In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular orbit, elliptic orbit, parabolic trajectory, hyperbolic trajectory, or radial trajectory) with the central body located at one of the two foci, or the focus (Kepler's first law).
If the conic section intersects the central body, then the actual trajectory can only be the part above the surface, but for that part the orbit equation and many related formulas still apply, as long as it is a freefall (situation of weightlessness).
In astrodynamics, an orbitequation defines the path of orbiting body m 2 {\displaystyle m_{2}\,\!} around central body m 1 {\displaystyle m_{1}\,\!}...
and m2, the orbital speed ( v {\displaystyle v\,} ) of one body traveling along an elliptic orbit can be computed from the vis-viva equation as: v = μ (...
{\displaystyle v_{o}} is orbital velocity of a body in circular orbit. For a body moving along this kind of trajectory the orbitalequation is: r = h 2 μ 1 1...
The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle...
{\displaystyle \mu =GM} , is the standard gravitational parameter. The orbitequation in polar coordinates, which in general gives r in terms of θ, reduces...
specific orbital energy ( ϵ {\displaystyle \epsilon \,} ) of elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation) for...
the Earth's orbit around the Sun, which is about 0.0167. The equation of time vanishes only for a planet with zero axial tilt and zero orbital eccentricity...
the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around...
above equation simplifies to (since M = Vρ = 4/3πa3ρ) T = 3 π G ρ {\displaystyle T={\sqrt {\frac {3\pi }{G\rho }}}} Thus the orbital period in low orbit depends...
astronautics, the Hohmann transfer orbit (/ˈhoʊmən/) is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around...
minimum radius for the circular orbit to be stable in Schwarzschild metric. An exact solution to the Einstein field equations is the Schwarzschild metric...
graveyard orbit, also called a junk orbit or disposal orbit, is an orbit that lies away from common operational orbits. One significant graveyard orbit is a...
\theta } is linked to the distance between the orbiting bodies ( r {\displaystyle r\,} ) by the orbitequation: r = ℓ 1 + e ⋅ cos θ {\displaystyle r={\frac...
unit mass. In order to get an equation for the orbit from equation (1), we need to eliminate time. (See also Binet equation.) In polar coordinates, this...
of the orbiting object and the location in the orbit at which it is closest to the central body (called the periapsis). Alternately, the equation can be...
maneuver, especially in a transfer orbit, it is said to be coasting. The Tsiolkovsky rocket equation, or ideal rocket equation, can be useful for analysis of...
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 (a tropical...
by the reduced mass. According to the orbital energy conservation equation (also referred to as vis-viva equation), it does not vary with time: ε = ε k...
A geostationary orbit, also referred to as a geosynchronous equatorial orbit (GEO), is a circular geosynchronous orbit 35,786 km (22,236 mi) in altitude...
A low Earth orbit (LEO) is an orbit around Earth with a period of 128 minutes or less (making at least 11.25 orbits per day) and an eccentricity less...
A Molniya orbit (Russian: Молния, IPA: [ˈmolnʲɪjə] , "Lightning") is a type of satellite orbit designed to provide communications and remote sensing coverage...
value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit (or capture orbit), and greater than 1 is...
the orbit is simply the sum of kinetic and gravitational potential energies, in an unperturbed two-body orbit. By substituting the vis-viva equation into...
Halo orbit A halo orbit is a periodic, three-dimensional orbit associated with one of the L1, L2 or L3 Lagrange points in the three-body problem of orbital...
A medium Earth orbit (MEO) is an Earth-centered orbit with an altitude above a low Earth orbit (LEO) and below a high Earth orbit (HEO) – between 2,000...
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