Transit satellite navigation
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.
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.
The radius of the satellite’s orbit is km. Since is proportional to the force of gravity, at the satellite’s orbit,
What is the satellite’s velocity if its orbit is stable?
For a stable orbit, the gravitational acceleration is balanced by the centripetal acceleration.
How long does it take for one orbit?
The length of the nearly circular orbit is km, so the time for one orbit is
How far away is the satellite when it first emerges over the horizon?
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
What is the maximum time of visibility on a single satellite pass?
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.
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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