Orbit
In celestial mechanics, an orbit is the curved trajectory of an object under the influence of an attracting force. Known as an orbital revolution, examples include the trajectory of a planet around a star, a natural satellite around a planet, or an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.
Planets revolve around a star, a natural satellite around a planet, or an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. Furthermore orbits are dynamic, perturbated by all masses, consisting of different trajectories, but most can be approximated as elliptic orbits, with the barycenter being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.
For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion.
History
Historically, the apparent motions of the planets were described by European and Arabic philosophers using the idea of celestial spheres. This model posited the existence of perfect moving spheres or rings to which the stars and planets were attached. It assumed the heavens were fixed apart from the motion of the spheres and was developed without any understanding of gravity. This concept originated with Hellenistic astronomy, particularly Eudoxus and Aristotle. After the planets' motions were more accurately measured, theoretical mechanisms such as deferent and epicycles were added by Ptolemy. Although the model was capable of reasonably accurately predicting the planets' positions in the sky, more and more epicycles were required as the measurements became more accurate, hence the model became increasingly unwieldy. Originally geocentric, it was modified by Copernicus to place the Sun at the centre to help simplify the model. The model was further challenged during the 16th century, as comets were observed traversing the spheres.The basis for the modern description of orbits was first formulated by Johannes Kepler whose results are summarised in his three laws of planetary motion. First, he found that the orbits of the planets in the Solar System are elliptical, not circular, as had previously been believed, and that the Sun is not located at the center of the orbits, but rather at one focus. Second, he found that the orbital speed of each planet is not constant, as had previously been thought, but rather that the speed depends on the planet's distance from the Sun. Third, Kepler found a universal relationship between the orbital properties of all the planets orbiting the Sun. For the planets, the cubes of their distances from the Sun are proportional to the squares of their orbital periods.
Jupiter and Venus, for example, are respectively about 5.2 and 0.723 AU distant from the Sun, their orbital periods respectively about 11.86 and 0.615 years. The proportionality is seen by the fact that the ratio for Jupiter:
is practically equal to that for Venus,
in accord with the relationship. Idealised orbits meeting these rules are known as Kepler orbits.
Isaac Newton demonstrated that Kepler's laws were derivable from his theory of gravitation, and that, in general, the orbits of bodies subject to gravity were conic sections, under his assumption that the force of gravity propagates instantaneously. To satisfy Kepler's third law, Newton showed that, for a pair of bodies, the orbit size, orbital period, and their combined masses are related to each other by:
and that those bodies orbit their common center of mass. Where one body is much more massive than the other, it is a convenient approximation to take the center of mass as coinciding with the center of the more massive body.
Advances in Newtonian mechanics were then used to explore variations from the simple assumptions behind Kepler orbits, such as the perturbations due to other bodies, or the impact of spheroidal rather than spherical bodies. Joseph-Louis Lagrange developed a new approach to Newtonian mechanics emphasizing energy more than force, and made progress on the three-body problem, discovering the Lagrangian points with Euler. In a dramatic vindication of classical mechanics, in 1846 Urbain Le Verrier was able to predict the position of Neptune based on unexplained perturbations in the orbit of Uranus.
Albert Einstein in his 1916 paper The Foundation of the General Theory of Relativity explained that gravity was due to curvature of space-time and removed Newton's assumption that changes in gravity propagate instantaneously. This led astronomers to recognize that Newtonian mechanics did not provide the highest accuracy in understanding orbits. In relativity theory, orbits follow geodesic trajectories which are usually approximated very well by the Newtonian predictions but the differences are measurable. Essentially all the experimental evidence that can distinguish between the theories agrees with relativity theory to within experimental measurement accuracy. The original vindication of general relativity is that it was able to account for the remaining unexplained amount in precession of Mercury's perihelion first noted by Le Verrier. However, Newton's solution is still used for most short term purposes since it is significantly easier to use and sufficiently accurate.
Planetary orbits
Within a planetary system, various non-stellar objects follow elliptical orbits around the system's barycenter. These objects include planets, dwarf planets, asteroids and other minor planets, comets, meteoroids, and even space debris. A comet in a parabolic or hyperbolic orbit about a barycenter is not gravitationally bound to the star and therefore is not considered part of the star's planetary system. Bodies that are gravitationally bound to one of the planets in a planetary system, including natural satellites, artificial satellites, and the objects within ring systems, follow orbits about a barycenter near or within that planet.Owing to mutual gravitational perturbations, the eccentricities and inclinations of the planetary orbits vary over time. Mercury, the smallest planet in the Solar System, has the most eccentric orbit. At the present epoch, Mars has the next largest eccentricity while the smallest orbital eccentricities are seen with Venus and Neptune.
As two objects orbit each other, the periapsis is that point at which the two objects are closest to each other. Less properly, "perifocus" or "pericentron" are used. The apoapsis is that point at which they are the farthest, or sometimes apifocus or apocentron. A line drawn from periapsis to apoapsis is the line-of-apsides. This is the major axis of the ellipse, the line through its longest part.
More specific terms are used for specific bodies. For example, perigee and apogee are the lowest and highest parts of an orbit around Earth, while perihelion and aphelion are the closest and farthest points of an orbit around the Sun. Things orbiting the Moon have a perilune and apolune. An orbit around any star, not just the Sun, has a periastron and an apastron.
In the case of planets orbiting a star, the mass of the star and all its satellites are calculated to be at a single point called the barycenter. The individual satellites of that star follow their own elliptical orbits with the barycenter at one focal point of that ellipse. At any point along its orbit, any satellite will have a certain value of kinetic and potential energy with respect to the barycenter, and the sum of those two energies is a constant value at every point along its orbit. As a result, as a planet approaches periapsis, the planet will increase in speed as its potential energy decreases; as a planet approaches apoapsis, its velocity will decrease as its potential energy increases.
Principles
An orbit can be explained by combining Newton's laws of motion with his law of universal gravitation. The laws of motion are as follows:- A body continues in a state of uniform rest or motion unless acted upon by an external force.
- The acceleration produced when a force acts is directly proportional to the force and takes place in the direction in which the force acts.
- To every action there is an equal and opposite reaction.
Because of the law of universal gravitation, the strength of the gravitational force depends on the masses of the two bodies and their separation. As the gravity varies over the course of the orbit, it reproduces Kepler's laws of planetary motion. Depending on the evolving energy state of the system, the velocity relationship of two moving objects with mass can be considered in four practical classes, with subtypes:
; No orbit
; Suborbital trajectories: a range of interrupted elliptical paths
; Orbital trajectories :
; Open trajectories:
To achieve orbit, conventional rockets are launched vertically at first to lift the rocket above the dense lower atmosphere, and gradually pitch over and finish firing the rocket engine parallel to the atmosphere to achieve orbital injection. Once in orbit, their speed keeps them above the atmosphere. If an elliptical orbit dips into dense air, the object will lose speed and re-enter, falling to the ground. Occasionally a space craft will intentionally intercept the atmosphere, in an act commonly referred to as an aerobraking maneuver.