492:
365:
springs are less affected by magnetic and electric fields while metal springs have a much lower drift due to elongation over time. The test mass is sealed in an air-tight container so that tiny changes of barometric pressure from blowing wind and other weather do not change the buoyancy of the test mass in air. Spring gravimeters are, in practice, relative instruments that measure the difference in gravity between different locations. A relative instrument also requires calibration by comparing instrument readings taken at locations with known absolute values of gravity.
40:
990:
143:
631:– MEMS gravimeters offer the potential for low-cost arrays of sensors. MEMS gravimeters are currently variations on spring type accelerometers where the motions of a tiny cantilever or mass are tracked to report acceleration. Much of the research is focused on different methods of detecting the position and movements of these small masses. In Atom gravimeters, the mass is a collection of atoms.
491:
129:
404:, measurements are made to the precision of microgals to find density variations in the rocks making up the Earth. Several types of gravimeters exist for making these measurements, including some that are essentially refined versions of the spring scale described above. These measurements are used to quantify
620:, so have the potential to improve earthquake early warning methods. There is some activity to design purpose-built gravimeters of sufficient sensitivity and bandwidth to detect these prompt gravity signals from earthquakes. Not just the magnitude 7+ events, but also the smaller, much more frequent, events.
582:), approximately one trillionth (10) of the Earth surface gravity. In a demonstration of the sensitivity of the superconducting gravimeter, Virtanen (2006), describes how an instrument at Metsähovi, Finland, detected the gradual increase in surface gravity as workmen cleared snow from its laboratory roof.
1232:
Aerogravity is an integrated system of gravimetry measurements and real-time navigation. Under certain circumstances, as in mountainous regions, aerogravity successfully competes with land-based gravimetry; the latter suffers from the uncertainties of the near field terrain effects. Airborne gravity
954:
Microgravimetry is an important branch developed on the foundation of classical gravimetry. Microgravity investigations are carried out in order to solve various problems of engineering geology, mainly location of voids and their monitoring. Very detailed measurements of high accuracy can indicate
475:
experiments monitor the changes with time in the gravitational potential itself, rather than the gradient of the potential that the gravimeter is tracking. This distinction is somewhat arbitrary. The subsystems of the gravitational radiation experiments are very sensitive to changes in the gradient
1542:
Tapley, Byron D.; Watkins, Michael M.; Flechtner, Frank; Reigber, Christoph; Bettadpur, Srinivas; Rodell, Matthew; Sasgen, Ingo; Famiglietti, James S.; Landerer, Felix W.; Chambers, Don P.; Reager, John T.; Gardner, Alex S.; Save, Himanshu; Ivins, Erik R.; Swenson, Sean C.; Boening, Carmen; Dahle,
611:
Many broadband three-axis seismometers in common use are sensitive enough to track the Sun and Moon. When operated to report acceleration, they are useful gravimeters. Because they have three axes, it is possible to solve for their position and orientation, by either tracking the arrival time and
697:
The term for the "force constant" changes if the restoring force is electrostatic, magnetostatic, electromagnetic, optical, microwave, acoustic, or any of dozens of different ways to keep the mass stationary. The "force constant" is just the coefficient of the displacement term in the equation of
925:
mode. They yielded detailed information about the Earth's time-varying gravity field. The spherical harmonic gravitational potential models are slowly improving in both spatial and temporal resolution. Taking the gradient of the potentials gives estimate of local acceleration which are what is
380:
and the clock is stable to ±0.03 ppb. Care must be taken to minimize the effects of perturbing forces such as residual air resistance (even in vacuum), vibration, and magnetic forces. Such instruments are capable of an accuracy of about two parts per billion or 0.002 mGal and reference
364:
of the spring–mass system can be made very long – approaching a thousand seconds. This detunes the test mass from most local vibration and mechanical noise, increasing the sensitivity and utility of the gravimeter. Quartz and metal springs are chosen for different reasons; quartz
391:
usually refer to differential comparisons of gravity from one place to another. They are designed to subtract the average vertical gravity automatically. They can be calibrated at a location where the gravity is known accurately and then transported to the location where the gravity is to be
529:
Atom interferometric and atomic fountain methods are used for precise measurement of the Earth's gravity, and atomic clocks and purpose-built instruments can use time dilation (also called general relativistic) measurements to track changes in the gravitational potential and gravitational
608:, changes in the density of the atmosphere, the effect of changes in the shape of the surface of the ocean, the effect of the atmosphere's pressure on the Earth, changes in the rate of rotation of the Earth, oscillations of the Earth's core, distant and nearby seismic events, and more.
