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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 ...
The formula is dimensionless, ... In Schwarzschild metric, the orbital velocity for a circular orbit with radius is given by the following formula: = where = is the ...
The eccentricity of an elliptical orbit can be used to obtain the ratio of the apoapsis radius to the periapsis radius: = (+) = + For Earth, orbital eccentricity e ≈ 0.016 71 , apoapsis is aphelion and periapsis is perihelion, relative to the Sun.
For a stationary synchronous orbit: = [2] G = Gravitational constant m 2 = Mass of the celestial body T = rotational period of the body = Radius of orbit. By this formula one can find the stationary orbit of an object in relation to a given body.
The formula for the velocity of a body in a circular orbit at ... The orbital period is equal to that for a circular orbit with the orbit radius equal to the ...
r is the sphere's radius; a is the orbit's semi-major axis in metres, G is the gravitational constant, ρ is the density of the sphere in kilograms per cubic metre. For instance, a small body in circular orbit 10.5 cm above the surface of a sphere of tungsten half a metre in radius would travel at slightly more than 1 mm/s, completing an orbit ...
For a path of radius r, when an angle θ is swept out, the distance traveled on the periphery of the orbit is s = rθ. Therefore, the speed of travel around the orbit is v = r d θ d t = r ω , {\displaystyle v=r{\frac {d\theta }{dt}}=r\omega ,} where the angular rate of rotation is ω .
The orbital radius and angular velocity of the planet in the elliptical orbit will vary. This is shown in the animation: the planet travels faster when closer to the Sun, then slower when farther from the Sun. Kepler's second law states that the blue sector has constant area.