Search results
Results from the WOW.Com Content Network
For elliptical orbits it can also be calculated from the periapsis and apoapsis since = and = (+), where a is the length of the semi-major axis. = + = / / + = + where: r a is the radius at apoapsis (also "apofocus", "aphelion", "apogee"), i.e., the farthest distance of the orbit to the center of mass of the system, which is a focus of the ellipse.
Also shown are: semi-major axis a, semi-minor axis b and semi-latus rectum p; center of ellipse and its two foci marked by large dots. For θ = 0°, r = r min and for θ = 180°, r = r max. Mathematically, an ellipse can be represented by the formula:
Halley's calculations enabled the comet's earlier appearances to be found in the historical record. The following table sets out the astronomical designations for every apparition of Halley's Comet from 240 BC, the earliest documented sighting. [7] [167] In the designations, "1P/" refers to Halley's Comet; the first periodic comet discovered.
is the semi-major axis, is the standard gravitational parameter. Conclusions: For a given semi-major axis the specific orbital energy is independent of the eccentricity. Using the virial theorem we find: the time-average of the specific potential energy is equal to
is the length of the semi-major axis. Conclusions: The orbital period is equal to that for a circular orbit with the orbital radius equal to the semi-major axis (), For a given semi-major axis the orbital period does not depend on the eccentricity (See also: Kepler's third law).
The semi-major axis is known if the mean motion and the gravitational mass are known. [ 2 ] [ 3 ] It is also quite common to see either the mean anomaly ( M ) or the mean longitude ( L ) expressed directly, without either M 0 or L 0 as intermediary steps, as a polynomial function with respect to time.
a is the orbit's semi-major axis; G is the gravitational constant, M is the mass of the more massive body. For all ellipses with a given semi-major axis the orbital period is the same, regardless of eccentricity. Inversely, for calculating the distance where a body has to orbit in order to have a given orbital period T:
His work in this area was the first major achievement in celestial mechanics since Isaac Newton. [ 1 ] These monographs include an idea of Poincaré, which later became the basis for mathematical " chaos theory " (see, in particular, the Poincaré recurrence theorem ) and the general theory of dynamical systems .