Interlude I -- Nibiru ala Kepler
Kepler's First Law states that all planets revolve about the Sun in elliptical orbits with the Sun located at one focal point (in the figure, the Sun is located at F1).
The equation for an ellipse is given by:
x2/a2 + y2/b2 = 1
where 2a is the length of the major axis, 2b the length of the minor axis, and 2c the distance between the focal points, F1 and F2. In this case,
a2 = b2 + c2
Solving the ellipse formula for y yields:
y = (b/a) [a2 - x2 ]1/2
The area under a curve from point x1 to point x2 (the limits on the definite integral) in this case the ellipse or a portion of the ellipse, is given by:
A = ò y dx = (b/a) ò [a2 - x2 ]1/2 dx
A = (b/2a) { x [a2 - x2 ]1/2 + a2 [arc sin (x/a)] } (from x1 to x2)
The area, AT, of the ellipse from perihelion (closest point to F1) to aphelion (closest point to F2) is given by setting x1 = - a and x2 = + a. Thus,
AT = (b/2a) { [ a (a2 - a2 )1/2 + a2 arc sin (a/a) ] - [ -a (a2 - a2 )1/2 + a2 arc sin (- a/a) ] }
AT = (b/2a) { [ 0 + a2 w ] - [ 0 + a2 (-w) ] } = a b w
where w = arc sin z is the solution for sin w = z. If z = 1, sin w = 1 and therefore w = p / 2. For z = - 1, sin w = -1 and w = - p / 2. Therefore,
AT = a b p / 2
Consider now, the shaded area where the distance from F1 to an arbitrary point, f, on the ellipse is s. f is also at a distance j along the x-axis and k along the y-axis from the origin. The area under the curve from perihelion (x = -a) to the point f is given by:
Af = (b/2a) { [ - j (a2 - j2 )1/2 + a2 arc sin (- j/a) ] + [ a2 p/2 ] }
The shaded area, Af, is given by:
As = Af - k ( c - j ) / 2
where k2 = s2 - ( c - j )2.
It follows from Kepler's Second Law, that the time, t, for a planet to move from perihelion to point f, will be related to the time, T, for a planet to move from perihelion to aphelion, by the relation: t / T = As / AT. In other words, the ratio of the area swept out in time t, As, to the area swept out in time T, AT, equals the ratio of time t to that of time T.
IN THE CASE OF NIBIRU, let us consider the situation where the orbital period of Nibiru is assumed to be 3600 Earth years. The question is then: For how long or for what portion of its orbit is Nibiru within the confines of the known solar system? If we know this answer, we can then have some idea as to when it would be visible, and also for what period of time "traffic" between Earth and Nibiru might be realistic.
According to Kepler's Third Law, the mean distance from the Sun, D, is related to the time of revolution about the Sun, T, by the following:
D3 / T2 = K
where K is a constant. If D is in Astronomical Units (1 A.U. = 93 million miles; the distance from the Sun to the Earth), and T is in years (Earth), then K = 1.
From Kepler's Third Law, we can calculate the mean distance from the Sun to Nibiru. The result is:
D = 234.89 (about 235 A.U.)
This can be compared to the mean distances of other solar system planets. For example, Saturn is 9.54 A.U. from the Sun, Uranus is 19.17 A.U., Neptune is 30.03 A.U., and Pluto is 39.42 A. U. Note, however, that these distances are the mean distances, i.e. an average of the perihelion and the aphelion. At the same time, the aphelion is simply the length of the major axis of the ellipse less the perihelion distance ( 2 a - p ), i.e.
D = ( p + h ) / 2 = [ p + (2 a - p)] / 2 = ( 2 a ) / 2 = a
In the case of Pluto, its perihelion is just slightly within the orbit of Neptune (about 29.74 A.U.), and its aphelion is 49.10 A.U. In the case of Nibiru, the orbit is much more eccentric, with the distance to aphelion the order of 467 A.U.
In order to calculate the length of the minor axis of Nibiru's elliptical orbit, we must make a second assumption. For this case, let us assume that Nibiru's perihelion is within the asteroid belt, at approximately the mean distance of Ceres (2.75 A.U.). Then,
b = [a2 - c2 ]1/2 = [a2 - (a - p)2 ]1/2 = [2 a p - p2 ]1/2 = [5.5 a - 7.56]1/2 A.U.
b = 35.8 A. U.
