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youtube-dl <url> The path of the output can be specified as: (file name to be included in the path) youtube-dl -o <path> <url> To see the list of all of the available file formats and sizes: youtube-dl -F <url> The video can be downloaded by selecting the format code from the list or typing the format manually: youtube-dl -f <format/code> <url>
Analog models of gravity are attempts to model various phenomena of general relativity (e.g., black holes or cosmological geometries) using other physical systems such as waves in a moving fluid and electromagnetic waves in a dielectric medium. [1]
The Hill sphere is a common model for the calculation of a gravitational sphere of influence. It is the most commonly used model to calculate the spatial extent of gravitational influence of an astronomical body (m) in which it dominates over the gravitational influence of other bodies, particularly a primary (M). [1]
For this the gravitational force, i.e. the gradient of the potential, must be computed. Efficient recursive algorithms have been designed to compute the gravitational force for any N z {\displaystyle N_{z}} and N t {\displaystyle N_{t}} (the max degree of zonal and tesseral terms) and such algorithms are used in standard orbit propagation software.
To make this into an equal-sided formula or equation, there needed to be a multiplying factor or constant that would give the correct force of gravity no matter the value of the masses or distance between them (the gravitational constant). Newton would need an accurate measure of this constant to prove his inverse-square law.
A hyperbolic trajectory is depicted in the bottom-right quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the hyperbolic trajectory is shown in red. The height of the kinetic energy decreases as the speed decreases and distance increases according to Kepler's laws.
Diagram regarding the confirmation of gravitomagnetism by Gravity Probe B. Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity.
The gravitational potential, , of a system is related to the acceleration and the gravitational field, by: = = (), = = ‖ ‖, whereas the potential is related to a (smoothened) mass density, , via the Poisson's equation in the integral form = ‖ ‖ or the more common differential form =.