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In celestial mechanics, the specific relative angular momentum (often denoted or ) of a body is the angular momentum of that body divided by its mass. [1] In the case of two orbiting bodies it is the vector product of their relative position and relative linear momentum, divided by the mass of the body in question.
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
In astronomy, minimum mass is the lower-bound calculated mass of observed objects such as planets, stars, binary systems, [1] nebulae, [2] and black holes.. Minimum mass is a widely cited statistic for extrasolar planets detected by the radial velocity method or Doppler spectroscopy, and is determined using the binary mass function.
Effective radial potential for various angular momenta. At small radii, the energy drops precipitously, causing the particle to be pulled inexorably inwards to r = 0. However, when the normalized angular momentum a/r s = L/mcr s equals the square root of three, a metastable circular orbit is possible at the radius highlighted with a green ...
This causes a degeneracy between mass and inclination. [5] [6] For example, if the measured radial velocity is low, this can mean that the true orbital velocity is low (implying low mass objects) and the inclination high (the orbit is seen edge-on), or that the true velocity is high (implying high mass objects) but the inclination low (the ...
To find a more precise measure of the mass requires knowledge of the inclination of the planet's orbit. A graph of measured radial velocity versus time will give a characteristic curve (sine curve in the case of a circular orbit), and the amplitude of the curve will allow the minimum mass of the planet to be calculated using the binary mass ...
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler. Their general vector form is
In mathematics, the Stieltjes transformation S ρ (z) of a measure of density ρ on a real interval I is the function of the complex variable z defined outside I by the formula S ρ ( z ) = ∫ I ρ ( t ) d t t − z , z ∈ C ∖ I . {\displaystyle S_{\rho }(z)=\int _{I}{\frac {\rho (t)\,dt}{t-z}},\qquad z\in \mathbb {C} \setminus I.}