We can now calculate the value of AT ( = a b p / 2 ). We obtain:
AT = 13,224 A.U.2
Let us now assume several values of the point f, corresponding to distances within the known solar system. For simplicity, we will consider the five cases where Nibiru is located at a distance within the outer reaches of the asteroid belt, a second distance where the position of Nibiru is on a line perpendicular to the major axis, a third distance at the equivalent to the mean distance of Saturn, a fourth distance at the equivalent of Uranus, and a fifth situation where f is located at the edge of our known solar system, just beyond the furthermost reach of Pluto.
For simplicity, we will assume:
a) s = 3.20 A.U. -- Asteroid Belt
b) s = 5.47 A.U. -- Nibiru perpendicular to major axis
c) 9.53 A.U., -- mean distance to Saturn
d) s = 19.17 A.U., -- mean distance to Uranus
e) s = 50 A.U. -- just beyond the furthermost reach of Pluto
Using the equation for the ellipse, with x = j and y = k, along with the relationships s2 = k2 + (c - j)2 and c = a - p; we obtain for values of j:
a) 234.29 A.U., b) 232.14, c) 227.98 A.U., d) 218.26 A.U., and e) 187.08 A.U.
This yields for the values of Af:
a) 4.41 A.U.2, b) 9.68 A.U.2, c) 39.18 A.U.2, d) 147.68 A.U.2, e) 706.23 A.U.2
We can then calculate values for As, in which case we obtain:
a) 6.96 A.U.2, b) 9.68 A.U.2, c) 21.32 A.U.2, d) 55.92 A.U.2, e) 218.00 A.U.2
We can now solve for t ( = T As / AT = 1800 As / AT years), the time that Nibiru would be within 3.20, 5.47, 9.53, 19.17, and 50.00 A.U. as it approached or when it departed from its perihelion with the Sun:
a) 0.95 yrs, (within the asteroid belt)
b) 1.32 yrs,
c) 2.90 yrs, (within the orbit of Saturn)
d) 7.61 yrs, (within the orbit of Uranus)
e) 29.67 yrs (within the outermost boundary of Pluto)
The total time that Nibiru would be within these distances is just 2 t, or:
a) 1.90 yrs, (within the asteroid belt)
b) 2.64 yrs,
c) 5.80 yrs, (within the orbit of Saturn)
d) 15.22 yrs, (within the orbit of Uranus)
e) 59.35 yrs (within the outermost boundary of Pluto)
In essence, Nibiru would be within the 50 A.U. limit for approximately 60 years, and within the orbits of Uranus and Saturn for only roughly 15 and 12 years. If Nibiru is approximately 4 times the size of the Earth, it should be visible to a powerful telescope within a reasonably wide time span. At the same time, however, its orbital speed would increase dramatically, averaging some 15,000 mph between the outer limit of Pluto and Uranus, 22,000 mph between Uranus and Saturn, 27,000 mph between Saturn and Jupiter, 55,000 mph in the vicinity of Jupiter, and 65,000 mph between Jupiter and the asteroid belt.
Disclaimer:
Some material presented will contain links, quotes, ideologies, etc., the contents of which should be understood to first, in their whole, reflect the views or opinions of their editors, and second, are used in my personal research as "fair use" sources only, and not espousement one way or the other. Researching for 'truth' leads one all over the place...a piece here, a piece there. As a researcher, I hunt, gather and disassemble resources, trying to put all the pieces into a coherent and logical whole. I encourage you to do the same. And please remember, these pages are only my effort to collect all the pieces I can find and see if they properly fit into the 'reality aggregate'.
Personal Position:
I've come to realize that 'truth' boils down to what we 'believe' the facts we've gathered point to. We only 'know' what we've 'experienced' firsthand. Everything else - what we read, what we watch, what we hear - is what someone else's gathered facts point to and 'they' 'believe' is 'truth', so that 'truth' seems to change in direct proportion to newly gathered facts divided by applied plausibility. Though I believe there is 'truth', until someone representing the celestial realm visibly appears and presents the heavenly records of Facts And Lies In The Order They Happened, I can't know for sure exactly what "the whole truth' on any given subject is, and what applies to me applies to everyone. Until then I'll continue to ask, "what does The Urantia Book say on the subject?"
~Gail Bird Allen
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Urantia Book, 44:0.11 - The Celestial Artisans
Never in your long ascendancy will you lose the power to recognize your associates of former existences. Always, as you ascend inward in the scale of life, will you retain the ability to recognize and fraternize with the fellow beings of your previous and lower levels of experience. Each new translation or resurrection will add one more group of spirit beings to your vision range without in the least depriving you of the ability to recognize your friends and fellows of former estates.
