiting the Sun, the Sun's orbital angular momentum has to increase
as a result according to equation (20), the dominant influence by
far being Jp, the approximate lower bound for the angular momentum
of the protostellar accretion disk. However large Jp may turn
out to be as our knowledge of planetary evolution improves, the
Sun's missing angular momentum has finally been accounted for, at
least theoretically.
One final idea to consider is that if the Sun is actually scribing
an elliptical arc through space, this motion is detectable!
Given that the Sun is a distance r from the dark star at any
particular point in time, then the instantaneous angular velocity of
the Sun's orbit according to celestial mechanics is
Omega = (G (M + m) / r 3 ) ˝ (21)
If the Sun is rotating through space at this rate, then so is the
Earth. For an orbital period of let's say 12500 years as an
example, the associated angular rate of the Sun turns out to be
about one degree of arc every 35 years on average, or about 1.7 arc
minutes per year. Modern instrumentation can certainly sense
this rate and distinguish it for the other motions the Earth is
undergoing. Mercury's perihelion precession, used as one of the
key benchmarks of general relativity, is 0.9 arc minutes per year,
which current technology has determined to four decimal places for
at least the past two decades. Within a month or so we should
be able to have a very good idea about whether a dark star is
dragging the Sun around or not.
Discussion
As we've argued, something fairly large is missing from conventional
astronomy's description of the solar system, perhaps something that
NASA has been watching for several decades. The solar system's
angular momentum is simply too small assuming even the most
conservative estimates of that which its accretion disk must have
had in the protostellar past, given the non-solar mass and angular
momentum in the solar system we have today. There are no
obvious ways to account for the difference between the measured and
theoretical momentum values without some fairly large object in
orbit around the Sun supplying it. The Kuiper Belt and Oort
Cloud are both too short of mass by current best estimates.
Examining a variety of different orbital scenarios proposed by
various researchers suggests that in fact it takes an object with a
mass larger than Jupiter's to supply the missing momentum in all the
cases examined, given that its period is at least 5000 years based
on current theories. NASA on several occasions affirmed that the
object exists and even claimed to have imaged the object in the
infrared frequency band in 1983 using the IRAS research
satellite. That this object exists and that NASA has been
carefully watching and analyzing it for over 30 years is all but
certain, even though nothing has come out officially since the mid
80s. Based on this analysis what else can we
infer?
We looked at orbital periods that various researchers have
proposed for Vulcan based on a various arguments, although
none that used angular momentum specifically. This approach
doesn't claim where the object should be located in space but rather
assuming that it has a given period and eccentricity the study has
showed about how massive the object has to be for a lower bound of
the radius of the protostellar accretion disk. To be very
clear, a higher value of the radius implies a larger mass for
Vulcan. As with the body's orbital period, we also of course
don't know what its eccentricity is either, and so we examined two.
The average eccentricity of visual binary stars is known to be about
0.50, but one writer seems so sure that his eccentricity is right at
0.54 that we used that number instead of 0.50. The other
eccentricity selected was 0.90 which produces a cometary orbit with
an elongated semi-major axis. These two eccentricities address two
of the more interesting orbital regimes.
Conclusion
The basic premise of this study is that angular momentum is missing
from the solar system in modern astronomy's standard
reckoning. The Sun's angular momentum is disproportionately
small compared to that of planets, and that of the entire solar
system is much too small relative to conservative estimates of the
amount that the accretion disk that spawned it must have
had. Something is missing from the reckoning, and that
something may just be a large body of several Jupiter masses
orbiting the Sun well beyond the orbit of Pluto. The above
analysis showed that a body of about two to ten Jovian masses
with a variety of different orbits can account for both
irregularities. Furthermore, there is even evidence from the
early 80s that the IRAS satellite probe very likely imaged the
object in 1983. The analytical argument is difficult to dismiss
and hard observational evidence may exist as well in NASA
archives. Time will tell but there is no other solid theory on
the table that does all these things, although conventional
astronomy does in fact have a somewhat tortured argument to explain
them [14]. The authors are even somewhat apologetic in stating
that they have no real evidence for the explanation they
propose.
