Constant angular momentum is extremely useful when dealing with the orbits of planets and satellites, and also when analyzing the Bohr model of the atom.

This is even more true of asteroids, since their orbits usually have a greater inclination to the ecliptic than planets.

That is, they have low-eccentricity and sometimes low-inclination orbits like the classical planets.

These pulsar planets are believed to have formed from the unusual remnants of the supernova that produced the pulsar, in a second round of planet formation, or else to be the remaining rocky cores of gas giants that somehow survived the supernova and then decayed into their current orbits.

: When multiple planets are present, each one slightly perturbs the others ' orbits.

In another form of the method, timing the eclipses in an eclipsing binary star can reveal an outer planet that orbits both stars ; as of November 2011, five planets have been found in that way.

The radial-velocity method and the transit method ( which between them are responsible for the vast majority of detections ) are most sensitive to large planets in small orbits.

Thus many known exoplanets are " hot Jupiters ": planets of Jovian mass or larger in very small orbits with periods of only a few days.

It also appears that there are more planets in large orbits than in small orbits.

Furthermore, Nasir al-Din al-Tusi ( 1201 – 1274 ), an astronomer and mathematician from Baghdad, authored the Treasury of Astronomy, a remarkably accurate table of planetary movements that reformed the existing planetary model of Roman astronomer Ptolemy by describing a uniform circular motion of all planets in their orbits.

The Hohmann transfer applies to any two orbits, not just those with planets involved.

It is possible to put stations or spacecraft on orbits that cycle between different planets, for example a Mars cycler would synchronously cycle between Mars and Earth, with very little propellant usage to maintain the trajectory.

Kepler's laws and his analysis of the observations on which they were based, the assertion that the Earth orbited the Sun, proof that the planets ' speeds varied, and use of elliptical orbits rather than circular orbits with epicycles — challenged the long-accepted geocentric models of Aristotle and Ptolemy, and generally supported the heliocentric theory of Nicolaus Copernicus ( although Kepler's ellipses likewise did away with Copernicus's circular orbits and epicycles ).

It also had to be massless and without viscosity, otherwise it would visibly affect the orbits of planets.

* Circular motion ( e. g. the orbits of planets )

Ecliptic comets have relatively small orbits, below 10 AU, and follow the ecliptic plane, the same plane in which the planets lie.

Those relatively rare comets with orbits of about 10, 000 AU have probably gone through one or more orbits through the Solar System and have had their orbits drawn inward by the gravity of the planets.

The most widely accepted hypothesis is that the Oort cloud's objects initially coalesced much closer to the Sun as part of the same process that formed the planets and asteroids, but that gravitational interaction with young gas giant planets such as Jupiter ejected the objects into extremely long elliptic or parabolic orbits.

Based on their orbits, it is believed they were long-period comets that were captured by the gravity of the giant planets and sent into the inner Solar System.

It has a radius of approximately 883 times that of the Sun ; if it were placed in the center of our solar system, its outer surface would lie between the orbits of Mars and Jupiter.

Numerical methods implemented on electronic computing machines have simplified the task of determining the orbits of a dynamical system.

It is in the neighborhood of singular points and periodic orbits that the structure of a phase space of a dynamical system can be well understood.

Kepler-16 contains the first discovered planet that orbits around a binary star system.

If a planet orbits one member of a binary star system, then an uppercase letter for the star will be followed by a lowercase letter for the planet.

More importantly, the incontrovertible discovery of celestial bodies orbiting something other than the Earth dealt a serious blow to the then-accepted Ptolemaic world system, or the geocentric theory in which everything orbits around the Earth.

These perfectly periodic orbits, referred to as " halo " orbits, do not exist in a full n-body dynamical system such as the Solar System.

However, quasi-periodic ( i. e., bounded but not precisely repeating ) orbits following Lissajous-curve trajectories do exist in the n-body system.

They proposed that, of all closed classical orbits traced by a mechanical system in its phase space, only the ones that enclosed an area which was a multiple of Planck's constant were actually allowed.

First, he found that the orbits of the planets in our solar system are elliptical, not circular ( or epicyclic ), as had previously been believed, and that the Sun is not located at the center of the orbits, but rather at one focus.

Within a planetary system, planets, dwarf planets, asteroids ( a. k. a. minor planets ), comets, and space debris orbit the barycenter in elliptical orbits.

Bodies which are gravitationally bound to one of the planets in a planetary system, either natural or artificial satellites, follow orbits about a barycenter near that planet.

In the elliptical orbit, the center of mass of the orbiting-orbited system is at one focus of both orbits, with nothing present at the other focus.

To this Newtonian approximation, for a system of two point masses or spherical bodies, only influenced by their mutual gravitation ( the two-body problem ), the orbits can be exactly calculated.

* February 1 – Belgian astronomer Jean Meeus ( b. 1928 ) asserts that the orbits of all the planets of the Solar system were within the same 90 ° arc of the solar system on this date.

The ecliptic coordinate system is a celestial coordinate system commonly used for representing the positions and orbits of Solar System objects.

Because most planets ( except Mercury ), and many small solar system bodies have orbits with small inclinations to the ecliptic, it is convenient to use it as the

When the system is treated quantum mechanically, these orbits are quantized.

Hilda asteroids do not visit of Jupiter-Sun system, though they do come close to it in their curious orbits.

Artist's impression of the sight from a ( hypothetical ) moon of planet HD 188753 Ab ( upper left ), which orbits a triple star system.

In reality, some orbital ranges are impossible for dynamical reasons ( the planet would be expelled from its orbit relatively quickly, being either ejected from the system altogether or transferred to a more inner or outer orbital range ), whilst other orbits present serious challenges for eventual biospheres because of likely extreme variations in surface temperature during different parts of the orbit.

At one astronomical unit from the sun ( the Earth's distance ) the dust orbits are probably nearly circular.

Hence S breaks up into uncountably many orbits under G. Using the axiom of choice, we could pick a single point from each orbit, obtaining an uncountable subset X of S with the property that all of its translates by G are disjoint from X.

The eccentricity ( orbit ) | eccentricities of the orbits are represented by segments ( extending from perihelion to aphelion ) with the inclination s represented on the vertical axis.

The ' hot ' and ' cold ' populations are strikingly different: more than 30 % of all cubewanos are in low inclination, near-circular orbits.

The parameters of the plutinos ’ orbits are more evenly distributed, with a local maximum in moderate eccentricities in 0. 15 – 0. 2 range and low inclinations 5 – 10 °.

When orbital inclinations are compared, ' hot ' cubewanos can be easily distinguished by their higher inclinations, as the plutinos typically keep orbits below 20 °.

Binaries are quite common on low-inclination orbits and are typically similar-brightness systems.

Binaries are less common on high-inclination orbits and their components typically differ in brightness.

Linear dynamical systems and systems that have two numbers describing a state are examples of dynamical systems where the possible classes of orbits are understood.

The orbits are organized in curves, or fibers, which are collections of points that map into themselves under the action of the map.

* Given a partition of A, G is a transformation group under composition, whose orbits are the cells of the partition ‡;

* Given a transformation group G over A, there exists an equivalence relation ~ over A, whose equivalence classes are the orbits of G.

In sum, given an equivalence relation ~ over A, there exists a transformation group G over A whose orbits are the equivalence classes of A under ~.

The equivalence classes of ~— also called the orbits of the action of H on G — are the right cosets of H in G. Interchanging a and b yields the left cosets.