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The second law establishes that when a planet is closer to the Sun, it travels faster. The third law expresses that the farther a planet is from the Sun, the longer its orbital period. Isaac Newton showed in 1687 that relationships like Kepler's would apply in the Solar System as a consequence of his own laws of motion and law of universal ...
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 ...
Note that the semi-major axis is proportional to the 2/3 power of the orbital period. For example, planets in a 2:3 orbital resonance (such as plutinos relative to Neptune) will vary in distance by (2/3) 2/3 = −23.69% and +31.04% relative to one another. 2 Ceres and Pluto are dwarf planets rather than major planets.
The period of the resultant orbit will be less than that of the original circular orbit. Thrust applied in the direction of the satellite's motion creates an elliptical orbit with its highest point 180 degrees away from the firing point. The period of the resultant orbit will be longer than that of the original circular orbit.
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 ...
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.
An orbit will be Sun-synchronous when the precession rate ρ = dΩ / dt equals the mean motion of the Earth about the Sun n E, which is 360° per sidereal year (1.990 968 71 × 10 −7 rad/s), so we must set n E = ΔΩ E / T E = ρ = ΔΩ / T , where T E is the Earth orbital period, while T is the period of the spacecraft ...
Orbital Parameters of a Cosmic Object: α - RA, right ascension, if the Greek letter does not appear, á letter will appear. δ - Dec, declination, if the Greek letter does not appear, ä letter will appear. P or P orb or T - orbital period; a - semi-major axis; b - semi-minor axis; q - periapsis, the minimum distance; Q - apoapsis, the maximum ...