Axial parallelism (also called gyroscopic stiffness, inertia or rigidity, or "rigidity in space") is the characteristic of a rotating body in which the direction of the axis of rotation remains fixed as the object moves through space. In astronomy, this characteristic is found in astronomical bodies in orbit. It is the same effect that causes a gyroscope's axis of rotation to remain constant as Earth rotates, allowing the devices to measure Earth's rotation. [1]
The Earth's orbit, with its axis tilted at 23.5 degrees, exhibits approximate axial parallelism, maintaining its direction towards Polaris (the "North Star") year-round. Together with the Earth's axial tilt, this is one of the primary reasons for the Earth's seasons, as illustrated by the diagram to the right. [2] [3] [4] [5] It is also the reason that the stars appear fixed in the night sky, such as a "fixed" pole star, throughout Earth's orbit around the Sun. [6]
Minor variation in the direction of the axis, known as axial precession, takes place over the course of 26,000 years. As a result, over the next 11,000 years the Earth's axis will move to point towards Vega instead of Polaris. [7]
Axial parallelism is widely observed in astronomy. For example, the axial parallelism of the Moon's orbital plane [8] is a key factor in the phenomenon of eclipses. The Moon's orbital axis precesses a full circle during the 18 year, 10 day saros cycle. When the Moon's orbital tilt is aligned with the ecliptic tilt, it is 29 degrees from the ecliptic, while when they are anti-aligned (9 years later), the orbital inclination is only 18 degrees.
In addition, the rings of Saturn remain in a fixed direction as that planet rotates around the Sun. [9]
Early gyroscopes were used to demonstrate the principle, most notably the Foucault's gyroscope experiment. [10] Prior to the invention of the gyroscope, it had been explained by scientists in various ways. [9] Early modern astronomer David Gregory, a contemporary of Isaac Newton, wrote:
To explain the Motion of the Celestial Bodies about their proper Axes, given in Position, and the Revolutions of them… If a Body be said to be moved about a given Axe, being in other respects not moved, that Axe is suppos'd to be unmov'd, and every point out of it to describe a Circle, to whose Plane the Axis is perpendicular. And for that reason, if a Body be carried along a line, and at the same time be revolved about a given Axe; the Axe, in all the time of the Body's motion, will continue parallel to it self. Nor is any thing else required to preserve this Parallelism, than that no other Motion besides these two be impressed upon the Body; for if there be no other third Motion in it, its Axe will continue always parallel to the Right-line, to which it was once parallel. [11]
This gyroscopic effect is described in modern times as "gyroscopic stiffness" or "rigidity in space". The Newtonian mechanical explanation is known as the conservation of angular momentum. [12]
Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference frame it can be defined as a change in the second Euler angle. If it is not caused by forces external to the body, it is called free nutation or Euler nutation. A pure nutation is a movement of a rotational axis such that the first Euler angle is constant. Therefore it can be seen that the circular red arrow in the diagram indicates the combined effects of precession and nutation, while nutation in the absence of precession would only change the tilt from vertical. However, in spacecraft dynamics, precession is sometimes referred to as nutation.
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation. In physics, there are two types of precession: torque-free and torque-induced.
Rotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation, in contrast to rotation around a fixed axis.
A gyroscope is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rotation is free to assume any orientation by itself. When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, according to the conservation of angular momentum.
The north and south celestial poles are the two points in the sky where Earth's axis of rotation, indefinitely extended, intersects the celestial sphere. The north and south celestial poles appear permanently directly overhead to observers at Earth's North Pole and South Pole, respectively. As Earth spins on its axis, the two celestial poles remain fixed in the sky, and all other celestial points appear to rotate around them, completing one circuit per day.
The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere, a primary direction towards the vernal equinox, and a right-handed convention.
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object.
In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In the absence of precession, the astronomical body's orbit would show axial parallelism. In particular, axial precession can refer to the gradual shift in the orientation of Earth's axis of rotation in a cycle of approximately 26,000 years. This is similar to the precession of a spinning top, with the axis tracing out a pair of cones joined at their apices. The term "precession" typically refers only to this largest part of the motion; other changes in the alignment of Earth's axis—nutation and polar motion—are much smaller in magnitude.
In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbital plane. It differs from orbital inclination.
The orbital period is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars. It may also refer to the time it takes a satellite orbiting a planet or moon to complete one orbit.
Lunar precession is a term used for three different precession motions related to the Moon. First, it can refer to change in orientation of the lunar rotational axis with respect to a reference plane, following the normal rules of precession followed by spinning objects. In addition, the orbit of the Moon undergoes two important types of precessional motion: apsidal and nodal.
In lunar astronomy, libration is the cyclic variation in the apparent position of the Moon perceived by Earth-bound observers and caused by changes between the orbital and rotational planes of the moon. It causes an observer to see slightly different hemispheres of the surface at different times. It is similar in both cause and effect to the changes in the Moon's apparent size due to changes in distance. It is caused by three mechanisms detailed below, two of which cause a relatively tiny physical libration via tidal forces exerted by the Earth. Such true librations are known as well for other moons with locked rotation.
