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  2. Gravitational time dilation - Wikipedia

    en.wikipedia.org/wiki/Gravitational_time_dilation

    Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events, as measured by observers situated at varying distances from a gravitating mass. The lower the gravitational potential (the closer the clock is to the source of gravitation), the slower time passes, speeding up as the gravitational ...

  3. Time dilation - Wikipedia

    en.wikipedia.org/wiki/Time_dilation

    Daily time dilation (gain or loss if negative) in microseconds as a function of (circular) orbit radius r = rs/re, where rs is satellite orbit radius and re is the equatorial Earth radius, calculated using the Schwarzschild metric. At r ≈ 1.497 [Note 1] there is no time dilation. Here the effects of motion and reduced gravity cancel.

  4. Free-fall time - Wikipedia

    en.wikipedia.org/wiki/Free-fall_time

    The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to oppose the collapse.. As such, it plays a fundamental role in setting the timescale for a wide variety of astrophysical processes—from star formation to helioseismology to supernovae—in which gravity plays a dominant ro

  5. Schwarzschild radius - Wikipedia

    en.wikipedia.org/wiki/Schwarzschild_radius

    Therefore, as the body accumulates matter at a given fixed density (in this example, 997 kg/m 3, the density of water), its Schwarzschild radius will increase more quickly than its physical radius. When a body of this density has grown to around 136 million solar masses (1.36 × 10 8 M ☉ ), its physical radius would be overtaken by its ...

  6. Equations for a falling body - Wikipedia

    en.wikipedia.org/wiki/Equations_for_a_falling_body

    The first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 1 2 = 4.9 m. After two seconds it will have fallen 1/2 × 9.8 × 2 2 = 19.6 m; and so on. On the other hand, the penultimate equation becomes grossly inaccurate at great distances.

  7. Two-body problem in general relativity - Wikipedia

    en.wikipedia.org/wiki/Two-body_problem_in...

    For example, the Schwarzschild radius r s of the Earth is roughly 9 mm (3 ⁄ 8 inch); at the surface of the Earth, the corrections to Newtonian gravity are only one part in a billion. The Schwarzschild radius of the Sun is much larger, roughly 2953 meters, but at its surface, the ratio r s / r is roughly 4 parts in a million.

  8. Introduction to general relativity - Wikipedia

    en.wikipedia.org/wiki/Introduction_to_general...

    The related gravitational time dilation effect has been measured by transporting atomic clocks to altitudes of between tens and tens of thousands of kilometers (first by Hafele and Keating in 1971; most accurately to date by Gravity Probe A launched in 1976).

  9. Introduction to the mathematics of general relativity - Wikipedia

    en.wikipedia.org/wiki/Introduction_to_the...

    The circle itself is characterized by coordinates y 1 and y 2 in the two-dimensional space. The circle itself is one-dimensional and can be characterized by its arc length x. The coordinate y is related to the coordinate x through the relation y 1 = r cos ⁠ x / r ⁠ and y 2 = r sin ⁠ x / r ⁠.