980:
They also invented most subsequent refinements, including the ship-mounted gravimeter, in 1965, temperature-resistant instruments for deep boreholes, and lightweight hand-carried instruments. Most of their designs remain in use with refinements in data collection and data processing.
426:), ships and submarines. These special gravimeters isolate acceleration from the movement of the vehicle and subtract it from measurements. The acceleration of the vehicles is often hundreds or thousands of times stronger than the changes in gravity being measured.
476:
of the potential. The local gravity signals on Earth that interfere with gravitational wave experiments are disparagingly referred to as "Newtonian noise", since
Newtonian gravity calculations are sufficient to characterize many of the local (earth-based) signals.
691:
518:. By counting and timing the interference fringes, the acceleration of the mass can be measured. A more recent development is a "rise and fall" version that tosses the mass upward and measures both upward and downward motion. This allows cancellation of some
255:
197:
Though similar in design to other accelerometers, gravimeters are typically designed to be much more sensitive. Their first uses were to measure the changes in gravity from the varying densities and distribution of masses inside the Earth, from temporal
185:
is used to counteract the force of gravity pulling on an object. The change in length of the spring may be calibrated to the force required to balance the gravitational pull. The resulting measurement may be made in units of force (such as the
302:
937:
to compensate for the masking effects of motion and vibration, a difficult engineering feat. The first transportable relative gravimeters were, reportedly, a secret military technology developed in the 1950–1960s as a navigational aid for
371:
provide such measurements by determining the gravitational acceleration of a test mass in vacuum. A test mass is allowed to fall freely inside a vacuum chamber and its position is measured with a laser interferometer and timed with an
533:
The term "absolute" does not convey the instrument's stability, sensitivity, accuracy, ease of use, and bandwidth. The words "Absolute" and "relative" should not be used when more specific characteristics can be given.
522:; however, "rise and fall" gravimeters are not yet in common use. Absolute gravimeters are used in the calibration of relative gravimeters, surveying for gravity anomalies (voids), and for establishing the vertical
615:
Recently, the SGs, and broadband three-axis seismometers operated in gravimeter mode, have begun to detect and characterize the small gravity signals from earthquakes. These signals arrive at the gravimeter at the
385:, and in geophysical studies requiring high accuracy and stability. However, absolute instruments are somewhat larger and significantly more expensive than relative spring gravimeters and are thus relatively rare.
550:
over those areas. They are basically a weight on a spring, and by measuring the amount by which the weight stretches the spring, local gravity can be measured. However, the strength of the spring must be
483:. This includes traditional 2D maps, but increasingly 3D video. Since gravity and acceleration are the same, "acceleration field" might be preferable, since "gravity" is an oft-misused prefix.
57:. Gravimetry may be used when either the magnitude of a gravitational field or the properties of matter responsible for its creation are of interest. The study of gravity changes belongs to
640:
910:
Precise GPS stations can be operated as gravimeters since they are increasingly measuring three-axis positions over time, which, when differentiated twice, give an acceleration signal.
506:
Gravimeters for measuring the Earth's gravity as precisely as possible are getting smaller and more portable. A common type measures the acceleration of small masses free falling in a
219:
205:
The resolution of gravimeters can be increased by averaging samples over longer periods. Fundamental characteristics of gravimeters are the accuracy of a single measurement (a single
471:
Most current work is Earth-based, with a few satellites around Earth, but gravimeters are also applicable to the Moon, Sun, planets, asteroids, stars, galaxies and other bodies.
1039:(GRACE) consisted of two satellites that detected gravitational changes across the Earth. Also these changes could be presented as gravity anomaly temporal variations. The
266:
570:; the current required to generate the magnetic field that suspends the niobium sphere is proportional to the strength of the Earth's gravitational acceleration. The
1074:
1021:
415:
and gravity changes from human activities. Depending on the interests of the researcher or operator, this might be counteracted by integral vibration isolation and
955:
voids of any origin, provided the size and depth are large enough to produce gravity effect stronger than is the level of confidence of relevant gravity signal.
319:. These changes can be the result of mass displacements inside the Earth, or of vertical movements of the Earth's crust on which measurements are being made.
