Cassini's Laws
Encyclopedia
Cassini's laws provide a compact description of the motion of the Moon
. They were established in 1693 by Giovanni Domenico Cassini
, a prominent scientist of his time.
Refinements of these laws to include physical libration
s have been made, and they have been generalized to treat other satellites and planets.
In the case of the Moon, its rotational axis always points some 1.5 degrees away from the North ecliptic pole
. The normal to the orbital plane and the rotational axis are always in opposite sides of the normal to the ecliptic.
Therefore, both the normal to the orbital plane and the Moon's rotational axis precess around the Ecliptic pole with the same period. The period is about 18 years and the motion is retrograde
.
are coplanar while the obliquity remains constant. The Laplace plane is defined as the plane about which a planet's orbit precesses with constant inclination to the equatorial and ecliptic planes.
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
. They were established in 1693 by Giovanni Domenico Cassini
Giovanni Domenico Cassini
This article is about the Italian-born astronomer. For his French-born great-grandson, see Jean-Dominique Cassini.Giovanni Domenico Cassini was an Italian/French mathematician, astronomer, engineer, and astrologer...
, a prominent scientist of his time.
Refinements of these laws to include physical libration
Libration
In astronomy, libration is an oscillating motion of orbiting bodies relative to each other, notably including the motion of the Moon relative to Earth, or of Trojan asteroids relative to planets.-Lunar libration:...
s have been made, and they have been generalized to treat other satellites and planets.
Cassini's laws
- The Moon has a 1:1 spin-orbit resonanceOrbital resonanceIn celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of...
. This means that the rotationRotationA rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...
/ orbitOrbitIn physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...
ratio of the Moon is such that the same side of it always faces the EarthEarthEarth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
. - The Moon's rotational axis maintains the same angle of inclinationInclinationInclination in general is the angle between a reference plane and another plane or axis of direction.-Orbits:The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit...
from the ecliptic planePlane of the eclipticThe plane of the ecliptic is the plane of the Earth's orbit around the Sun. It is the primary reference plane when describing the position of bodies in the Solar System, with celestial latitude being measured relative to the ecliptic plane. In the course of a year, the Sun's apparent path through...
. The Moon's rotational axis forms a cone that intersects the ecliptic plane as a circle. - A plane formed from a normalSurface normalA surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...
to the ecliptic plane and a normal to the Moon's orbital planeOrbital plane (astronomy)All of the planets, comets, and asteroids in the solar system are in orbit around the Sun. All of those orbits line up with each other making a semi-flat disk called the orbital plane. The orbital plane of an object orbiting another is the geometrical plane in which the orbit is embedded...
will contain the Moon's rotational axis.
In the case of the Moon, its rotational axis always points some 1.5 degrees away from the North ecliptic pole
Ecliptic pole
The ecliptic pole is the point on the celestial sphere where the sphere meets the imaginary line perpendicular to the ecliptic plane, the path the Earth travels on its orbit around the Sun.There are two ecliptic poles:...
. The normal to the orbital plane and the rotational axis are always in opposite sides of the normal to the ecliptic.
Therefore, both the normal to the orbital plane and the Moon's rotational axis precess around the Ecliptic pole with the same period. The period is about 18 years and the motion is retrograde
Retrograde motion
Retrograde motion is motion in the direction opposite to the movement of something else, and is the contrary of direct or prograde motion. This motion can be the orbit of one body about another body or about some other point, or the rotation of a single body about its axis, or other phenomena such...
.
Cassini state
A system obeying these laws is said to be in a Cassini state, that is: an evolved rotational state where the spin axis, orbit normal, and normal to the Laplace planeLaplace plane
The Laplace plane or Laplacian plane of a planetary satellite, named after its discoverer Pierre-Simon Laplace , is a mean or reference plane about whose axis the instantaneous orbital plane of a satellite precesses....
are coplanar while the obliquity remains constant. The Laplace plane is defined as the plane about which a planet's orbit precesses with constant inclination to the equatorial and ecliptic planes.