Milankovitch cycles describe the collective effects of changes in the Earth's movements on its climate over thousands of years. The term was coined and named after the Serbian geophysicist and astronomer Milutin Milanković. In the 1920s, he hypothesized that variations in eccentricity, axial tilt, and precession combined to result in cyclical variations in the intra-annual and latitudinal distribution of solar radiation at the Earth's surface, and that this orbital forcing strongly influenced the Earth's climatic patterns.
Earth orbits the Sun at an average distance of 149.60 million km in a counterclockwise direction as viewed from above the Northern Hemisphere. One complete orbit takes 365.256 days, during which time Earth has traveled 940 million km. Ignoring the influence of other Solar System bodies, Earth's orbit, also known as Earth's revolution, is an ellipse with the Earth-Sun barycenter as one focus with a current eccentricity of 0.0167. Since this value is close to zero, the center of the orbit is relatively close to the center of the Sun.
The term Great Year has more than one major meaning. It is defined by scientific astronomy as "The period of one complete cycle of the equinoxes around the ecliptic, or about 25,800 years". Ptolemy reported that his teacher Hipparchus, by comparing the position of the vernal equinox against the fixed stars in his time and in earlier observations, discovered that it shifts westward approximately one degree every 72 years. Thus the time it would take the equinox to make a complete revolution through all the zodiac constellations and return to its original position would be approximately 25,920 years. In the heliocentric model, the precession can be pictured as the axis of the Earth's rotation making a slow revolution around the normal to the plane of the ecliptic. The position of the Earth's axis in the northern night sky currently almost aligns with the star Polaris, the North Star. But as the direction of the axis is changing, this is a passing coincidence which was not always so and will not be so again until a Great Year has passed.
The Moon orbits Earth in the prograde direction and completes one revolution relative to the Vernal Equinox and the stars in about 27.32 days and one revolution relative to the Sun in about 29.53 days. Earth and the Moon orbit about their barycentre, which lies about 4,670 km (2,900 mi) from Earth's centre, forming a satellite system called the Earth–Moon system. On average, the distance to the Moon is about 385,000 km (239,000 mi) from Earth's centre, which corresponds to about 60 Earth radii or 1.282 light-seconds.
Precession refers to a specific change in the direction of the rotation axis of a rotating object, in which the second Euler angle is constant
Earth-centered inertial (ECI) coordinate frames have their origins at the center of mass of Earth and are fixed with respect to the stars. "I" in "ECI" stands for inertial, in contrast to the "Earth-centered – Earth-fixed" (ECEF) frames, which remains fixed with respect to Earth's surface in its rotation, and then rotates with respect to stars.
True polar wander is a solid-body rotation of a planet or moon with respect to its spin axis, causing the geographic locations of the north and south poles to change, or "wander". Unless the body is totally rigid its stable state rotation has the largest moment of inertia axis aligned with the spin axis, with the smaller two moments of inertia axes lying in the plane of the equator. If the body is not in this steady state, true polar wander will occur: the planet or moon will rotate as a rigid body to realign the largest moment of inertia axis with the spin axis.
Astronomical nutation is a phenomenon which causes the orientation of the axis of rotation of a spinning astronomical object to vary over time. It is caused by the gravitational forces of other nearby bodies acting upon the spinning object. Although they are caused by the same effect operating over different timescales, astronomers usually make a distinction between precession, which is a steady long-term change in the axis of rotation, and nutation, which is the combined effect of similar shorter-term variations.
Because of rigidity in space, a gyroscope does not tilt its axis of rotation as the earth rotates.
Although these distances seem counterintuitive to residents of the Northern Hemisphere who experience summer in July and winter in January—the seasons are not nearly as greatly affected by distance as they are by changes in solar illumination caused by the fact that Earth's polar axis is inclined 23.5 degrees from the perpendicular to the ecliptic (the plane of the solar system through or near which most of the planet's orbits travel) and because the Earth exhibits parallelism (currently toward Polaris, the North Star) as it revolves about the Sun.
During revolution about the Sun, the earth's polar axis exhibits parallelism to Polaris (also known as the North Star). Although observing parallelism, the orientation of Earth's polar axis exhibits precession—a circular wobbling exhibited by gyroscopes—that results in a 28,000-year-long precessional cycle. Currently, Earth's polar axis points roughly in the direction of Polaris (the North Star). As a result of precession, over the next 11,000 years, Earth's axis will precess or wobble so that it assumes an orientation toward the star Vega.
The Axis of the Moon is not perpendicular to the Plane of its Orbit, but a little inclin'd to it: The Axis keeps its Parallelism in its Motion round the Earth
Under the title of precession instruments, various pieces of apparatus, involving the gyroscope principle, have been in use for a number of years for illustrating the precession of the equinoxes, and the parallelism of the earth's axis as it revolves round the sun.