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The synodic period refers not to the orbital relation to the parent star, but to other celestial objects, making it not a merely different approach to the orbit of an object around its parent, but a period of orbital relations with other objects, normally Earth, and their orbits around the Sun.
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.
High Planet orbiting the Sun in a circular orbit (e=0.0) Planet orbiting the Sun in an orbit with e=0.5 Planet orbiting the Sun in an orbit with e=0.2 Planet orbiting the Sun in an orbit with e=0.8 The red ray rotates at a constant angular velocity and with the same orbital time period as the planet, =.
A line drawn from the planet to the satellite sweeps out equal areas in equal times no matter which portion of the orbit is measured. The square of a satellite's orbital period is proportional to the cube of its average distance from the planet.
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit . There are many different ways to mathematically describe the same orbit, but certain schemes are commonly used in astronomy and orbital mechanics .
where p r is the radial momentum canonically conjugate to the coordinate q, which is the radial position, and T is one full orbital period. The integral is the action of action-angle coordinates . This condition, suggested by the correspondence principle , is the only one possible, since the quantum numbers are adiabatic invariants .
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.
Orbital decay is a gradual decrease of the distance between two orbiting bodies at their closest approach (the periapsis) over many orbital periods. These orbiting bodies can be a planet and its satellite , a star and any object orbiting it, or components of any binary system .
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