Search results
Results from the WOW.Com Content Network
The value obtained agrees approximately with the measured value of g. The difference may be attributed to several factors, mentioned above under "Variation in magnitude": The Earth is not homogeneous; The Earth is not a perfect sphere, and an average value must be used for its radius; This calculated value of g only includes true gravity. It ...
The constant of proportionality, G, in this non-relativistic formulation is the gravitational constant. Colloquially, the gravitational constant is also called "Big G", distinct from "small g" (g), which is the local gravitational field of Earth (also referred to as free-fall acceleration).
Determined in this way, the gravitational field g around a single particle of mass M is a vector field consisting at every point of a vector pointing directly towards the particle. The magnitude of the field at every point is calculated by applying the universal law, and represents the force per unit mass on any object at that point in space.
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.
It is a generalisation of the vector form, which becomes particularly useful if more than two objects are involved (such as a rocket between the Earth and the Moon). For two objects (e.g. object 2 is a rocket, object 1 the Earth), we simply write r instead of r 12 and m instead of m 2 and define the gravitational field g(r) as:
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 acceleration due to Earth's gravity at its surface is 976 to 983 Gal, the variation being due mainly to differences in latitude and elevation. Standard gravity is 980.665 Gal. Mountains and masses of lesser density within the Earth's crust typically cause variations in gravitational acceleration of tens to hundreds of milligals (mGal).
By making this assumption, g takes the following form: = (i.e., the direction of g is antiparallel to the direction of r, and the magnitude of g depends only on the magnitude, not direction, of r). Plugging this in, and using the fact that ∂ V is a spherical surface with constant r and area 4 π r 2 {\displaystyle 4\pi r^{2}} ,