Do all objects have gravitational potential energy and why does every object have potential energy even when it is not moving?
No object has gravitational potential energy. Only the gravitational field contains energy or more exactly an energy density.
The mechanic energy involved in moving objects under the influence of gravitational forces corresponds to the modification of the field energy contained in the field overlay caused by the objects.
The energy density of the gravitational field is proportional to the field strength squared. Therefor a field overlay contains less energy as the undisturbed field. By the way, the gravitational field strength is the gravitational acceleration g.
The energy content W of the gravitational field with strength g is given by:
W=W0-g²/(8πG). G is the gravitational constant. W0 is some omnipresent background energy, which prevents W to get absolutely negative.
No, not everything has potential energy. There are many types of potential energy and one is nuclear potential energy which is axiomatic to an atom (ergo the packing of protons and neutrons in the nucleus): This means that everything with mass has potential energy. All objects above Earth's surface have gravitational potential energy because they are affected by the force of gravity because there is a constant and continuous gravitational attraction between every object and the Earth. A single object cannot have potential energy with itself, but only with respect to another object. For example, the Moon only has gravitational potential energy relative to the Earth (or another object). Sometimes people forget that gravitational potential energy at large distances is negative. You are giving the ball potential energy, specifically gravitational potential energy. Gravitational potential energy is the energy gained by an object as its height above ground level increases. As the ball falls towards the ground, its gravitational potential energy is transformed into kinetic energy. Potential energy is energy that is stored in an object or substance. Gravitational potential energy is energy in an object that is held in a vertical position. As an orbiting object decreases in altitude or orbital radius r, its gravitational potential energy decreases and is transformed into kinetic energy. Thus, kinetic energy increases. Many objects possess energy because of their position; potential energy is energy due to an object's position or configuration stored energy. An object that is not moving has zero kinetic energy. Stationary objects possess potential energy (the other main type of energy). Potential energy is converted to kinetic energy when a force such as gravity acts upon the object to set it in motion. Objects can have both kinetic energy and potential energy at the same time. An object can be moving (have kinetic energy) and be elevated above the ground at the same time (and also have potential energy). Potential energy, expressed in science as U, is energy that is stored within an object, not in motion but capable of becoming active. When at rest, every object has rest mass potential energy; if the object is in a position to be affected by gravity and to fall, it has gravitational potential energy.
Rk Naresh
It is not too difficult to proof that all energy associated to potential energy is contained in the gravitational field.
The mathematical proof is based on integrating over the potential energy W=1/2*∫ρɸ over all space. ρ is the mass density. ɸ is the potential generated by that mass density.
Replacing ρ=∇²ɸ/(4πG) from the poisson equation and the partial integration which transforms the integrand ɸ∇²ɸ to -(∇ɸ)² leads to
W=- 1/(8πG)*∫(∇ɸ)². Please note ∇ɸ=g. g is the gravitational acceleration, the field strength of the gravitational field. This integral relation holds for all configurations of mass where the potential vanishes in infinity.
This is an incontrovertible mathematically proven fact, which shows that all potential energy of a mass assembly in its own field is contained in the field energy.
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