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...a [[Kepler orbit]]. It is the angle between the [[ascending node]] and the body. [[Category:Orbits]] ...

...Kirill Alexandrovitch Sitnikov]] that attempts to describe the movement of three celestial bodies due to their mutual gravitational attraction. A special ca ...tion, the [[gravitational constant]] is 1. In such a system that the third body only moves in one dimension – it moves only along the z-axis. ...

...ematics)|eccentricity]] {{nobr| {{math|''e'' : 0 ≤ ''e'' < 1}} )}} to open orbits (parabolas and hyperbolas, {{nobr|( {{math|''e'' ≥ 1}} ),}} with no singula ...orbits use the sinh and cosh relations. Parabolic orbits (marginal escape orbits) formulas are a special in-between case. ...

...[Earth]]. This precession is due to the non-spherical nature of a rotating body, which creates a non-uniform [[gravitational field]]. The following discuss ...ct that causes orbits to precess around the rotational axis of the primary body. ...

...nity of massive planets, during which processes the approximating two-body orbits can have widely varying [[orbital eccentricity|eccentricities]], almost alw ...ixed original time <math>\ t_\mathsf{o}\ ,</math> find the position of the body at some later time <math>\ t ~.</math> For [[elliptical orbit]]s with a rea ...

There are three types of radial trajectories (orbits).<ref>Thomson, William Tyrrell; ''Introduction to Space Dynamics'', Dover, ...dard orbits which are classified by their [[orbital eccentricity]], radial orbits are classified by their [[specific orbital energy]], the constant sum of th ...

==Stationary and synchronous orbits== ...ial body, and T is the [[Sidereal time|sidereal rotational period]] of the body. ...

...[[Inclined orbit|inclined]] and [[Sun-synchronous orbit|sun-synchronous]] orbits depend on launch altitude, inclination, and time.<ref>{{Cite journal |last= ...g on the Sun defines a beta angle as positive if the satellite in question orbits in a counterclockwise direction and negative if it revolves [[clockwise]].< ...

...e:Two-body Jacobi coordinates.JPG|thumb|300px|Jacobi coordinates for [[two-body problem]]; Jacobi coordinates are <math>\boldsymbol{R}=\frac {m_1}{M} \bold ...four bodies.svg|thumb|300px|A possible set of Jacobi coordinates for four-body problem; the Jacobi coordinates are '''r'''₁, '''r'''<sub>2</sub ...

...int|opposite sides]] of the [[celestial sphere]], as observed from a given body (usually [[Earth]]). ...ly straight line, or [[syzygy (astronomy)|syzygy]]; that is, Earth and the body are in the same direction as seen from the Sun. Opposition occurs only for ...

...escription|Time between earliest and latest observations of a Solar System body like an asteroid or comet}} ...period between its earliest and latest observations, used for tracing the body's path. It is usually given in days or years. The term is mostly used in th ...

...gularity|singularities]] among the solutions to the [[n-body problem|''n''-body problem]]: there are noncollision singularities for&nbsp;''n''&nbsp;≥&nbsp; ...name="Xue2">{{Cite journal|title=Non-collision singularities in a planar 4-body problem ...

...nce a particle will miss the focus by if its journey is unperturbed by the body at the focus.{{cn|date=August 2019}} ...ite web|url=http://www.bogan.ca/orbits/geometry.html|title=The Geometry of Orbits: Ellipses, Parabolas, and Hyperbolas|website=www.bogan.ca}}</ref>}}<!--NOTE ...

...rial Coordinate System]]), the [[direction cosine]] vector of the orbiting body from the observation points (from Topocentric Equatorial Coordinate System) ...more effort because the observations were taken from [[Earth]] while Ceres orbits the [[Sun]]. ...

...lanet|lost]]. However, large numbers of smaller NEAs have highly uncertain orbits.<ref name="MPC-NEA"/>]] ...lso known as '''condition code''' in JPL's [[JPL Small-Body Database|Small-Body Database Browser]].<ref name="User-Guide"/><ref name="Strategic-Implication ...

Suppose a target body is moving in a circular orbit and a chaser body is moving in an elliptical orbit. ...<math>z</math> is along the orbital angular momentum vector of the target body (i.e., <math>x,y,z</math> form a right-handed triad). ...

[[Image:Helicube-black.jpg|thumb|right|Mèffert's Helicopter Cube, black body]] ...6200450/http://www.puzzlemaster.ca/browse/other/3256-helicopter-cube-white-body | archive-date = 2011-07-06 | url-status = dead }}</ref><ref>{{cite web | u ...

...vity]], will be suffered by a particle in orbit around a (slowly) spinning body, such as a typical [[planet]] or [[star]]. ...ts weak-field and low-velocity linearized approximation, a slowly spinning body induces an additional component of the [[gravitational field]] that acts on ...

...ube law are known as [[Cotes spiral]]s. The Binet equation shows that the orbits must be solutions to the equation The differential equation has three kinds of solutions, in analogy to the different conic sections of the Keple ...

...provide the four conserved quantities necessary to uniquely determine all orbits in the [[Kerr–Newman metric|Kerr–Newman]] spacetime (even those of charged ...rved quantities are also conserved, any function of <math>C</math> and the three other constants of the motion can be used as a fourth constant in place of ...