time dilation in a gravitational well is equal to the velocity time dilation for a speed that is needed to escape that gravitational well (given that the metric is of the form , i. e. it is time invariant and there are no "movement" terms ). To show that, one can apply Noether's theorem to a body that freely falls into the well from infinity. Then the time invariance of the metric implies conservation of the quantity , where is the time component of the 4-velocity of the body. At the infinity , so , or, in coordinates adjusted to the local time dilation, ; that is, time dilation due to acquired velocity (as measured at the falling body's position) equals to the gravitational time dilation in the well the body fell into. Applying this argument more generally one gets that (under the same assumptions on the metric) the relative gravitational time dilation between two points equals to the time dilation due to velocity needed to climb from the lower point to the higher. Experimental confirmation Gravitational time dilation has been experimentally measured using atomic clocks on airplanes, such as the Hafele–Keating experiment. The clocks aboard the airplanes were slightly faster than clocks on the ground. The effect is significant enough that the Global Positioning System's artificial satellites need to have their clocks corrected. Additionally, time dilations due to height differences of less than one metre have been experimentally verified in the laboratory. Gravitational time dilation in the form of gravitational redshift has also been confirmed by the Pound–Rebka experiment and observations of the spectra of the white dwarf Sirius B. Gravitational time dilation has been measured in experiments with time signals sent to and from the Viking 1 Mars lander. See also Clock hypothesis Gravitational redshift Hafele–Keating experiment Relative velocity time dilation Twin paradox Barycentric Coordinate Time References Further reading Effects of gravitation Theory of relativity