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(Tagged November 2005) The Shapiro time delay effect, or gravitational time delay effect, is one of the four classic solar system tests of General relativity. Radar signals passing near a massive object takes slightly longer to travel to a target and longer to return (as measured by the observer) than it would if the mass of the object were not present. General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ...
This long range radar antenna (approximately 40m (130ft) in diameter) rotates on a track to observe activities near the horizon. ...
History The time delay effect was first noticed in 1964, by Irwin I. Shapiro. Shapiro proposed an observational test of his prediction: bounce radar beams off the surface of Venus and Mercury, and measure the round trip travel time. When the Earth, Sun, and Venus are most favorably aligned, Shapiro showed that the expected time delay, due to the presence of the Sun, of a radar signal traveling from the Earth to Venus and back, would be about 200 milliseconds, well within the limitations of 1960s era technology.
The first test, using the MIT Haystack radar antenna, was successful, matching the predicted amount of time delay. The experiments have been repeated many times since, with increasing accuracy. The Massachusetts Institute of Technology, or MIT, is a university located in the city of Cambridge, Massachusetts, USA. MIT is one of the worlds leading research institutions in science and technology, as well as in numerous other fields, including management, economics, linguistics, political science, and philosophy. ...
Calculating time delay The speed of light in meters per given interval of "proper time" is a constant, however the travel time of any electromagnetic wave, or signal, moving at 299,792,458 meters per "second" can be affected by the gravitational time dilation in regions of spacetime through which it travels. This is because the coordinate time and proper time diverge as the gravitational field strength increases. Gravitational time dilation is a phenomenon of the time running at the vicinity of a mass slower than at infinite distance from that mass (in space without any other masses). ...
Coordinate time is the interval of time independent of relativistic time dilation. ...
Proper time is time as measured by the clock for an observer who is traveling through spacetime. ...
Time delay due light travelling around a single mass For a signal going around a massive object, the time delay can be computed as the following:
Vectors with unit length: In physics and in vector calculus, a spatial vector is a concept characterized by a magnitude, which is a scalar, and a direction (which can be defined in a 3-dimensional space by the Euler angles). ...
 a vector pointing from the observer to the source
 a vector from the source to the gravitating mass M
See Dot product. In mathematics, the dot product, also known as the scalar product, is a binary operation which takes two vectors and returns a scalar quantity. ...
The above formula can be rearranged like this:
Which is the extra distance the light has to travel.
Where:
Rs is the Schwarzchild radius. The Schwarzschild radius (sometimes inappropriately referred to as the gravitational radius[1]) is a characteristic radius associated with every mass. ...
This is the same as:
Special cases
Shapiro delay and interstellar probes Shapiro delay must be considered along with ranging data when trying to accurately determine the distance to interstellar probes such as the Voyager and Pioneer spacecraft (see the Voyager program, the Pioneer program, and the Pioneer anomaly). The Voyager spacecraft Launch of Voyager 2 Voyager is also the name of a planned series of unmanned probes to Mars, cancelled in 1968. ...
The American Pioneer program of unmanned space missions was designed for planetary exploration. ...
The Pioneer anomaly or Pioneer effect refers to the observed deviation from expectations of the trajectories of various unmanned spacecraft visiting the outer Solar system, notably Pioneer 10 and 11. ...
Quote by Einstein "In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlinlited domain of validity ; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light)." - Albert Einstein (The General Theory of Relativity: Chapter 22 - A Few Inferences from the General Principle of Relativity)
References - "Boost for General Relativity." Nature. 12 July 2001. <http://www.nature.com/physics/highlights/6843-1.html>.
- Einstein, Albert. "Relativity : the Special and General Theory by Albert Einstein." Project Gutenberg. <http://www.gutenberg.org/etext/5001.>
- Irwin I. Shapiro (December 1964). Fourth Test of General Relativity. Physical Review Letters 13: 789-791.
- Irwin I. Shapiro, Gordon H. Pettengill, Michael E. Ash, Melvin L. Stone, William B. Smith, Richard P. Ingalls, and Richard A. Brockelman (May 1968). Fourth Test of General Relativity: Preliminary Results. Physical Review Letters 20: 1265–1269.
- d'Inverno, Ray (1992). Introducing Einstein's Relativity, Oxford: Clarendon Press. ISBN 0-19-859686-3. See Section 15.6 for an excellent advanced undergraduate level introduction to the Shapiro effect.
- Will, Clifford M. (2001). The Confrontation between General Relativity and Experiment. Living Rev. Rel. 4: 4-107. See also gr-qc/0103044 A graduate level survey of the solar system tests, and more.
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