Search results
Results from the WOW.Com Content Network
A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
This is approximately the work done lifting a 1 kg object from ground level to over a person's head against the force of gravity. The work is doubled either by lifting twice the weight the same distance or by lifting the same weight twice the distance. Work is closely related to energy.
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.
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 work needed to move the body over a small distance dr against this force is therefore given by d W = F d r = G M m r 2 d r . {\displaystyle dW=F\,dr=G{\frac {Mm}{r^{2}}}\,dr.} The total work needed to move the body from the surface r 0 of the gravitating body to infinity is then [ 20 ]
The gravitational potential (V) at a location is the gravitational potential energy (U) at that location per unit mass: =, where m is the mass of the object. Potential energy is equal (in magnitude, but negative) to the work done by the gravitational field moving a body to its given position in space from infinity.
This is illustrated in the figure to the right: The work done by the gravitational force on an object depends only on its change in height because the gravitational force is conservative. The work done by a conservative force is equal to the negative of change in potential energy during that process.
Instruments like GRAVITY provide a powerful probe for gravity force detection. [73] Newton's law of gravitation is an example of action at a distance: one body, like the Sun, exerts an influence upon any other body, like the Earth, no matter how far apart they are. Moreover, this action at a distance is instantaneous.