Computer simulation of the possible evolution of the orbits of Pluto and bodies of the trans-Neptune belt (original) (raw)

Review of the works on the orbital evolution of solar system major planets

Solar System Research, 2007

The cognition history of the basic laws of motion of Solar system major planets is presented. Before Newton, the description of motion was purely kinematic, without relying on physics in view of its underdevelopment. From the standpoint of the modern mathematical theory of approximation, all of the models from Ptolemy's predecessors to Kepler inclusive differ only in details. The mathematical theory worked on an infinite time scale; the motion was represented by P. Bohl's quasi-periodic functions (a special case of H. Bohr's quasi-periodic functions). After Newton, the mathematical description of motion came to be based on physical principles and took the form of ordinary differential equations. The advent of General Relativity (GR) and other relativistic theories of gravitation in the 20th century changed little the mathematical situation in the field under consideration. Indeed, the GR effects in the Solar system are so small that the post-post-Newtonian approximation is sufficient. Therefore, the mathematical description using ordinary differential equations is retained. Moreover, the Lagrangian and Hamiltonian forms of the equations are retained. From the 18th century until the mid-20th century, all the theories of planetary motion needed for practice were constructed analytically by the small parameter method. In the early 20th century, Lyapunov and Poincaré established the convergence of the corresponding series for a sufficiently small time interval. Subsequently, K. Kholshevnikov estimated this interval to be on the order of several tens of thousands of years, which is in agreement with numerical experiments. The first works describing analytically (in the first approximation) the evolution on cosmogonic time scales appeared in the first half of the 19th century (Laplace, Lagrange, Gauss, Poisson). The averaging method was developed in the early 20th century based on these works. Powerful analytical and numerical methods that have allowed us to make significant progress in describing the orbital evolution of Solar system major planets appeared in the second half of the 20th century. This paper is devoted to their description.

Solar System dynamics, beyond the two-body-problem approach

AIP Conference Proceedings, 2006

When one thinks of the solar system, he has usually in mind the picture based on the solution of the two-body problem approximation presented by Newton, namely the ordered clockwork motion of planets on fixed, non-intersecting orbits around the Sun. However, already by the end of the 18th century this picture was proven to be wrong. As discussed by Laplace and Lagrange (for a modern approach see or [2]), the interaction between the various planets leads to secular changes in their orbits, which nevertheless were believed to be corrections of higher order to the Keplerian elliptical motion.

MIGRATION OF CELESTIAL BODIES IN THE SOLAR SYSTEM

Astronomical and Astrophysical Transactions, v. 15. pp. 241-247, 1998

We investigated several cases of migration of celestial bodies (planetesimals, forming planets, asteroids , and transneptunian and near-Earth objects) in the forming and present Solar System. These investigations were based on computer simulation results and on some analytical estimates. The evolution of orbits of several gravitating objects mainly waa investigated by numerical integration of the N-body problem. The method of spheres (i.e. two two-body problems) was used for investigations of the evolution of discs consisting of hundreds bodies. It was found that the embryos of Uranus and Neptune may have originated near the orbit of Saturn and then due to gravitational interaction with migrating planetesimals may have migrated to their present distances from the Sun moving a l l the time in orbits with small eccentricities. Under the gravitational influence of the giant planets, some transneptunian bodies can decrease their perihelia from 34 to 1 AU in several tens of million years. Some bodies of the Kuiper belt can migrate from the outer part of tlus belt to its inner part due to the gravitational iduence of the largest bodies of the belt. A large number of small celestial bodies can exist inside the orbit of the Earth.

NUMERICAL STUDY OF THE MIGRATION OF BODIES IN THE FORMATION OF THE SOLAR SYSTEM

International Applied Mechanics, 1992

Our results are consistent with an initial mass of the protoplanetary cloud of MN ~0.04-0.1 Ms ( Ms is the mass of the Sun) assumed by many authors. More icy and stony matter may have entered the core and shell of Jupiter than any other planet. The total mass of bodies penetrating into the asteroid belt from the zones of the giant planets could have been tens of times the mass of the Earth. The system of giant planets expanded during accumulation of these planets. In order for Jupiter and Saturn to have their current eccentricities and their present periods of axial rotation and inclinations of the axes of rotation, nuclei of unformed planets with masses equal to several times the mass of the Earth must have existed in their feed zones. The nuclei of Uranus and Neptune with initial masses equal to several times the mass of the Earth could have migrated from the zone of Saturn, moving along slightly elliptical orbits. The same conclusion can be made for the migration from the zone of Jupiter of the nucleus of Saturn with a mass equal to several dozen times the mass of the Earth. In addition to the nuclei of Uranus and Neptune, other smaller objects could have migrated in the same way from the zones of Jupiter and Saturn into the zones of Uranus and Neptune. The total mass of bodies reaching beyond Neptune's orbit could have reached tens of times the mass of the Earth. Planetesimals could exist at the present time in the zone of Neptune, moving along eccentric and inclined orbits [4]. The average eccentricity of the orbits of bodies migrating into the trans-Neptune belt from the zones of the giant planets is larger than the average eccentricity of bodies formed in the trans-Neptune belt. At the present time bodies could migrate to the Earth's orbit from the asteroid and trans-Neptune belts, and also from the zones of Uranus and Neptune and from the Oort and Hills clouds.

