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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 ...
Conversely, measurements of the smaller body's orbit only provide information on the product, μ, not G and M separately. The gravitational constant, G, is difficult to measure with high accuracy, [12] while orbits, at least in the solar system, can be measured with great precision and used to determine μ with similar precision.
NOTE: Gauss's method is a preliminary orbit determination, with emphasis on preliminary. The approximation of the Lagrange coefficients and the limitations of the required observation conditions (i.e., insignificant curvature in the arc between observations, refer to Gronchi [2] for more details) causes
The longitude of the ascending node, Ω, the inclination, i, and the argument of periapsis, ω, or the longitude of periapsis, ϖ, specify the orientation of the orbit in its plane. Either the longitude at epoch, L 0, the mean anomaly at epoch, M 0, or the time of perihelion passage, T 0, are used to specify a known point in the orbit. The ...
A 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 a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section.
In calculating the position of the body around its orbit, it is often convenient to begin by assuming circular motion. This first approximation is then simply a constant angular rate multiplied by an amount of time. However, the actual solution, assuming Newtonian physics, is an elliptical orbit (a Keplerian orbit).
Orbital position vector, orbital velocity vector, other orbital elements. In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position and velocity that together with their time () uniquely determine the trajectory of the orbiting body in space.
The different coefficients J n, C n m, S n m, are then given the values for which the best possible agreement between the computed and the observed spacecraft orbits is obtained. As P 0 n (x) = −P 0 n (−x) non-zero coefficients J n for odd n correspond to a lack of symmetry "north–south" relative the equatorial plane for the mass ...