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Inversely, for calculating the distance where a body has to orbit in order to have a given orbital period T: a = G M T 2 4 π 2 3 {\displaystyle a={\sqrt[{3}]{\frac {GMT^{2}}{4\pi ^{2}}}}} For instance, for completing an orbit every 24 hours around a mass of 100 kg , a small body has to orbit at a distance of 1.08 meters from the central body's ...
As an example, with a = 7200 km, i.e., for an altitude a − R E ≈ 800 km of the spacecraft over Earth's surface, this formula gives a Sun-synchronous inclination of 98.7°. 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.
Orbital period can be found from n given the fact that the mean motion can be described as a frequency (number of orbits per unit time), which is the inverse of period. P = 2 π n {\displaystyle P={\frac {2\pi }{n}}} if n is in radians, or P = 360 ∘ n {\displaystyle P={\frac {360^{\circ }}{n}}} if n is in degrees.
The distance between the points and is , the distance between the points and is = and the distance between the points and is = +. The value A {\displaystyle A} is positive or negative depending on which of the points P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} that is furthest away from the point F 1 {\displaystyle F_{1}} .
The period of the resultant orbit will be longer than that of the original circular orbit. The consequences of the rules of orbital mechanics are sometimes counter-intuitive. For example, if two spacecrafts are in the same circular orbit and wish to dock, unless they are very close, the trailing craft cannot simply fire its engines to go faster.
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 a 3 ∝ P 2 , {\displaystyle {a^{3}}\propto {P^{2}},} where a is the semi-major axis or mean distance, and P is the orbital period as above.
The classical method of finding the position of an object in an elliptical orbit from a set of orbital elements is to calculate the mean anomaly by this equation, and then to solve Kepler's equation for the eccentric anomaly. Define ϖ as the longitude of the pericenter, the angular
Radial velocity curve with peak radial velocity K=1 m/s and orbital period 2 years. The peak radial velocity is the semi-amplitude of the radial velocity curve, as shown in the figure. The orbital period is found from the periodicity in the radial velocity curve. These are the two observable quantities needed to calculate the binary mass function.