585:
The largest component of the signal recorded by a superconducting gravimeter is the tidal gravity of the Sun and Moon acting at the station. This is roughly
628:
624:
1374:
158:. Every mass has an associated gravitational potential. The gradient of this potential is a force. A gravimeter measures this gravitational force.
1458:
Stelkens-Kobsch, Tim (2006). "Further
Development of a High Precision Two-Frame Inertial Navigation System for Application in Airborne Gravimetry".
974:
423:
1340:
495:
Illustration of the effects of different underground geological features on the local gravity field. A volume of low density, 2, reduces
194:(cm/s), and parts per million, parts per billion, or parts per trillion of the average vertical acceleration with respect to the Earth.
1024:. These satellite missions aim at the recovery of a detailed gravity field model of the Earth, typically presented in the form of a
330:
on the Earth's surface. The Earth's vertical gravity varies from place to place over its surface by about ±0.5%. It varies by about
1491:
Meyer, Ulrich; Sosnica, Krzysztof; Arnold, Daniel; Dahle, Christoph; Thaller, Daniela; Dach, Rolf; Jäggi, Adrian (22 April 2019).
1604:
Sośnica, Krzysztof; Jäggi, Adrian; Meyer, Ulrich; Thaller, Daniela; Beutler, Gerhard; Arnold, Daniel; Dach, Rolf (October 2015).
1036:
997:
Currently, the static and time-variable Earth's gravity field parameters are determined using modern satellite missions, such as
918:
1308:
381:
their measurement to atomic standards of length and time. Their primary use is for calibrating relative instruments, monitoring
1475:
1177:
349:(nanometers per second squared) at any location because of the changing positions of the Sun and Moon relative to the Earth.
1220:
1052:
1249:
1206:
930:
the satellite potentials. This should eventually improve both the satellite and Earth-based methods and intercomparisons.
1043:(GRAIL) also consisted of two spacecraft orbiting the Moon, which orbited for three years before their deorbit in 2015.
934:
686:{\displaystyle \omega =2\pi \times {\text{Frequency}}={\sqrt {{\text{Force Constant}} \over {\text{Effective Mass}}}}}
1271:
1214:
1126:
Some newer units are pm/s (picometers per second squared), fm/s (femto), am/s (atto) for very sensitive instruments.
250:{\displaystyle {\text{Resolution}}={{\text{SingleMeasurementResolution}} \over {\sqrt {\text{NumberOfSamples}}}}}
136:
1233:
radiometers, on the other hand, are less sensitive to platform movement and are now achieving high accuracies .
1020:
Large-scale gravity anomalies can be detected from space, as a by-product of satellite gravity missions, e.g.,
1013:. The lowest-degree parameters, including the Earth's oblateness and geocenter motion are best determined from
1062:
1365:
604:(nanometers per second squared) at most locations. "SGs", as they are called, can detect and characterize
400:
Researchers use more sophisticated gravimeters when precise measurements are needed. When measuring the
1202:
Gravity
Interpretation: Fundamentals and Application of Gravity Inversion and Geological Interpretation
327:
155:
17:
1270:
J. M. Brown; T. M. Niebauer; B. Richter; F. J. Klopping; J. G. Valentine; W. K. Buxton (1999-08-10).
612:
pattern of seismic waves from earthquakes, or by referencing them to the Sun and Moon tidal gravity.
78:
515:
297:{\displaystyle {\text{Resolution per minute}}={{\text{Resolution per second}} \over {\sqrt {60}}}}
1057:
1028:
expansion of the Earth's gravitational potential, but alternative presentations, such as maps of
1014:
946:
by the civilian sector for use on ship, then in air and finally satellite-borne gravity surveys.
1329:
308:
546:-based. They are used in gravity surveys over large areas for establishing the figure of the
170:
1617:
1560:
1504:
1422:
926:
measured by the gravimeter arrays. The superconducting gravimeter network has been used to
422:
Gravimeters have been designed to mount in vehicles, including aircraft (note the field of
31:
8:
1651:
1094:
1025:
943:
922:
382:
54:
1621:
1564:
1508:
1426:
1581:
1548:
1544:
1412:
1100:
1068:
1010:
1006:
634:
For a given restoring force, the central frequency of the instrument is often given by
472:
457:
357:
353:
162:
315:
is also an important property for a gravimeter as it allows the monitoring of gravity
202:
variations in the shape and distribution of mass in the oceans, atmosphere and earth.
