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The object orbits the Sun but makes slow close approaches to the Earth–Moon system. Between 29 September (19:54 UTC) and 25 November 2024 (16:43 UTC) (a period of 1 month and 27 days) [4] it passed just outside Earth's Hill sphere (roughly 0.01 AU [1.5 million km; 0.93 million mi]) at a low relative velocity (in the range 0.002 km/s (4.5 mph) – 0.439 km/s [980 mph]) and became temporarily ...
A major study of the Earth–Moon–Sun system was undertaken by Charles-Eugène Delaunay, who published two volumes on the topic, each of 900 pages in length, in 1860 and 1867. Among many other accomplishments, the work already hints at chaos, and clearly demonstrates the problem of so-called "small denominators" in perturbation theory .
The path of a satellite closely orbiting the Earth can be accurately modeled starting from the 2-body elliptical orbit around the center of the Earth, and adding small corrections due to the oblateness of the Earth, gravitational attraction of the Sun and Moon, atmospheric drag, etc. It is possible to find a frozen orbit without calculating the ...
In essence this mathematical simulation of the Solar System is a form of the N-body problem. The symbol N represents the number of bodies, which can grow quite large if one includes the Sun, 8 planets, dozens of moons, and countless planetoids, comets and so forth. However the influence of the Sun on any other body is so large, and the ...
An eclipse of the Moon or Sun can occur when the nodes align with the Sun, roughly every 173.3 days. Lunar orbit inclination also determines eclipses; shadows cross when nodes coincide with full and new moon when the Sun, Earth, and Moon align in three dimensions. In effect, this means that the "tropical year" on the Moon is only 347 days long.
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This is an artificial animation of one lunar orbit; in reality, the visible hemisphere would go through phases of dark and light as the Moon rotates with respect to the Sun. Earth's Moon's rotation and orbital periods are tidally locked with each other, so no matter when the Moon is observed from Earth, the same hemisphere of the Moon is always ...
Astronomers were surprised at this, as the Moon is the only large object in orbit around the Earth, [a] and anything else would have been ejected long ago due to perturbations with the Earth, the Moon and the Sun. Therefore, it probably entered into Earth orbit very recently, yet there was no recently launched spacecraft that matched the orbit ...