Fifth planet of Solar System - Phaeton.
Fifth planet of the Solar System - Phaethon.
Igor Krivosheev, M.E.
General Provisions. This article is dedicated to the legendary planet Phaethon. The main criteria for proving its existence will be given, which reflect the physical essence of the processes in the Solar System. Criteria based on applied mathematics are only complementary to physical criteria, although they are misinterpreted by experts. The physical criteria are excellent and adequate, and the evidence base is logical and consistent. The scientific format of the article is fully maintained.
1. Inclination of the planes of the orbits of asteroids. Inclination of the diurnal axes of rotation of the known planets of the solar system.
a. Necessary and sufficient condition for the Lidov-Kozai mechanism. Private solution " Three bodies problem". Reliable determination of the inclination of the plane of the Fifth planet's orbit .
In 1961, Mikhail Lidov and in 1962 Yoshihide Kozai independently discovered the following statistical law, according to which the eccentricity of the orbit "can be exchanged" for inclination and vice versa. And when the angle of inclination of the asteroid's orbit plane reaches 39.2 degrees, the line of the apses becomes perpendicular to the line of nodes. In this case, the argument of perihelion passes into a state of libration. This phenomenon is called the Kozai-Lidov resonance.
The "Three bodies problem" has the form of a vector equation:
a (r) = gradU + n^2 · r + 2 [n × v] (1)
The minimum angle of inclination of the asteroid's orbital plane is 39.231 degrees
(140.8 degrees for retrograde orbits), in which the precession of the perihelion argument goes into a state of libration in the Lidov-Kozai mechanism.
The precession of the perihelion argument has the following reason: the precession of the nodes of the asteroid's orbit. Elimination of the cause - an equilibrium state of inertial forces in the nodes. Let us write down the vector equation of equilibrium at the nodes.
n^2 · r + 2 [n × v] = 0 (2)
In scalar form, this equation looks like this:n^2· r - 2· n· v· Sin (n; v) = 0 (3)
n^2· r = 2· n· v· Sin (n; v) (4)
where v = n · r , we've next result:
n^2· r = 2 · n^2· r ·Sin (n; v) (5)
The final solution comes down to determining the sine between the vectors n and v.
Sin (n; v) = 0.5
(6)
Conclusion: the angle between the plane of motion of a massive body and the
plane of the asteroid is 60 degrees. In
such a situation, an equilibrium state of inertial forces is created at the nodes
of the asteroid's orbit and the angle between the vectors v and n is 30 degrees. The inclination of the orbit of an unknown massive
body is determined by a simple solution of angles in the context of spherical
geometry. Accordingly, the inclination of the plane of the unknown massive body
will be i = 20.768 °.
The basic formula of the Kozai - Lidov resonance shows that eccentricity
can be replaced by inclination and vice versa. This formula is statistical character
.
[(1-e^2) ^ 0.5] Cos i = Const (7)
The mechanical component of the Kozai - Lidov resonance at the nodes looks like this:
n ^ 2 · r + 2 [n × v] = 0 (8)
Note. The orbital planes of the giant planets have a slight inclination to the ecliptic plane: Jupiter i = 1.31 °, Saturn i = 2.49 °, Uranus i = 0.77 °, Neptune i = 1.77 °. With this in mind, the gravity of the giant planets can put any asteroid into an orbit with an inclination angle of the plane relative to the ecliptic no more than i = 1.6 °. The vector form of the disturbing acceleration can be applied by the following expression (in the context of the postulate of the resultant force):
a=a(x)+a(y)+a(z) (9) In this situation, a (z) = 0. In other words, in the projection to the OZ axis, the body will be at rest.
The principle of inertia states: any isolated point can be in a state of rest or rectilinear and uniform motion until the applied forces or force take it out of this state.
For example: Ceres has inclination of the orbital plane to the ecliptic i = 10.6 °, Pallas has an inclination of the orbital plane to the ecliptic i = 34.8 °.
This solution of the "Three bodies problem" gives an answer to the question "Why is the inclination of the planes of the orbits of asteroids greater than i = 1.6° ?" and reflects the physical essence of the process, the so-called "Kozai-Lidov resonance ".
