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The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes. Important in navigation , it is a special case of a more general formula in spherical trigonometry , the law of haversines , that relates the sides and angles of spherical triangles.
The Fourier number can be derived by nondimensionalizing the time-dependent diffusion equation. As an example, consider a rod of length L {\displaystyle L} that is being heated from an initial temperature T 0 {\displaystyle T_{0}} by imposing a heat source of temperature T L > T 0 {\displaystyle T_{L}>T_{0}} at time t = 0 {\displaystyle t=0 ...
Spatial diffusion is the gradual spread of culture, ideas, and institutions across space over time, in which the desirability of one place adopting the traits of a separate place overcome the friction of distance. Time geography explores how human activity is affected by the constraints of movement, especially temporal costs. [11]
Also, the velocities in the directions perpendicular to the frame changes are affected, as shown above. This is due to time dilation, as encapsulated in the dt/dt′ transformation. The V′ y and V′ z equations were both derived by dividing the appropriate space differential (e.g. dy′ or dz′) by the time differential.
[5] [6] Additional lines of research in the 1960s further developed the nature of the cost rate field as a manifestation of the concept of friction of distance, studying how it was affected by various geographic features. [7] At the time, this solution was only theoretical, lacking the data and computing power for the continuous solution.
A static spacetime is one in which all metric components are independent of the time coordinate (so that =) and the geometry of the spacetime is unchanged under a time-reversal . A vacuum solution is one that satisfies the equation T a b = 0 {\displaystyle T_{ab}=0} .
where is the time passed at a distance from the center of the Earth and is the time passed for a far away observer. For small values of G M / ( r c 2 ) {\displaystyle GM/(rc^{2})} this approximates to:
Also equations of motion can be formulated which connect acceleration and force. Equations for several forms of acceleration of bodies and their curved world lines follow from these formulas by integration. Well known special cases are hyperbolic motion for constant longitudinal proper acceleration or uniform circular motion.