1586:
1471:
1440:
1300:
1210:
1002:
939:
519:
416:
377:
356:
to support the test mass. The special property of these springs is that the natural
1656:
1625:
1576:
1568:
1522:
1512:
1463:
1430:
1106:
1089:
401:
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measured. Or they can be calibrated in absolute units at their operating location.
117:
312:
1269:
1200:
571:
555:
by placing the instrument in a location with a known gravitational acceleration.
543:
523:
405:
182:
1245:
970:
933:
Transportable relative gravimeters also exist; they employ an extremely stable
617:
567:
511:
510:, when the accelerometer is firmly attached to the ground. The mass includes a
178:
85:
1630:
1605:
1572:
1373:. Academic Dissertation at the University of Helsinki, Geodetiska Institutet.
1173:
1645:
1467:
1444:
989:
323:
210:
187:
174:
39:
468:. Their fundamental purpose is to map the gravity field in space and time.
1590:
927:
373:
166:
70:
1435:
1401:"Quantum sensing with nanoparticles for gravimetry: when bigger is better"
1400:
1301:"Professor Robert B. Laughlin, Department of Physics, Stanford University"
1279:
352:
The majority of modern gravimeters use specially designed metal or quartz
1148:
Near the Earth's surface gravity decreases 0.308 mGal for every metre of
1136:
1084:
1078:
964:
605:
461:
445:
361:
58:
1527:
142:
1517:
1492:
579:
479:
There are many methods for displaying acceleration fields, also called
449:
191:
132:
93:
1109: – Study of the physical properties of the Earth's gravity field
1081:
containing pairs of gravimeters (accelerometers), launched March 2009
1071: – Systematic collection of geophysical data for spatial studies
942:. Subsequently in the 1980s, transportable relative gravimeters were
552:
465:
434:
412:
165:
predicts gravitational effects indistinguishable from the effects of
82:
1276:
Eos, Transactions, American
Geophysical Union, electronic supplement
1417:
1493:"SLR, GRACE and Swarm Gravity Field Determination and Combination"
563:
453:
437:
mission did not work due to a design error. A second device (the
98:
1543:
Christoph; Wiese, David N.; Dobslaw, Henryk; Tamisiea, Mark E.;
1097: – Measurement of variations in Earth's gravitational field
120:, although the actual acceleration varies slightly by location.
1149:
507:
190:), however, gravimeters display their measurements in units of
1399:
Rademacher, Markus; Millen, James; Li, Ying Lia (2020-10-01).
1541:
1040:
1029:
547:
181:
may be regarded as simple gravimeters. In one common form, a
43:
1330:"Operating Principles of the Superconducting Gravity Meter"
998:
914:
786:
external force as a function of location/position and time.
199:
1272:"Miniaturized Gravimeter May Greatly Improve Measurements"
128:
1606:"Time variable Earth's gravity field from SLR satellites"
1367:
Studies of earth dynamics with superconducting gravimeter
1075:
Gravity Field and Steady-State Ocean
Circulation Explorer
1603:
1549:"Contributions of GRACE to understanding climate change"
173:. Thus, gravimeters can be regarded as special-purpose
1490:
558:
The current standard for sensitive gravimeters are the
74:
433:) deployed on the surface of the Moon during the 1972
77:
system of units, the standard unit of acceleration is
1032:
undulations or gravity anomalies, are also produced.
643:
269:
222:
27:
Measurement of the strength of a gravitational field
1398:
685:
486:
326:, specialized for measuring the constant downward
296:
249:
118:acceleration due to gravity at the Earth's surface
92:, in either case with symbol Gal), which equals 1
1643:
562:, which operate by suspending a superconducting
1457:
1451:
444:Gravimeters are used for petroleum and mineral
376:. The laser wavelength is known to ±0.025
109:), equal to 9.80665 m/s. The value of the
1198:
1199:Jacoby, Wolfgang; Smilde, Peter L. (2009).
906:+ higher derivatives of the restoring force
1460:Observation of the Earth System from Space
499:while high-density material, 3, increases
146:An Autograv CG-5 gravimeter being operated
1629:
1580:
1526:
1516:
1434:
1416:
116:is defined as approximately equal to the
46:undulations based on satellite gravimetry
30:For the chemical analysis technique, see
1363:
1357:
1065: – Dutch geophysicist and geodesist
1041:Gravity Recovery and Interior Laboratory
988:
490:
141:
127:
69:Gravity is usually measured in units of
53:is the measurement of the strength of a
38:
1058:Kibble balance § Effect of gravity
1037:Gravity Recovery and Climate Experiment
984:
969:The modern gravimeter was developed by
537:
64:
14:
1644:
1174:"Micro-g LaCoste Absolute Gravimeters"
1207:Springer Science & Business Media
574:gravimeter achieves sensitivities of
322:The first gravimeters were vertical
1205:. Earth and Environmental Science.