The "Three bodies problem" is one of the problems of celestial mechanics. Only a few exact solutions are known. The first three solutions were found by Euler in 1767 (the so-called "collinear libration points"). Two more solutions were found by Lagrange in 1772 (the so-called "triangular libration points").
This solution of " Three bodies problem " proposed by the author of the article can be safely called "The sixth exact solution".
b. The inclination of the diurnal axes of rotation of the known planets Solar System
The daily rotation of the planets fully fits into the properties of the gyroscope.
If a rapidly rotating axis of the free gyro exert a force couple ( P - F ) a torque M = P · h ( h off-shoulder forces), then (contrary to expectation) further gyroscope starts to rotate around an axis not x perpendicular to the plane pair, and about an axis y , lying in this plane and perpendicular to the body's own axis z. This additional movement is called precession. The precession of the gyroscope will occur in relation to the inertial reference system ( to the axes directed to the fixed stars) with an angular velocity:
ω = M / IΩ (10)
where I is the moment of inertia of the gyroscope relative to the z- axis , Ω is the angular velocity of the proper. rotation of the gyroscope about the same axis.
Accordingly, if the angle between the axis of the moment M and the axis of rotation of the gyroscope z is equal to 0 °, then there will be no precession. The angular velocity vector is determined by the Zhukovsky rule. The scalar value directly depends at Sin [ M ; Ω ].
Accordingly, the angle of inclination of the diurnal axes of rotation of the planets of the solar system can be safely called the angle of precession.
Note. With the existing known model of the Solar System, the slopes of the diurnal axes of rotation have the following values: for the Earth ε = 23.44 °, for Mars ε = 25.19 °, for Jupiter ε = 3.13 °, for Saturn ε = 26.73 °, for Uranus ε = 97.7 °, for Neptune ε = 28.32 °.
Additional calculations (even if you create some absurd situation when some of the planets will occupy a constant maximum northern declination relative to the ecliptic plane, and the other part, respectively, the maximum southern declination) will give the following results: The Earth will have an inclination of the diurnal rotation axis of no more than ε = 4.1 °, Mars no more ε = 2.5 °, it will be slightly less with giant planets. But in fact, Uranus is practically on its side.
Conclusion: the gravity of massive body, which has a significant inclination of the plane of its orbit with respect to the ecliptic, is required to create a turning moment and, accordingly, precession.
The inclination of the Earth's diurnal axis ε = 23.44° is due to massive planet located in the inner part of the Solar System.
2. Visibility conditions.
The conditions of visibility, or rather invisibility in the context of the "Lambert-Beer law", can be explained by the presence of a massive satellite.
Due to the strong tidal acceleration, dust does not settle on the surface of the planet and its satellite, but is always in suspension. As a result, which is quite possible, taking into account the "darkening to the edge" effect, this celestial body can be identified by infrared sensors as an asteroid.
For a real reduction in gloss by an additional + 25.0 m, the dust concentration must be at least 160,000 particles per cubic meter in a volume comparable to the volume of the object. (The minimum distance to the Earth is about 1.0 AU).
Initially, sunlight is absorbed by dust in the vicinity of planetary space, after which the reflected light is absorbed by the same dust.
The absorption efficiency of the absorbing layer r depends on the optical thickness, which includes the thickness of the absorbing layer r, the concentration of particles n and the particle size σ.
τ=σ·n·r (11)
σ=π·ρ^2 (12)
If ρ = 1.0 e - 5 , 1.0 e - 4 cm , then σ = (5.0 – 8.0) e - 9 cm^2.
The Lambert-Beer law say:
I (ν) = I o (ν) e^ [- τ(ν)] (13)
Star's brightness reduced by:
∆m = −2,5lg (E / Eo) = lge^[- τ (ν)] (14)
We can calculate the concentration of dust :
n = ∆m / σ· r (15)
Note: in this situation, forcalculations, we use the average albedo of the giant planets, equal to 0. 333. The magnitude of the brightness of a given object in opposition (near the perihelion) should be dust-free Magn V - 5.5 m, -5.0 The celestial sphere has been repeatedly scanned by space observatories. However, by coincidence, the Nearest Giant Planet was at a distant distance from the Sun and Earth. During the Akari scan , the Nearest Giant Planet was at a distance of at least 3.85 AE from the Earth and had a brightness magnitude (not brighter) than Magn V = + 22.1 m . For IRAS: the distance to the Earth is not less than 5.26 AE, the magnitude of the brightness( not brighter ) Magn V = +22.8 m . For ISO, WISE, Herschel: the distance to the Earth is not less than 6.27 AE ,( not brighter ) Magn V = + 23.2 m . Maximum permeability WISE + 22.0 m.
