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In triangulation, the point at which astronomical observations for the azimuth and the longitude are made by use of Laplace equation is called __________.
subsidiary station
base line
base station
Laplace station
Laplace station
A Laplace station is a triangulation station where astronomical observations for both latitude, longitude, and azimuth are conducted. These observations are necessary to calculate the Laplace correction to mitigate the discrepancy between geodetic azimuth and astronomical azimuth caused by the deflection of the vertical.
A Laplace station is a triangulation station where astronomical observations for both latitude, longitude, and azimuth are conducted. These observations are necessary to calculate the Laplace correction to mitigate the discrepancy between geodetic azimuth and astronomical azimuth caused by the deflection of the vertical.
AAтАЛтИТAGтАЛ=(╬╗AтАЛтИТ╬╗GтАЛ)sin╧Х тАФ The Laplace Equation where AAтАЛ is astronomical azimuth, AGтАЛ is geodetic azimuth, ╬╗AтАЛтИТ╬╗GтАЛ is the difference in longitude, and ╧Х is the latitude.
In geodetic triangulation, the measured geodetic azimuths are corrected using the Laplace equation to account for the difference between the geodetic and astronomical coordinates. The relation is established as AAтАЛтИТAGтАЛ=(╬╗AтАЛтИТ╬╗GтАЛ)sin╧Х, where ╬╗ represents longitude and ╧Х is the latitude. By observing at specific stations, the accumulation of azimuth error in the triangulation network is controlled.
Laplace stations are essential for maintaining the orientation accuracy of a large triangulation chain.
The discrepancy between the geodetic and astronomical azimuth is due to the non-parallelism of the plumb line with the normal to the reference ellipsoid.
Approximately one Laplace station is usually placed at every 10 to 20 triangles in a major triangulation network.
Prevents azimuth error accumulation in long triangulation chains.
Improves the consistency between local geodetic surveys and global coordinate systems.
Requires high-precision astronomical observation equipment and expert surveyors.
Observations are time-consuming and weather-dependent.
Large-scale geodetic triangulation networks.
Control surveys for national mapping projects.
Option A (subsidiary station) is used for extending the survey to areas not directly reachable from the main stations.
Option B (base line) is the precisely measured length used to scale the triangulation network.
Option C (base station) is a term usually related to GPS/GNSS reference points rather than classical triangulation.
D is correct тАФ A Laplace station is a triangulation station equipped for astronomical observations to apply the Laplace correction.
Always remember that the Laplace equation bridges the gap between the reference ellipsoid used in geodetics and the actual gravity field observed in astronomical surveying.
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