astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

and

orbital mechanics Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to rockets, satellites, and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal ...

, the Laplace sphere concerns a specific kind of

Three-body problem In physics, specifically classical mechanics, the three-body problem is to take the initial positions and velocities (or momenta) of three point masses orbiting each other in space and then calculate their subsequent trajectories using Newton' ...

with orbits. The prototype idea is to study the

Sun The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...

system, and determine if it would be possible for the Sun to steal away the Moon from Earth orbit, into solar orbit. More generally, it is applied to any

satellite A satellite or an artificial satellite is an object, typically a spacecraft, placed into orbit around a celestial body. They have a variety of uses, including communication relay, weather forecasting, navigation ( GPS), broadcasting, scient ...

of a body (often called the 'planet') that is, in turn, orbiting a much more massive body (often called the 'star'). Besides the moon, the satellite is usually a small planetoid,

exoplanet An exoplanet or extrasolar planet is a planet outside the Solar System. The first confirmed detection of an exoplanet was in 1992 around a pulsar, and the first detection around a main-sequence star was in 1995. A different planet, first det ...

, or a spacecraft that is orbiting the earth. The Laplace sphere is a region around a planet where a satellite would maintain a stable orbit around the planet, rather than being pulled off toward the star, with its greater

gravitational force Newton's law of universal gravitation describes gravity as a force by stating that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the sq ...

, despite its larger distance. The 'sphere' region is actually an

ellipsoid An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a Surface (mathemat ...

, specifically a

prolate spheroid A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has cir ...

with its long axis perpendicular to the star-planet orbit. This results in the fact that the satellite with an eccentric orbit is safer with its

apsis An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides perta ...

pointing up or down, than pointing in the plane of the planet's orbit. The derivation eliminates higher-order terms on the assumption that the star's mass is much larger than the planet's, and the planet's mass is much larger than the satellite's.Roy, A.E. (2004). Orbital Motion (4th ed.). CRC Press. https://doi.org/10.1201/9780367806620

References

Orbits {{astronomy-stub

See also

References