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Orbit equation information


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).

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Orbit equation

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In astrodynamics, an orbit equation defines the path of orbiting body m 2 {\displaystyle m_{2}\,\!} around central body m 1 {\displaystyle m_{1}\,\!}...

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Elliptic orbit

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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 (...

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Parabolic trajectory

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{\displaystyle v_{o}} is orbital velocity of a body in circular orbit. For a body moving along this kind of trajectory the orbital equation is: r = h 2 μ 1 1...

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Tsiolkovsky rocket equation

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The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle...

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Orbital mechanics

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specific orbital energy ( ϵ {\displaystyle \epsilon \,} ) of elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation) for...

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Circular orbit

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{\displaystyle \mu =GM} , is the standard gravitational parameter. The orbit equation in polar coordinates, which in general gives r in terms of θ, reduces...

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Orbital speed

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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...

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Hohmann transfer orbit

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astronautics, the Hohmann transfer orbit (/ˈhoʊmən/) is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around...

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Orbital period

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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...

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Specific orbital energy

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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...

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Hyperbolic trajectory

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\theta } is linked to the distance between the orbiting bodies ( r {\displaystyle r\,} ) by the orbit equation: r = ℓ 1 + e ⋅ cos ⁡ θ {\displaystyle r={\frac...

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Graveyard orbit

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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...

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Kepler orbit

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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...

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Orbital decay

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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...

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Orbit

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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...

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Schwarzschild geodesics

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minimum radius for the circular orbit to be stable in Schwarzschild metric. An exact solution to the Einstein field equations is the Schwarzschild metric...

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Orbital maneuver

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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...

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Orbit of the Moon

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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...

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Orbit phasing

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the phasing orbit using the following equation. T 2 = T 1 − t {\displaystyle T_{2}=T_{1}-t} where T1 is defined as period of original orbit T2 is defined...

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Molniya orbit

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A Molniya orbit (Russian: Молния, IPA: [ˈmolnʲɪjə] , "Lightning") is a type of satellite orbit designed to provide communications and remote sensing coverage...

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Geostationary orbit

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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...

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Equation of time

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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...

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Orbital eccentricity

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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...

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Low Earth orbit

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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...

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