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For two pairwise interacting point particles, the gravitational potential energy is the work that an outside agent must do in order to quasi-statically bring the masses together (which is therefore, exactly opposite the work done by the gravitational field on the masses): = = where is the displacement vector of the mass, is gravitational force acting on it and denotes scalar product.
To calculate the velocity distribution of particles hitting this small area, we must take into account that all the particles with (,,) that hit the area within the time interval are contained in the tilted pipe with a height of and a volume of (); Therefore, compared to the Maxwell distribution, the velocity distribution will have an ...
When we calculate the field energy we obtain not only a contribution from particles and forces that may be present but also a contribution from the vacuum field itself i.e. the zero-point field energy. In other words, the zero-point energy reappears even though we may have deleted it from the Hamiltonian. [94]
In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor (also referred to as the stress–energy tensor). The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately 6.6743 × 10 −11 m 3 kg −1 s −2 ...
Before Newton's law of gravity, there were many theories explaining gravity. Philoshophers made observations about things falling down − and developed theories why they do – as early as Aristotle who thought that rocks fall to the ground because seeking the ground was an essential part of their nature. [6]
Additionally, it can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field would couple to the stress–energy tensor in the same way gravitational interactions do. This result suggests that, if a massless spin-2 particle is discovered, it must be the graviton. [5]
The terms kinetic energy and work in their present scientific meanings date back to the mid-19th century. Early understandings of these ideas can be attributed to Thomas Young, who in his 1802 lecture to the Royal Society, was the first to use the term energy to refer to kinetic energy in its modern sense, instead of vis viva.
As the gas in a star becomes more relativistic, the gravitational binding energy required for hydrostatic equilibrium approaches zero and the star becomes unstable (highly sensitive to perturbations), which may lead to a supernova in the case of a high-mass star due to strong radiation pressure or to a black hole in the case of a neutron star.