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Gravitational redshift has been measured in the laboratory [65] and using astronomical observations. [66] Gravitational time dilation in the Earth's gravitational field has been measured numerous times using atomic clocks, [67] while ongoing validation is provided as a side effect of the operation of the Global Positioning System (GPS). [68]
The geodetic effect is an effect caused by space-time being "curved" by the mass of the Earth. A gyroscope's axis when parallel transported around the Earth in one complete revolution does not end up pointing in exactly the same direction as before. The angle "missing" may be thought of as the amount the gyroscope "leans over" into the slope of ...
In special relativity, parallel geodesics remain parallel. In a gravitational field with tidal effects, this will not, in general, be the case. If, for example, two bodies are initially at rest relative to each other, but are then dropped in the Earth's gravitational field, they will move towards each other as they fall towards the Earth's center.
If Earth's shape were perfectly known together with the exact mass density ρ = ρ(x, y, z), it could be integrated numerically (when combined with a reciprocal distance kernel) to find an accurate model for Earth's gravitational field. However, the situation is in fact the opposite: by observing the orbits of spacecraft and the Moon, Earth's ...
Maximum speed is finite: No physical object, message or field line can travel faster than the speed of light in vacuum. The effect of gravity can only travel through space at the speed of light, not faster or instantaneously. Mass–energy equivalence: E = mc 2, energy and mass are equivalent and transmutable.
The gravitational force that a celestial body exerts on a space vehicle is modeled with the body and vehicle taken as point masses; the bodies (Earth, Moon, etc.) are simplified as spheres; and the mass of the vehicle is much smaller than the mass of the body so that its effect on the gravitational acceleration can be neglected.
In Minkowski space, the geodesic will be a straight line. Any curve that differs from the geodesic purely spatially ( i.e. does not change the time coordinate) in any inertial frame of reference will have a longer proper length than the geodesic, but a curve that differs from the geodesic purely temporally ( i.e. does not change the space ...
In classical mechanics, a gravitational field is a physical quantity. [5] A gravitational field can be defined using Newton's law of universal gravitation. Determined in this way, the gravitational field g around a single particle of mass M is a vector field consisting at every point of a vector pointing directly towards the particle. The ...