Accordingly, the search method is very simple - the search for object eclipsing stars that are in the same plane.
3. Kirkwood gaps. Slowdown the movement of asteroids.
The explanation that Kirkwood gaps were formed by resonance with Jupiter's orbital motion ("low-order resonance") is unconvincing. But by and large, this resonance is only a component of the general, complex orbital resonance - the synchronization of the motion of objects in the Solar System.
It is more reasonable to assume that Kirkwood gaps were formed as a result of the gravitational capture of asteroids by massive body and are the nodes of the orbit.
Accordingly, it is not difficult to determine other orbital parameters of the unknown massive planet of the solar system. The orbital period will be P = 3088.78 ± 5.4 days, the semi-major axis is a = 4.1485 ± 0.003 AE. The total precession will be about(node precession+ anomalous perihelion precession) 36°, of which about 30.6 ° for node precession, about 5.4 ° for anomalous perihelion precession (of course with small error), eccentricity e = 0.534 ± 0.001.
Considering that not only dust, but also asteroids are subjected to gravitational capture, it was necessary to find an indicator object, the orbital parameters approximately correspond to the calculated ones.
In 2015, the asteroid K15P00T / 2015 PT was discovered , which was used as an indicator object. Based on this, observations were started.
Observations indicate deceleration of unknown character, which can be completely classified as additional gravitational perturbations from of the massive celestial body. Evaluation of the additional gravitational perturbations 6. 36 ± 0. 95e − 8 m/s^2. Observations were made at Station de la Universidad de los Andes (University of the Andes station), observatory code (302). Observations were made in 2014.
For the first time, an unknown planet and its satellite were discovered on the night of October 1, 2016.The search method is transit. Observatory Chervishevo (М90 Chervishevo).
4. Pioneer Anomaly. The Yarkovsky effect. Anomalous precession of the Mercury perihelion.
The slowdown of "Pioneer-10" and "Pioneer-11" in 8.74 ± 1.33 e-10 m / s^ 2 is directed towards the Sun. Let's calculate the following: on 01/01/1990 "Pioneer-10" crossed the aphelion point of Pluto, which is located at distance of 49.3 AU from the Sun.
The slowdown of the Cassini-Huygens mission is estimated at (26.7 ± 1.1) e-10 m / s^2 and cannot confirm or deny the existence of anomalies.
The Yarkovsky effect is a force acting on a celestial body in space, caused by anisotropic radiation of thermal photons, as a result of which a reactive impulse is created and, as a result, the celestial body acquires additional acceleration (deceleration).
The acceleration of a celestial body relative to the Sun is equal to:
a = GM / R^2 (16)
The amount of energy emitted per unit area per second.
ε=L/4πR^2 (17)
Where possible to deduce acceleration dependence caused by pulse jet from the amount of energy:
a (1) / a (2) = ε (1) / ε (2) (18)
Based on this effect, the asteroid Golevka (6489) deviated from its trajectory by 15 km after 12 years. From this data, we can calculate an acceleration of 2.09 e -13 m / s^ 2. The average value of the solar flux 218.72 W/m^2 or 0.31344 cal / cm^2·min. The Pioneer Anomaly has a deceleration value of 8.74 ± 1.33 e-10 m / s^2.
If we assume that this anomaly is due to temperature phenomena, taking into account the proportions, the emitter should give out the amount of energy emitted by a unit surface per second and equal in magnitude:
ε = [8.74 e - 10 / 2.09 e - 13] · 218 . 72 = 914 647. 27 W / m^ 2 or 1310.75 cal / cm^2 · min.
