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Jupiter might have shaped the Solar System on its grand tack. In planetary astronomy, the grand tack hypothesis proposes that Jupiter formed at a distance of 3.5 AU from the Sun, then migrated inward to 1.5 AU, before reversing course due to capturing Saturn in an orbital resonance, eventually halting near its current orbit at 5.2 AU.
The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun
Eccentricity varies primarily due to the gravitational pull of Jupiter and Saturn. The semi-major axis of the orbital ellipse, however, remains unchanged; according to perturbation theory , which computes the evolution of the orbit, the semi-major axis is invariant .
The most prominent example of the classical two-body problem is the gravitational case (see also Kepler problem), arising in astronomy for predicting the orbits (or escapes from orbit) of objects such as satellites, planets, and stars. A two-point-particle model of such a system nearly always describes its behavior well enough to provide useful ...
At one point, the two may fall into sync, at which time Jupiter's constant gravitational tugs could accumulate and pull Mercury off course, with 1–2% probability, 3–4 billion years into the future. This could eject it from the Solar System altogether [1] or send it on a collision course with Venus, the Sun, or Earth. [11]
A prototypical example of a planetary problem is the Sun–Jupiter–Saturn system, where the mass of the Sun is about 1000 times larger than the masses of Jupiter or Saturn. [18] An approximate solution to the problem is to decompose it into n − 1 pairs of star–planet Kepler problems , treating interactions among the planets as perturbations.
The original core of the Nice model is a triplet of papers published in the general science journal Nature in 2005 by an international collaboration of scientists. [4] [5] [6] In these publications, the four authors proposed that after the dissipation of the gas and dust of the primordial Solar System disk, the four giant planets (Jupiter, Saturn, Uranus, and Neptune) were originally found on ...
The complex motions of gravitational perturbations can be broken down. The hypothetical motion that the body follows under the gravitational effect of one other body only is a conic section, and can be described in geometrical terms. This is called a two-body problem, or an unperturbed Keplerian orbit. The differences between that and the ...