# Hyperbolic navigation

Long Range Navigation (LORAN)
System based on the difference in timing between the reception of two signals, without reference to a common clock. This timing reveals the difference in distance from the receiver to the two stations.

Set of points, such that for any point P of the set, the absolute differences of the distances |PA| |PB| to two fixed points A, B (the foci), is constant, usually denoted by 2a.
Two ground-based radio stations A, B are the foci of a hyperbola.
2e = |AB| = 300 km
By measuring diference time td, they could determine constant 2a.
2a = ||PA| - PB|| = c.td
where c is light speed.

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