### Abstract

The global positioning system (GPS) provides an excellent educational example of how the theory of general relativity is put into practice and becomes part of our everyday life. This paper gives a short and instructive derivation of an important formula used in the GPS, and is aimed at graduate students and general physicists. The theoretical background of the GPS (see [1]) uses the Schwarzschild spacetime to deduce the approximate formula, , for the relation between the proper time rate s of a satellite clock and the coordinate time rate t. Here V is the gravitational potential at the position of the satellite and is its velocity (with light-speed being normalized as c = 1). In this paper we give a different derivation of this formula, without using approximations, to arrive at , where is the normal vector pointing outwards from the centre of Earth to the satellite. In particular, if the satellite moves along a circular orbit then the formula simplifies to . We emphasize that this derivation is useful mainly for educational purposes, as the approximation above is already satisfactory in practice.

Original language | English |
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Pages (from-to) | 1147-1151 |

Number of pages | 5 |

Journal | European Journal of Physics |

Volume | 29 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2008 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*European Journal of Physics*,

*29*(6), 1147-1151. https://doi.org/10.1088/0143-0807/29/6/003

**Coordinate time and proper time in the GPS.** / Matolcsi, T.; Matolcsi, M.

Research output: Contribution to journal › Article

*European Journal of Physics*, vol. 29, no. 6, pp. 1147-1151. https://doi.org/10.1088/0143-0807/29/6/003

}

TY - JOUR

T1 - Coordinate time and proper time in the GPS

AU - Matolcsi, T.

AU - Matolcsi, M.

PY - 2008

Y1 - 2008

N2 - The global positioning system (GPS) provides an excellent educational example of how the theory of general relativity is put into practice and becomes part of our everyday life. This paper gives a short and instructive derivation of an important formula used in the GPS, and is aimed at graduate students and general physicists. The theoretical background of the GPS (see [1]) uses the Schwarzschild spacetime to deduce the approximate formula, , for the relation between the proper time rate s of a satellite clock and the coordinate time rate t. Here V is the gravitational potential at the position of the satellite and is its velocity (with light-speed being normalized as c = 1). In this paper we give a different derivation of this formula, without using approximations, to arrive at , where is the normal vector pointing outwards from the centre of Earth to the satellite. In particular, if the satellite moves along a circular orbit then the formula simplifies to . We emphasize that this derivation is useful mainly for educational purposes, as the approximation above is already satisfactory in practice.

AB - The global positioning system (GPS) provides an excellent educational example of how the theory of general relativity is put into practice and becomes part of our everyday life. This paper gives a short and instructive derivation of an important formula used in the GPS, and is aimed at graduate students and general physicists. The theoretical background of the GPS (see [1]) uses the Schwarzschild spacetime to deduce the approximate formula, , for the relation between the proper time rate s of a satellite clock and the coordinate time rate t. Here V is the gravitational potential at the position of the satellite and is its velocity (with light-speed being normalized as c = 1). In this paper we give a different derivation of this formula, without using approximations, to arrive at , where is the normal vector pointing outwards from the centre of Earth to the satellite. In particular, if the satellite moves along a circular orbit then the formula simplifies to . We emphasize that this derivation is useful mainly for educational purposes, as the approximation above is already satisfactory in practice.

UR - http://www.scopus.com/inward/record.url?scp=62649133247&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62649133247&partnerID=8YFLogxK

U2 - 10.1088/0143-0807/29/6/003

DO - 10.1088/0143-0807/29/6/003

M3 - Article

AN - SCOPUS:62649133247

VL - 29

SP - 1147

EP - 1151

JO - European Journal of Physics

JF - European Journal of Physics

SN - 0143-0807

IS - 6

ER -