This means to have a temperature:
T= (ε / σ)^0.25 (19)
T = 2004 K, where ε = 914 647.27 W / m^2- energy, σ = 5.67e - 8 W / m^2 K^4 -Stefan-Boltzmann's constant.Note: the Yarkovsky effect is estimated in the range from 1 e-15 m / s^2 to 1 e-12 m/s^2. With such data, taking into account the proportions of the "Pioneer Anomaly" and the Yarkovsky effect, the temperature of the emitter should be at least 1335 K.
Conclusion: on the basis of an elementary thermodynamic calculations, it was found that for the generation of a pulse caused by anisotropic radiation and giving the result of a deceleration of 8.74 ± 1.33 e-10 m / s^2, a radiator is required that heats up to T = 2004 K at an approximated value (but not less than 1335 K). The role of anisotropic emission in Pioneers Anomaly is greatly exaggerated.
As for the anomalous precession of the perihelion of Mercury, it must be considered in the context of the "Perturbing Theory".
To do this, use:
1. Simon Newcomb's formula.
2. Pioneer anomaly .
For Mercury:
a = GM / r^(2 + k) (20)
where k = 1.574 e-7 is the modified Simon Newcomb coefficient, and formula (20) is replaced by the next formula:
a=[GM/r^2]+Σa(p) (21)
where:
Σ a (p) is the sum of additional perturbing accelerations, M - the mass of the Sun.
Σ a (p) = 1.544 e-7 m / s^2 (direction from the Sun) from distance of 0.3871 AU.
The "Pioneer anomaly" are affected by a force that gives slowdown a = 8.74 e-10 m/s^2 from a distance of 46.2656 AU. (direction to the Sun).
How can we calculate that there is perturbing acceleration from a body with
a mass of 89.36 Earth, which has an orbit with a semi-major axis of 3.6 AU.
(Excluding the perturbation of the acceleration of the displaced part of the
center of mass of the Sun. If this
perturbation is taken into account, then the mass of the unknown planet should
be greater). The result obtained using GTR
is random coincidence.
Note: Einstein never claimed that general relativity was the cause of the anomalous perihelion precession of Mercury.
5. Condition of stability. The movement of the Sun within the Solar System.
Based on the "Law of conservation of momentum", a rotating system is stable if the center of mass, center of gravity, center of rotation are at the same point. In our case, this point coincides with the central body, i.e. with the Sun. This situation is in complete harmony with all three of Kepler's Generalized Laws.
Some publications indicate that the Sun rotates about the Sun-Jupiter center of mass. This is an erroneous statement. It's not hard to prove it. For this, it is enough to solve the geometric problem, taking for the calculation of the ephemeris of the planets of the Solar System. All foci will converge on the Sun.
Another circumstance that confirms the fallacy is the movement of the Moon in the context of the "Perturbing Theory". It is necessary to consider the motion of the Moon in the Relative (movable) coordinate system. Every 206.6 days (on average) the perigee changes places with an apogee. The maximum displacement of the Sun from the physical center of mass, center of rotation, center of gravity with the known and existing model of the Solar System will be 5,471.0 km.
Note. The theory of the Moon’s motion, which was developed by Ernest William Brown. In this theory, Brown used the 1400 coefficients. Currently, for the calculation of the Moon motion used the expression of tens thousands of coefficients. There is no limit to their number, if required even more high precision. But still it belongs to the category of statistic.
Taking into account the found mass of the unknown binary planetary system, the motion of the Sun must be considered in the context of the "Complex motion of a point". The calculations gave the following results of the movement of the Sun:
1. The angular velocity in the basic or "stationary" coordinate system is n = 3.93221 e-7 rad / sec;
2. The angular velocity in relative or "moving" coordinate system is n = 2.68943 e-6 rad / sec.
The calculated period is August 2015 - October 2024. The maximum value of the displacement of the Sun's center of mass from the physical center of mass, center of rotation, center of gravity will be - 21500.0 ± δ km on August 25, 2015, and - 24500.0 ± δ km on September 28, 2015, where δ- possible error.
Note. The displacement or amplitude in each of the coordinate systems is to be calculated in detail in the future, after determining the exact physical and orbital characteristics of the binary planetary system. It's just a matter of time.
6. General and additional conclusions. Orbital and physical characteristics of the Phaethon-Kiknos binary system. Hypotheses.
