Search results
Results from the WOW.Com Content Network
The eccentricity can be defined as the ratio of the linear eccentricity to the semimajor axis a: that is, = (lacking a center, the linear eccentricity for parabolas is not defined). It is worth to note that a parabola can be treated as an ellipse or a hyperbola, but with one focal point at infinity .
With eccentricity just over 1 the hyperbola is a sharp "v" shape. At = the asymptotes are at right angles. With > the asymptotes are more than 120° apart, and the periapsis distance is greater than the semi major axis. As eccentricity increases further the motion approaches a straight line.
Since the eccentricity of a hyperbola is always greater than one, the center B must lie outside of the reciprocating circle C. This definition implies that the hyperbola is both the locus of the poles of the tangent lines to the circle B, as well as the envelope of the polar lines of the points on B.
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 ...
To simplify the calculation, let = without loss of generality (any other confocal net can be obtained by uniform scaling) and among the four intersections between an ellipse and a hyperbola choose those in the positive quadrant (other sign combinations yield the same result after an analogous calculation).
Figure 1: is the centre of attraction, is the point corresponding to vector ¯, and is the point corresponding to vector ¯ Figure 2: Hyperbola with the points and as foci passing through Figure 3: Ellipse with the points and as foci passing through and
The mean eccentricity of an object is the average eccentricity as a result of perturbations over a given time period. Neptune currently has an instant (current epoch ) eccentricity of 0.011 3 , [ 13 ] but from 1800 to 2050 has a mean eccentricity of 0.008 59 .
A special case of this is the circular orbit, which is an ellipse of zero eccentricity. The formula for the velocity of a body in a circular orbit at distance r from the center of gravity of mass M can be derived as follows: