Search results
Results From The WOW.Com Content Network
A velocity potential is not unique. If ϕ is a velocity potential, then ϕ + f(t) is also a velocity potential for u, where f(t) is a scalar function of time and can be constant. Velocity potentials are unique up to a constant, or a function solely of the temporal variable. The Laplacian of a velocity potential is equal to the divergence of the ...
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...
Geopotential height differs from geometric height (as given by a tape measure) because Earth's gravity is not constant, varying markedly with altitude and latitude; thus, a 1-m geopotential height difference implies a different vertical distance in physical space: "the unit-mass must be lifted higher at the equator than at the pole, if the same ...
The formula for an escape velocity is derived as follows. The specific energy (energy per unit mass) of any space vehicle is composed of two components, the specific potential energy and the specific kinetic energy. The specific potential energy associated with a planet of mass M is given by =
The potential energy of an object can be defined as the object's ability to do work and is increased as the object is moved in the opposite direction of the direction of the force. [ nb 1 ] [ 1 ] If F represents the conservative force and x the position, the potential energy of the force between the two positions x 1 and x 2 is defined as the ...
The escape velocity at a given height is times the speed in a circular orbit at the same height, (compare this with the velocity equation in circular orbit). This corresponds to the fact that the potential energy with respect to infinity of an object in such an orbit is minus two times its kinetic energy, while to escape the sum of potential ...
To find the angle giving the maximum height for a given speed calculate the derivative of the maximum height = / with respect to , that is = / which is zero when = / =. So the maximum height H m a x = v 2 2 g {\displaystyle H_{\mathrm {max} }={v^{2} \over 2g}} is obtained when the projectile is fired straight up.
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 ).