# Transit satellite navigation

Series | Geophysical References Series |
---|---|

Title | Problems in Exploration Seismology and their Solutions |

Author | Lloyd P. Geldart and Robert E. Sheriff |

Chapter | 7 |

Pages | 221 - 252 |

DOI | http://dx.doi.org/10.1190/1.9781560801733 |

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Problem 7.3a

Determine the acceleration of gravity at the orbit of a Transit satellite 1070 km above the Earth, knowing that at the surface of the Earth is 9.81 m/s, and that the gravitational force varies inversely as the square of the distance between the centers of gravity of the masses. The radius of the Earth is 6370 km.

### Background

A satellite is in a stable orbit around the Earth when the gravitational force pulling it earthward equals the centrifugal force , where is the acceleration of gravity, and the satellite’s mass and velocity, and the radius of its orbit about the center of the Earth.

### Solution

The radius of the satellite’s orbit is km. Since is proportional to the force of gravity, at the satellite’s orbit,

## Problem 7.3b

What is the satellite’s velocity if its orbit is stable?

### Solution

For a stable orbit, the gravitational acceleration is balanced by the centripetal acceleration.

Thus,

## Problem 7.3c

How long does it take for one orbit?

### Solution

The length of the nearly circular orbit is km, so the time for one orbit is

## Problem 7.3d

How far away is the satellite when it first emerges over the horizon?

### Solution

In Figure 7.3a, is the point of observation. The satellite first becomes visible when it reaches the tangent to the Earth at . The tangent is normal to the radius at , so

## Problem 7.3e

What is the maximum time of visibility on a single satellite pass?

### Solution

In Figure 7.3a the angle subtended at the center of the Earth by is

The satellite is visible while it traverses an arc subtending . Since the entire orbit is traversed in 6395 s, the time of visibility is minutes, 25 seconds.

## Continue reading

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Effect of station angle on location errors | Effective penetration of profiler sources |

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Characteristics of seismic events | Reflection field methods |

## Also in this chapter

- Radiolocation errors because of velocity variations
- Effect of station angle on location errors
- Transit satellite navigation
- Effective penetration of profiler sources
- Directivity of linear sources
- Sosie method
- Energy from an air-gun array
- Dominant frequencies of marine sources
- Effect of coil inductance on geophone equation
- Streamer feathering due to cross-currents
- Filtering effect of geophones and amplifiers
- Filter effects on waveshape
- Effect of filtering on event picking
- Binary numbers