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valid in the present case of linear periodic waves. Orbital motion under linear waves. The yellow dots indicate the momentary position of fluid particles on their (orange) orbits. The black dots are the centres of the orbits. Particle motion in an ocean wave at deep (A) and shallow (B) depths. 1) Propagation direction. 2) Wave crest. 3) Wave ...
Description: * the dark blue line is the surface elevation of the 3rd-order Stokes wave, * the black line is the fundamental wave component, with wavenumber k (wavelength λ, k = 2π / λ), * the light blue line is the harmonic at 2 k (wavelength 1 ⁄ 2 λ), and * the red line is the harmonic at 3 k (wavelength 1 ⁄ 3 λ).
In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter (the combined center of mass) or, if one body is much more massive than the other bodies of the system combined, its speed relative to the center of mass of the most massive body.
The speed (or the magnitude of velocity) relative to the centre of mass is constant: [1]: 30 = = where: , is the gravitational constant, is the mass of both orbiting bodies (+), although in common practice, if the greater mass is significantly larger, the lesser mass is often neglected, with minimal change in the result.
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space. For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as ...
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 ...
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.