The angular momentum missing from the solar system is consistent
with the existence of a binary companion of the Sun. What is
particularly surprising is that the mass of companion doesn't vary
drastically in size for a variety of presumed values of the
companion's orbital period and eccentricity. In almost all
cases examined the size of the object is well under 1% of the Sun's
mass, falling between 3.0 and 11.2 Jovian masses ? not small by
any means but the smallest possible given the presumed orbital
characteristics and the lower bound for the angular momentum of the
solar system's protostellar accretion disk that spawned the our
planetary system. The hidden object could just as well be much
larger. What this means remains to be seen, but the likelihood
that our Sun does have a hidden Jovian-sized companion now seems
much more likely. The angular momentum apparently missing from the
solar system can be provided by a large body although having
considerably less than 1% of the Sun's mass.
One of the most fascinating aspects of this theory is that it's
testable. If the Sun is scribing an elliptical orbit through
space then so is the Earth and all the other planets, and current
instrumentation can sense it. A similar measurement was done
with Mercury's perihelion precession several decades ago. If we
really want to know if the solar system's missing angular momentum
is due to a large distant object in orbit around the Sun, we have
the technology to determine it. The only question is do we have
the will. And that very much remains to be
seen.
The real question of the hour is does Vulcan pose a threat to the
Earth? The best answer for now is it depends. All of the
orbits examined or that are reasonably likely imply that Vulcan's
perihelion is well outside the orbit of Pluto, but even if that's so
an object of several Jovian masses coming that close to the Sun
would be sorely felt throughout the solar system you can be
certain. Possibly a larger threat is that Vulcan may well have
its own retinue of satellites which at perihelion could come
careening through the inner solar system to create cataclysmic havoc
on a scale difficult to imagine. The other major threat of such
an object is its likely ability to drive any number of comets
hurtling in our direction. As more about Vulcan's orbit and
properties becomes known, the threat assessment will become more
realistic. For now, stay tuned.
© R.F.
February 14, 2015
Last updating, Febr. 25, 2015 - March 30, 2015
[with appropriate corrections and comments in interpreting
Dr. Warmkessel's work.]
Reproduction is allowed on the Web if accompanied by
the statement
© L. Scantamburlo - www.angelismarriti.it
Reproduced by permission.
References:
1. ?Search for the Tenth Planet?, Astronomy, Dec. 1981, p 17.
2. ?Does the Sun Have a Dark Companion??, Newsweek, June 28, 1982,
p 83.
3. Hynek, J. Allen, ?Mysterious Planet X?, Science Digest, Nov.
1982, p 42.
4. O'Toole, Thomas, ?Mystery Heavenly Body Discovered,?, The
Washington Post, Dec. 30, 1983, pg A1.
5. ?Planet X ? Is it Really Out There??, US News & World
Report, Sept. 10, 1984, p 74.
6. Houck, J., Neugebauer, G., et. al., ?Unidentified Point Sources
in the IRAS Minisurvey?, The Astrophysical Journal, 278, March
1984, pp L63- L67. This article identifies each of the nine
point sources by name and coordinate location.
7. Houck, J., Neugebauer, G., et. al., ?Unidentified IRAS
Sources: Ultrahigh-Luminosity Galaxies?, The Astrophysical
Journal, 290, March 1985, pp L5- L8.
8. Williams, J., Cieza, L., ?Protoplanetary Disks and Their
Evolution?, Annual Review of Astronomy and Astrophysics 49, 2011,
pp 67- 117.
9. Beskin, V., et. al., Accretion Disks, Jets and High Energy
Phenomena in Astrophysics, Springer Verlag, Berlin, 2003.
10. Benacquista, M., An Introduction to the Evolution of Single
and Binary Stars, Springer Verlag, Berlin, 2013. Many of the
ideas herein are described in Chapter 2 of this excellent
source.
11. Kuehne, H., Warmkessel, B., ?Vulcan's New Orbital Parameters?,
http://www.barry.warmkessel.com/2002Paper.html.
12. Cruttenden, W., ?Calculations?,
http://www.binaryresearchinstitute.org/bri/research/calculations/size.shtml
He
also suggests other orbital periods as well that corresponds to
the length of the precession cycle in times past.
13. Kleppner, D., Kolendow, R., An Introduction to Mechanics,
McGraw-Hill, New York, 1973.
14. Rozelot, J., Neiner, C. ed., The Rotation of Sun and Stars,
Springer Verlag, Berlin, 2010, pp 1- 14.
15. Nibiru, Mystery Heavenly Body Solved? 2013,
https://www.youtube.com/watch?v=R_iHAhU_gE4 This is an
interesting video on the early publications about the IRAS mission
findings.
