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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 .
In the special case where there are only two bodies in the Solar System, Earth and Sun, the acceleration becomes ¨ =, ^, which is the acceleration of the Kepler motion. So this Earth moves around the Sun according to Kepler's laws.
According to Shlomo Pines, al-Baghdādī's theory of motion was "the oldest negation of Aristotle's fundamental dynamic law [namely, that a constant force produces a uniform motion], [and is thus an] anticipation in a vague fashion of the fundamental law of classical mechanics [namely, that a force applied continuously produces acceleration]." [54]
Entering a Hohmann transfer orbit from Earth to Jupiter from low Earth orbit requires a delta-v of 6.3 km/s, [170] which is comparable to the 9.7 km/s delta-v needed to reach low Earth orbit. [171] Gravity assists through planetary flybys can be used to reduce the energy required to reach Jupiter.
Gravitational field strength within the Earth Gravity field near the surface of the Earth – an object is shown accelerating toward the surface If the bodies in question have spatial extent (as opposed to being point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses that ...
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]
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
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.