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The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section.
Kepler's 3rd law of planetary motion states, the square of the periodic time is proportional to the cube of the mean distance, [4] or , where a is the semi-major axis or mean distance, and P is the orbital period as above.
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:
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.
Note that according to this approximation cos i equals −1 when the semi-major axis equals 12 352 km, which means that only lower orbits can be Sun-synchronous. The period can be in the range from 88 minutes for a very low orbit ( a = 6554 km , i = 96°) to 3.8 hours ( a = 12 352 km , but this orbit would be equatorial, with i = 180°).
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.
semi-major axis = 23001 km; eccentricity = 0.566613; true anomaly at time t 1 = −7.577° true anomaly at time t 2 = 92.423° This y-value corresponds to Figure 3. With r 1 = 10000 km; r 2 = 16000 km; α = 260° one gets the same ellipse with the opposite direction of motion, i.e. true anomaly at time t 1 = 7.577°
The International Space Station has an orbital period of 91.74 minutes (5504 s), hence by Kepler's Third Law the semi-major axis of its orbit is 6,738 km. [citation needed] The specific orbital energy associated with this orbit is −29.6 MJ/kg: the potential energy is −59.2 MJ/kg, and the kinetic energy 29.6 MJ/kg.