mass and gravitational mass are the same, and all accelerated reference frames (such as a uniformly rotating reference frame with its proper time dilation) are physically equivalent to a gravitational field of the same strength. Consider a family of observers along a straight "vertical" line, each of whom experiences a distinct constant g-force directed along this line (e.g., a long accelerating spacecraft, a skyscraper, a shaft on a planet). Let be the dependence of g-force on "height", a coordinate along the aforementioned line. The equation with respect to a base observer at is where is the total time dilation at a distant position , is the dependence of g-force on "height" , is the speed of light, and denotes exponentiation by e. For simplicity, in a Rindler's family of observers in a flat spacetime, the dependence would be with constant , which yields . On the other hand, when is nearly constant and is much smaller than , the linear "weak field" approximation can also be used. See Ehrenfest paradox for application of the same formula to a rotating reference frame in flat spacetime. Outside a non-rotating sphere A common equation used to determine gravitational time dilation is derived from the Schwarzschild metric, which describes spacetime in the vicinity of a non-rotating massive spherically symmetric object. The equation is where is the proper time between two events for an observer close to the massive sphere, i.e. deep within the gravitational field is the coordinate time between the events for an observer at an arbitrarily large distance from the massive object (this assumes the far-away observer is using Schwarzschild coordinates, a coordinate system where a clock at infinite distance from the massive sphere would tick at one second per second of coordinate time, while closer clocks would tick at less than that rate), is the gravitational constant, is the mass of the object creating the gravitational field, is the radial coordinate of the observer within the gravitational field (this coordinate is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate; the equation in this form has real solutions for ), is the speed of light, is the Schwarzschild radius of , is the escape velocity, and is the escape velocity, expressed as a fraction of the speed of light c. To illustrate then, without accounting for the effects of rotation, proximity to Earth's