Notes on the Motion of Celestial Bodies

JAMP, 2020

A novel method for the computation of the motion of multi-body systems is proposed against the traditional one, based on the dynamic exchange of attraction forces or using complex field equations, that hardly face two-body problems. The Newton gravitational model is interpreted as the emission of neutrino/gravitons from celestial bodies that combine to yield a cumulative flux that interacts with single bodies through a momentum balance. The neu-trino was first found by Fermi to justify the energy conservation in β decay and, using his model; we found that the emission of neutrino from matter is almost constant independently from the nuclides involved. This flux can be correlated to Gauss constant G, allowing the rebuilding of Newton law on the basis of nuclear data, the neutrino weight and the speed of light. Similarly to nature, we can therefore separate in the calculations the neutrino flux, that represents the gravitational field, is dependent on masses and is not bound to the number of bodies involved, from the motion of each body that, given the field, is independent of the mass of bodies themselves. The conflict between exchanges of forces is avoided, the mathematics is simplified, the computational time is reduced to seconds and the stability of result is guaranteed. The example of computation of the solar system including the Sun and eight planets over a period of one to one hundred years is reported, together with the evolution of the shape of the orbits.

The Motion of Celestial Bodies

2011

The history of celestial mechanics is first briefly surveyed, identifying the major contributors and their contributions. The Ptolemaic and Copernican world models, Kepler’s laws of planetary motion and Newton’s laws of universal gravity are presented. It is shown that the orbit of a body moving under the gravitational attraction of another body can be represented by a conic section. The six orbital elements are defined, and it is indicated how they can be determined from observed positions of the body on the sky. Some special cases, permitting exact solutions of the motion of three gravitating bodies, are also treated. With two-body motion as a first approximation, the perturbing effects of other bodies are next derived and applied to the motions of planets, satellites, asteroids and ring particles. The main effects of the Earth’s oblateness on the motions of artificial satellites are explained, and trajectories for sending a space probe from one planet to another are shown. The in...

A review of the motion of Pluto

Celestial Mechanics, 1980

A review is given of the determination of the long-term motion of Pluto. In particular, the discovery of the librational character of the two critical arguments is discussed. The stability of the motion of Pluto is shown to have been established when all known gravitational forces are considered.

Notes on an initial satellite system of Neptune

Earth, Moon and Planets, 1989

The comparison of masses and sizes of the Neptunian satellites and of Pluto and Charon to the secondaries of the planetary, Jovian, Saturnian and Uranian systems support the hypotheses, first, that an initial Neptune's satellite system may have been disrupted, second, that Triton may have been the system perturber and, third, that Pluto (or a parent body of Pluto and Charon) was initially a giant satellite of Neptune. Based on recent theoretical works on perturbed proto-planetary nebula and noting the similarity of some characteristics of Neptune and Uranus, a theoretical mean distance ratio of primeval gaseous rings around Neptune is tentatively deduced to be about 1.475, close to the value of the Uranian system. An exponential distance relation gives possible ranges of distances at which smalI satellites and/or ring structures could be found by Voyager 2, close to Neptune.

The Orbit of Planet Nine Derived from Engineering Physics

arXiv: Earth and Planetary Astrophysics, 2020

Several papers have recently suggested the possible presence of a ninth planet (Planet X) that might explain the gravitational perturbations of a number of detached Trans-Neptunian objects. To analyze the possibility further, we have applied celestial mechanics, engineering physics and statistical analysis to develop improved estimates of the planet's primary orbital elements and mass from first engineering principles, using the orbital characteristics of both the original group of 6 objects analyzed and also a second group comprising the original 6 together with 6 additional long-period asteroids selected by the authors. We show that the driving force behind the observed clustering is gravitational torque that arranges the orbits of asteroids in a systematic, orderly manner, and we develop the associated equations of motion. As evidence we show that the expected effects are fully apparent in the orbital characteristics of the correlated bodies involved, including most strikingl...

THE ASTRODYNAMICS OF NEW PLANETARY SYSTEMS: THE ELLIPTIC RESTRICTED 3-BODY PROBLEM

Astrodynamics Specialists Conference Proceedings, American Astronautical Society, 1997

Elliptic Restricted 3-Body Problem (ER3BP) simulations illustrate measures of relative stability for extra-solar planets, using terrestrial analogs as 3rd bodies in binary systems Centauri, Procyon, Sirius, Jupiter-Sun, 47 Ursae Majoris and 70 Virginis. Initial conditions placed hypothetical planets in nominally circular orbits at Earth analogous radiative flux regions (400 o K effective stellar temperature at orbital radius), plus increments above and below. As tracked for 10 3-10 5 years, secondary bodies (star, brown dwarf or planet) perturbed nominally circular, co-planar planetary orbits at pericentron passage, causing eccentricity and angular momentum to cycle from 10 2 to 10 5 years as planet periastron precessed. Cases include satellites of jovian planets or brown dwarfs. Cycle magnitudes and periods varied with star system case and thermal environment. In some instances, stable orbit bounds were established by capture, ejection or advent of chaotic motions. Effective temperature bounds of stable regions varied with each binary system. For calibrating detection projects, observations of Earth from deep space are suggested.