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The important point of this is that the zero-point field energy H F does not affect the Heisenberg equation for a kλ since it is a c-number or constant (i.e. an ordinary number rather than an operator) and commutes with a kλ. We can therefore drop the zero-point field energy from the Hamiltonian, as is usually done.
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.
The gravity g′ at depth d is given by g′ = g(1 − d/R) where g is acceleration due to gravity on the surface of the Earth, d is depth and R is the radius of the Earth. If the density decreased linearly with increasing radius from a density ρ 0 at the center to ρ 1 at the surface, then ρ ( r ) = ρ 0 − ( ρ 0 − ρ 1 ) r / R , and the ...
At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation. [2] [3] At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834 m/s 2 (32.03 to 32.26 ft/s 2), [4] depending on altitude, latitude, and longitude.
Geopotential is the potential of the Earth's gravity field.For convenience it is often defined as the negative of the potential energy per unit mass, so that the gravity vector is obtained as the gradient of the geopotential, without the negation.
In this scenario, the gravitational force is mostly, but not entirely, diminished; anyone in the elevator would experience an absence of the usual gravitational pull, however the force is not exactly zero. Since gravity is a force directed towards the center of the Earth, two balls a horizontal distance apart would be pulled in slightly ...
Due to Earth's rotation, its surface is not an inertial frame of reference. The Coriolis effect can deflect certain forms of motion as seen from Earth, and the centrifugal force will reduce the effective gravity at the equator. Nevertheless, for many applications the Earth is an adequate approximation of an inertial reference frame.
To obtain a straight-line motion in the rotating world, a force exactly opposite in sign to the fictitious force must be applied to reduce the net force on the walker to zero, so Newton's law of inertia will predict a straight line motion, in agreement with what the rotating observer sees.