16. The Binary Star of the Sun, 2013,
https://angeliinastronave.wordpress.com/2013/02/26/la-stella-binaria-del-sole-parte-1-di-2-lombra-del-pianeta-x-
dietro-la-pioggia-di-meteoriti/
An interesting web article on the Sun's alleged binary companion.
17. Cruttenden, W., The Lost Star, St. Lynn's Press, Pittsburgh,
PA, 2005.
18. Lloyd, A., The Dark Star: The Planet X Evidence,
Timeless Voyager Press, Santa Barbara, CA, 2005.

COMMENT
AND FURTHER REFERECENS
by Luca Scantamburlo
I
suggest to the public to read or just to refer to the
following writings and books:
The
Scientific Search for a Missing Planet. SCIENTIFIC
ARTICLES AND STUDIES ON PLANET X. IS IT NIBIRU/MARDUK VENERATED
IN MESOPOTAMIA?
by Luca
Scantamburlo,
February 22, 2008, www.angelismarriti.it
Article in English language
Alla ricerca
di Nibiru. Forze occulte del papato nell'epoca del contatto
Youcanprint.it, Borč Srl, (Tricase, Lecce), Italy
PAPERBACK and EBOOK edition
February 22, 2008, www.angelismarriti.it
Article in English language
Alla ricerca di Nibiru. Forze occulte del papato nell'epoca del contatto
Youcanprint.it, Borč Srl, (Tricase, Lecce), Italy
PAPERBACK and EBOOK edition
by Luca Scantamburlo
Fist edition
in Italian language, May 2014
Nel segno di
Nibiru. Dalla Mesopotamia ai segreti vaticani
Nel segno di Nibiru. Dalla Mesopotamia ai segreti vaticani
by Luca Scantamburlo
Youcanprint.it, Borč Srl, (Tricase, Lecce), Italy
PAPERBACK
and
EBOOK edition
New edition, June 2013
First edition (The
American Armageddon), with Lulu.com, Lulu Press,
Inc.,USA, 2009
Youcanprint.it, Borč Srl, (Tricase, Lecce),
L'ombra
del Pianeta X. Storia del Decimo pianeta, fra Servizi segreti ed
insider
by Luca Scantamburlo
Youcanprint.it, Borč Srl, (Tricase, Lecce), Italy
PAPERBACK
and
EBOOK edition
First
edition in Italian language, May 2013
Apocalisse
dallo Spazio. L'avvento di Nibiru e dei Vigilanti
Youcanprint.it, Borč Srl, (Tricase, Lecce),
Apocalisse dallo Spazio. L'avvento di Nibiru e dei Vigilanti
by Luca Scantamburlo
Youcanprint, Borč Srl, (Tricase, Lecce), Italy
Youcanprint, Borč Srl, (Tricase, Lecce), Italy
PAPERBACK and EBOOK edition
New and
revised edition in Italian language, Jan. 2015
First edition with Lulu.com, Lulu Press, Inc., Lulu
Enterprises, Inc., USA,October 2011
First edition with Lulu.com, Lulu Press, Inc., Lulu Enterprises, Inc., USA,October 2011
Other interesting and well written books on the subject are the
following:
Planet
X and Pluto
by William Graves Hoyt, The University of Arizona Press
Tucson, Arizona, 1980
The
Elements of Astronomy
by Edward Arthur Fath, McGraw-Hill Book Company,
New York and London, 1944
by Edward Arthur Fath, McGraw-Hill Book Company,
New York and London, 1944
1 statute mile (sta.mi.) = 1.61 km
1 nautical mile (knot) = 1.853 km (1.15 sta.mi)
1 Astronomical Unit (A.U.) = 149597870 km.
1 statute mile (sta.mi.) = 1.61 km
1 nautical mile (knot) = 1.853 km (1.15 sta.mi)
1 Astronomical Unit (A.U.) = 149597870 km.
Reproduction is allowed on the Web if accompanied by the
statement
© L. Scantamburlo - www.angelismarriti.it
Reproduced by permission.
PRIVACY WARNING
This Website contains cookies analytics and can contain
cookies of third parts! The visitor is informed and allows the use
of the cookies, otherwise, please abandon the Website or discharging
this function of allocation of cookies, acting on the configuration
and preferences of the browser navigation. For more information,
please go to the link privacy.
