Search results
Results From The WOW.Com Content Network
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.
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.
Compared with the potential energy at the surface, which is −62.6 MJ/kg., the extra potential energy is 3.4 MJ/kg, and the total extra energy is 33.0 MJ/kg. The average speed is 7.7 km/s, the net delta-v to reach this orbit is 8.1 km/s (the actual delta-v is typically 1.5–2.0 km/s more for atmospheric drag and gravity drag ).
For this the gravitational force, i.e. the gradient of the potential, must be computed. Efficient recursive algorithms have been designed to compute the gravitational force for any N z {\displaystyle N_{z}} and N t {\displaystyle N_{t}} (the max degree of zonal and tesseral terms) and such algorithms are used in standard orbit propagation software.
A common misconception occurs between centre of mass and centre of gravity.They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical description of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts.
Siméon Denis Poisson. Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics.For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate the corresponding electrostatic or gravitational (force) field.
There are various types of potential energy, each associated with a particular type of force. For example, the work of an elastic force is called elastic potential energy; work of the gravitational force is called gravitational potential energy; work of the Coulomb force is called electric potential energy; work of the strong nuclear force or weak nuclear force acting on the baryon charge is ...
The second equation says that the kinetic energy (seen from the origin) of a particle of unit mass moving with the expansion plus its (negative) gravitational potential energy (relative to the mass contained in the sphere of matter closer to the origin) is equal to a constant related to the curvature of the universe. In other words, the energy ...