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Princess Bride 1987 Wallace Shawn (Vizzini) and Mandy Patinkin (Inigo Montoya)
Vizzini: HE DIDN'T FALL? INCONCEIVABLE.
Inigo Montoya: You keep using that word. I do not think it means what you think it means. -
Urantia Book, 117:4.14 - The Finite God
And here is mystery: The more closely man approaches God through love, the greater the reality -- actuality -- of that man. The more man withdraws from God, the more nearly he approaches nonreality -- cessation of existence. When man consecrates his will to the doing of the Father's will, when man gives God all that he has, then does God make that man more than he is.
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Urantia Book, 167:7.4 - The Talk About Angels
"And do you not remember that I said to you once before that, if you had your spiritual eyes anointed, you would then see the heavens opened and behold the angels of God ascending and descending? It is by the ministry of the angels that one world may be kept in touch with other worlds, for have I not repeatedly told you that I have other sheep not of this fold?"
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Urantia Book, Foreword - 0:12.12 - The Trinities
But we know that there dwells within the human mind a fragment of God, and that there sojourns with the human soul the Spirit of Truth; and we further know that these spirit forces conspire to enable material man to grasp the reality of spiritual values and to comprehend the philosophy of universe meanings. But even more certainly we know that these spirits of the Divine Presence are able to assist man in the spiritual appropriation of all truth contributory to the enhancement of the ever-progressing reality of personal religious experience—God-consciousness.
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Urantia Book, 1:4.3 - The Mystery Of God
When you are through down here, when your course has been run in temporary form on earth, when your trial trip in the flesh is finished, when the dust that composes the mortal tabernacle "returns to the earth whence it came"; then, it is revealed, the indwelling "Spirit shall return to God who gave it." There sojourns within each moral being of this planet a fragment of God, a part and parcel of divinity. It is not yet yours by right of possession, but it is designedly intended to be one with you if you survive the mortal existence.
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Urantia Book, 1:4.1 - The Mystery Of God
And the greatest of all the unfathomable mysteries of God is the phenomenon of the divine indwelling of mortal minds. The manner in which the Universal Father sojourns with the creatures of time is the most profound of all universe mysteries; the divine presence in the mind of man is the mystery of mysteries.
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Urantia Book, 1:4.6 - The Mystery Of God
To every spirit being and to every mortal creature in every sphere and on every world of the universe of universes, the Universal Father reveals all of his gracious and divine self that can be discerned or comprehended by such spirit beings and by such mortal creatures. God is no respecter of persons, either spiritual or material. The divine presence which any child of the universe enjoys at any given moment is limited only by the capacity of such a creature to receive and to discern the spirit actualities of the supermaterial world.
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Urantia Book, 11:0.1 - The Eternal Isle Of Paradise
Paradise is the eternal center of the universe of universes and the abiding place of the Universal Father, the Eternal Son, the Infinite Spirit, and their divine co-ordinates and associates. This central Isle is the most gigantic organized body of cosmic reality in all the master universe. Paradise is a material sphere as well as a spiritual abode. All of the intelligent creation of the Universal Father is domiciled on material abodes; hence must the absolute controlling center also be material, literal. And again it should be reiterated that spirit things and spiritual beings are real.
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Urantia Book, 50:6.4 - Planetary Culture
Culture presupposes quality of mind; culture cannot be enhanced unless mind is elevated. Superior intellect will seek a noble culture and find some way to attain such a goal. Inferior minds will spurn the highest culture even when presented to them ready-made.
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Urantia Book, 54:1.6 - True And False Liberty
True liberty is the associate of genuine self-respect; false liberty is the consort of self-admiration. True liberty is the fruit of self-control; false liberty, the assumption of self-assertion. Self-control leads to altruistic service; self-admiration tends towards the exploitation of others for the selfish aggrandizement of such a mistaken individual as is willing to sacrifice righteous attainment for the sake of possessing unjust power over his fellow beings.
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Urantia Book, 54:1.9 - True And False Liberty
How dare the self-willed creature encroach upon the rights of his fellows in the name of personal liberty when the Supreme Rulers of the universe stand back in merciful respect for these prerogatives of will and potentials of personality! No being, in the exercise of his supposed personal liberty, has a right to deprive any other being of those privileges of existence conferred by the Creators and duly respected by all their loyal associates, subordinates, and subjects.
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Urantia Book, 54:1.8 - True And False Liberty
There is no error greater than that species of self-deception which leads intelligent beings to crave the exercise of power over other beings for the purpose of depriving these persons of their natural liberties. The golden rule of human fairness cries out against all such fraud, unfairness, selfishness, and unrighteousness.