Precise definition of the effective measurement height of free-fall absolute gravimeters

authored by: Ludger Timmen
Abstract: For up-to-date absolute gravimeters, the trajectory of the test mass during a free-fall experiment (drop) is about 20 cm along the vertical, and the corresponding gravity change is about 60 × 10^-8 m s^-2. The reference height of the derived free-fall acceleration g has to be defined with an accuracy of 1 mm to 2 mm within the dropping distance to preserve the accuracy of the measurement system (e.g. FG5: 1 × 10^-8 m s^-2 to 2 × 10^-8 m s^-2). The equation of motion comprises a vertical gravity gradient to take the height dependence of g into account. In general, a linear vertical gravity gradient γ is introduced that has been measured by relative gravimeters. In that case, the g-value refers to the origin of the coordinate system (z = 0), which is normally the starting position of the drop. In the case of an unknown or uncertain gradient we recommend an alternative approach. A simple parabolic equation (assumption γ = 0) can be used to evaluate the time/distance data pairs, and later these g-determinations have to be corrected for the vertical gravity gradient using the effective measurement height. The solution presented is not restricted to low initial velocities. It considers time/distance measurements equally spaced in distance. Also, in extreme cases, unknown non-linearities within the vertical gravity gradient do not significantly affect the result of the absolute gravity determination.
Organisation(s): Institute of Geodesy
Type: Article
Journal: METROLOGIA
Volume: 40
Pages: 62-65
No. of pages: 4
ISSN: 0026-1394
Publication date: 01.04.2003
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Engineering(all)
Electronic version(s): https://doi.org/10.1088/0026-1394/40/2/310 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{9fd53a693f544b17926051f39a6c60fd,
title = "Precise definition of the effective measurement height of free-fall absolute gravimeters",
abstract = "For up-to-date absolute gravimeters, the trajectory of the test mass during a free-fall experiment (drop) is about 20 cm along the vertical, and the corresponding gravity change is about 60 × 10-8 m s-2. The reference height of the derived free-fall acceleration g has to be defined with an accuracy of 1 mm to 2 mm within the dropping distance to preserve the accuracy of the measurement system (e.g. FG5: 1 × 10-8 m s-2 to 2 × 10-8 m s-2). The equation of motion comprises a vertical gravity gradient to take the height dependence of g into account. In general, a linear vertical gravity gradient γ is introduced that has been measured by relative gravimeters. In that case, the g-value refers to the origin of the coordinate system (z = 0), which is normally the starting position of the drop. In the case of an unknown or uncertain gradient we recommend an alternative approach. A simple parabolic equation (assumption γ = 0) can be used to evaluate the time/distance data pairs, and later these g-determinations have to be corrected for the vertical gravity gradient using the effective measurement height. The solution presented is not restricted to low initial velocities. It considers time/distance measurements equally spaced in distance. Also, in extreme cases, unknown non-linearities within the vertical gravity gradient do not significantly affect the result of the absolute gravity determination.",
author = "Ludger Timmen",
year = "2003",
month = apr,
day = "1",
doi = "10.1088/0026-1394/40/2/310",
language = "English",
volume = "40",
pages = "62--65",
journal = "METROLOGIA",
issn = "0026-1394",
publisher = "IOP Publishing Ltd.",
number = "2",
}