In triangulation, the point at which astronomical observations for the azimuth and the longitude are made by use of Laplace equation is called:
- ALaplace stationCorrect
- Bbase line
- Cbase station
- Dsubsidiary station
Solution
Concept
A Laplace station is a triangulation station where astronomical azimuth and longitude are observed to control azimuth errors using the Laplace equation.
Formula
Aa - Ag = (λa - λg) sin φ
Step-by-step solution
1. In a long triangulation chain, error in azimuth slowly builds up. 2. To control this, astronomical azimuth and longitude are observed at some stations. 3. The Laplace equation links the astronomical and geodetic azimuth through the difference in longitude. 4. A station where these observations are made is called a Laplace station. 5. Answer is (A).
Explanation
In big triangulation work, azimuth error grows along the chain. At some selected stations, astronomical azimuth and longitude are observed and corrected with the Laplace equation. These stations are called Laplace stations.
Why the other options are wrong
B: Base line is an accurately measured line used to start the triangulation and give scale. C: Base station is a general term for a reference station, not linked to the Laplace equation. D: Subsidiary station is an extra point used to see main stations, not for astronomical control.
Shortcut
Laplace equation used means Laplace station.
Common mistake
Confusing the Laplace station with the base line, which controls scale, not azimuth.
Correct answer: A) Laplace station