24:
1180:from the original on June 27, 2012
1053:Gravity measurement with pendulums
949:
25:
1668:
1380:from the original on June 5, 2011
795:is the force being measured, and
154:is an instrument used to measure
1103:, spacecraft launched March 2002
1077:(GOCE) A modern satellite-borne
913:The satellite borne gravimeters
542:The most common gravimeters are
1597:
1535:
1484:
1392:
1346:from the original on 2022-02-02
1311:from the original on 2016-06-17
1252:from the original on 2018-04-10
1223:from the original on 2020-08-02
487:Commercial absolute gravimeters
395:
81:(m/s). Other units include the
1322:
1293:
1263:
1238:
1192:
1176:. Micro-g LaCoste, Inc. 2012.
1166:
1142:
1129:
1120:
993:Gravity anomaly map from GRACE
566:sphere in an extremely stable
439:Traverse Gravimeter Experiment
123:
13:
1:
1405:Advanced Optical Technologies
1159:
1135:Assumes measurement noise is
441:) functioned as anticipated.
1063:Felix Andries Vening Meinesz
514:and terminates one arm of a
96:per second squared, and the
7:
1046:
560:superconducting gravimeters
530:acceleration on the Earth.
402:Earth's gravitational field
235:SingleMeasurementResolution
10:
1673:
962:
958:
156:gravitational acceleration
29:
1631:10.1007/s00190-015-0825-1
1573:10.1038/s41558-019-0456-2
79:metres per second squared
1468:10.1007/3-540-29522-4_31
1339:. gwrinstruments. 2011.
1113:
516:Michelson interferometer
431:Lunar Surface Gravimeter
1337:principles-of-operation
1015:satellite laser ranging
693:(in radians per second)
411:Gravimeters can detect
328:acceleration of gravity
137:Repsold–Bessel pendulum
1246:"Micro-g LaCoste, Inc"
994:
687:
503:
298:
251:
147:
139:
88:(sometimes known as a
47:
1553:Nature Climate Change
1436:10.1515/aot-2020-0019
1364:Virtanen, H. (2006).
992:
921:, mostly operated in
819:is the acceleration.
688:
494:
299:
282:Resolution per second
272:Resolution per minute
252:
171:equivalence principle
145:
131:
42:
1462:. pp. 479–494.
985:Satellite gravimetry
641:
538:Relative gravimeters
369:Absolute gravimeters
267:
220:
65:Units of measurement
32:Gravimetric analysis
1622:2015JGeod..89..945S
1565:2019NatCC...9..358T
1545:Velicogna, Isabella
1509:2019RemS...11..956M
1427:2020AdOT....9..227R
1139:of the measurement.
1095:Gravity gradiometry
923:gravity gradiometer
458:geophysical surveys
389:Relative gravimeter
383:crustal deformation
354:zero-length springs
55:gravitational field
1610:Journal of Geodesy
1518:10.3390/rs11080956
1305:large.stanford.edu
1101:GRACE and GRACE-FO
1069:Geophysical survey
1026:spherical-harmonic
1011:GRACE and GRACE-FO
995:
944:reverse engineered
940:nuclear submarines
683:
520:measurement errors
504:
473:Gravitational wave
464:research, and for
429:A gravimeter (the
294:
247:
163:general relativity
161:For a small body,
148:
140:
48:
1477:978-3-540-29520-4
935:inertial platform
681:
680:
678:
673:
662:
417:signal processing
406:gravity anomalies
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273:
245:
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16:(Redirected from
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1287:
1278:. Archived from
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1190:
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1107:Physical geodesy
1090:Gravity of Earth
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883:
882:
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862:
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772:force constant,
737:
692:
690:
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684:
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671:
669:
668:
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660:
629:atom gravimeters
625:MEMS gravimeters
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135:with variant of
21:
1672:
1671:
1667:
1666:
1665:
1663:
1662:
1661:
1642:
1641:
1640:
1639:
1616:(10): 945–960.
1602:
1598:
1540:
1536:
1489:
1485:
1478:
1456:
1452:
1397:
1393:
1383:
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1217:
1209:. p. 124.
