Isochrone
Isochrone may refer to: * Stellar isochrone, the curve on the Hertzsprung–Russell diagram representing stars of the same age *Isochrone curve, the curve (a cycloid) for which objects starting at different points finish at the same time and point when released *Isochrone map An isochrone map in geography and urban planning is a map that depicts the area accessible from a point within a certain time threshold. An isochrone (iso = equal, chrone = time) is defined as "a line drawn on a map connecting points at which som ...

Stellar Isochrone
In stellar evolution, an isochrone is a curve on the Hertzsprung-Russell diagram, representing a population of stars of the same age but with different mass. The Hertzsprung-Russell diagram plots a star's luminosity against its temperature, or equivalently, its color. Stars change their positions on the HR diagram throughout their life. Newborn stars of low or intermediate mass are born cold but extremely luminous. They contract and dim along the Hayashi track, decreasing in luminosity but staying at roughly the same temperature, until reaching the main sequence directly or by passing through the Henyey track. Stars evolve relatively slowly along the main sequence as they fuse hydrogen, and after the vast majority of their lifespan, all but the least massive stars become giants. They then evolve quickly towards their stellar endpoints: white dwarfs, neutron stars, or black holes. Isochrones can be used to date open clusters because their members all have roughly the same age. O ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Isochrone Curve
A tautochrone or isochrone curve (from Greek prefixes tauto- meaning ''same'' or iso- ''equal'', and chrono ''time'') is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the curve. The curve is a cycloid, and the time is equal to π times the square root of the radius (of the circle which generates the cycloid) over the acceleration of gravity. The tautochrone curve is related to the brachistochrone curve, which is also a cycloid. The tautochrone problem The tautochrone problem, the attempt to identify this curve, was solved by Christiaan Huygens in 1659. He proved geometrically in his ''Horologium Oscillatorium'', originally published in 1673, that the curve is a cycloid. The cycloid is given by a point on a circle of radius r tracing a curve as the circle rolls along the x axis, as: \begin x &= r(\theta - \sin \theta) \\ y &= r(1 - \cos \theta), \end Huygens al ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]