Several unsolved problems in physics have been solved:
1.The Pioneers anomaly is caused by the gravity of a massive body.
2.The anomalous precession of the perihelion of Mercury is caused by the gravity of a massive body and the movement of the Sun in the context of the "complex motion of a point".
3. The problem of determining the mechanical causes of the Kozai-Lidov resonance has been solved, showing the physical essence of the process and reliably determining the inclination of the orbital plane of an unknown planet.
4. Found binary planetary system Phaethon-Kyknos, as a missing link in the solar system. It was Phaeton that Heinrich Olbers was looking for at one time.
5. The condition for the stability of the solar system as a rotating system is closed. The search for additional massive celestial bodies is doomed to failure, in particular the so-called Planet Nine.
6. The asteroid belt is the result of a cosmic catastrophe. In particular, the Phaeton satellite Kiknos and Venus.
Reason: Retrograde diurnal rotation of Venus.
To believe that the asteroid belt was formed as a result of the gravitational influence of Jupiter is too dubious an idea. There is a well-formed Ceres spheroid in the belt. The destruction of a celestial body can occur only in the case of gravitational capture of the body and the body hitting the Roche limit. In addition, objects in the asteroid belt are satellites of the Sun. Therefore, the hypothesis of a space catastrophe seems to be more reliable.
7. The complex motion of the Sun and the Phaeton-Kiknos binary planetary system must be taken into account when designing interplanetary flights, as well as for calculating MOID (the object crossing the Earth's orbit at a minimum distance) in the NEO (near terrestrial objects) and PHO (potentially dangerous objects) program.
8. It should be noted that clustering of distant TNO's takes place. But clustering is not in a strictly differentiated area.
Reason: complex (compound) motion of the Sun.
9. Orbital parameters for the Phaeton-Kiknos binary planetary system:
Epoch 8.367 September 2015.0 = 2457273.867 JDT (at perihelion)
Node 193.30614 °, Arg 142.46791 °, a = 4.1484455,e = 0.5338644, Period P = 8.449.
Abnormal perihelion precession p (a) = 6.67894 arc sec per day;
Precession of nodes p ( n ) = 34.8088 arc sec per day.
10. Physical parameters for the Phaeton-Kyknos binary planetary system:
The mass of a binary system is 6.468 (± 0.388) e + 26 kg or 108.3 ± 6.5 Earth masses.
Phaeton diameter 93750.0 ± 250.0 km (with dust);
Kyknos diameter 37500.0 ± 250.0 km (with dust);
The density of the substance is 2500-2900 kg per cubic meter.
The calculated dust concentration is not less than 160,000 particles per cubic meter.
Mass ratio 16.67: 1.
The maximum search and detection radius is not more than 1.0 degrees. [1]
Note. Correction of phisical and orbital parametres on :
https://search-for-near-giant-planet.blogspot.com/2021/04/applications.html
References.
1.Ephemeris:
https://search-for-near-giant-planet.blogspot.com/2021/02/calculated-ephemeris-for-near-giant.html
https://search-for-near-giant-planet.blogspot.com/2021/04/applications.html
Note. Actual Magn V no brighter +24.0m - +24.5m.
2. Dagaev. M.M., Demin V.G., Klimishin I.A., Charugin V.M., Astronomy .: Enlightenment, 1983. - 384. - ISBN 1-11-1
3. John D. Anderson, Philip A. Laing, Eunice L. Lau, Anthony S. Liu, Michael Martin Nieto, Slava G. Turyshev. Study of the anomalous acceleration of Pioneer 10 and 11.
4. http : //www.minorplanetcenter.net/mpec/K15/K15P20.html
5. Support for the Thermal Origin of the Pioneer Anomaly.
6. Anomalous Orbital-Energy Changes Observed during Spacecraft Flybys of Earth.
7.Direct Detection of the Yarkovsky Effect by Radar Ranging to Asteroid 6489 Golevka.
Correction:
ОтветитьУдалить1. The angular velocity in the basic or "stationary" coordinate system is n = 3.743193769 e-7 rad / sec;
2. The angular velocity in relative or "moving" coordinate system is n = 2.661672561 e-6 rad / sec.