Details
| Original language | English |
|---|---|
| Pages (from-to) | 62-65 |
| Number of pages | 4 |
| Journal | METROLOGIA |
| Volume | 40 |
| Issue number | 2 |
| Publication status | Published - 1 Apr 2003 |
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.
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In: METROLOGIA, Vol. 40, No. 2, 01.04.2003, p. 62-65.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Precise definition of the effective measurement height of free-fall absolute gravimeters
AU - Timmen, Ludger
PY - 2003/4/1
Y1 - 2003/4/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0038290217&partnerID=8YFLogxK
U2 - 10.1088/0026-1394/40/2/310
DO - 10.1088/0026-1394/40/2/310
M3 - Article
AN - SCOPUS:0038290217
VL - 40
SP - 62
EP - 65
JO - METROLOGIA
JF - METROLOGIA
SN - 0026-1394
IS - 2
ER -