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1193:
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1181:
1172:
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1162:
1157:
1156:
1147:
1143:
1134:
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1116:
1049:
987:
967:
961:
952:
950:Microgravimetry
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703:
675:
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597:
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572:superconducting
540:
524:control network
489:
398:
358:resonant period
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241:NumberOfSamples
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179:weighing scales
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115:
108:
67:
35:
28:
23:
22:
15:
12:
11:
5:
1670:
1660:
1659:
1654:
1638:
1637:
1596:
1559:(5): 358–369.
1534:
1497:Remote Sensing
1483:
1476:
1450:
1411:(5): 227–239.
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1321:
1292:
1262:
1237:
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1191:
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983:
975:Arnold Romberg
971:Lucien LaCoste
960:
957:
951:
948:
908:
907:
788:
787:
779:
754:acceleration,
740:
739:
695:
694:
677:Effective Mass
672:Force Constant
666:
658:
655:
652:
649:
646:
618:speed of light
568:magnetic field
539:
536:
512:retroreflector
488:
485:
481:gravity fields
397:
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324:accelerometers
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175:accelerometers
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1282:on 2009-07-26
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329:
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260:for example:
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211:sampling rate
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1552:
1547:(May 2019).
1537:
1528:10281/240694
1500:
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1459:
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1394:
1382:. Retrieved
1366:
1359:
1348:. Retrieved
1336:
1324:
1313:. Retrieved
1304:
1295:
1284:. Retrieved
1280:the original
1275:
1265:
1254:. Retrieved
1240:
1231:
1225:. Retrieved
1201:
1194:
1182:. Retrieved
1168:
1144:
1131:
1122:
1034:
1019:
996:
979:
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953:
932:
928:ground truth
912:
909:
897:
879:
871:
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837:
833:
829:
825:
823:
811:
810:
801:
800:
791:
790:
789:
782:
781:
778:displacement
774:
773:
768:
767:
762:
761:
756:
755:
750:
749:
744:
743:
733:
729:
725:
721:
718:
714:
711:
707:
704:
702:
696:
633:
622:
614:
610:
584:
559:
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528:
505:
500:
496:
480:
478:
470:
443:
438:
430:
428:
421:
410:
399:
396:Applications
388:
387:
374:atomic clock
368:
367:
351:
321:
316:
306:
259:
206:
204:
196:
167:acceleration
160:
151:
149:
110:
103:
97:
89:
71:acceleration
68:
50:
49:
36:
1137:independent
1085:Gravity map
1079:gradiometer
965:Jean Richer
760:viscosity,
606:Earth tides
462:geophysical
446:prospecting
424:aerogravity
362:oscillation
124:Gravimeters
59:geodynamics
1652:Gravimetry
1646:Categories
1503:(8): 956.
1418:2005.14642
1350:2021-04-06
1315:2016-03-15
1286:2021-04-06
1256:2021-04-06
1227:2014-09-16
1160:References
963:See also:
766:velocity,
553:calibrated
460:and other
450:seismology
413:vibrations
225:Resolution
209:) and the
152:gravimeter
133:Gravimeter
94:centimetre
51:Gravimetry
18:Gravimeter
1445:2192-8584
977:in 1936.
661:Frequency
657:×
654:π
645:ω
466:metrology
435:Apollo 17
313:stability
309:precision
73:. In the
1591:31534490
1375:Archived
1341:Archived
1309:Archived
1250:Archived
1221:Archived
1184:July 27,
1178:Archived
1047:See also
891:constant
698:motion:
307:Besides
177:. Many
1657:Geodesy
1618:Bibcode
1582:6750016
1561:Bibcode
1505:Bibcode
1423:Bibcode
959:History
902:
888:
884:
865:
861:
842:
817:
797:
601:
589:
580:nanogal
564:niobium
454:geodesy
346:
334:
317:changes
169:by the
90:galileo
1589:
1579:
1474:
1443:
1213:
1150:height
748:mass,
623:Newer
587:±1000
576:10 m·s
544:spring
508:vacuum
332:±1000
207:sample
188:newton
183:spring
1413:arXiv
1378:(PDF)
1371:(PDF)
1344:(PDF)
1333:(PDF)
1114:Notes
1030:geoid
1007:Swarm
1003:CHAMP
919:GRACE
578:(one
548:geoid
200:tidal
44:Geoid
1587:PMID
1472:ISBN
1441:ISSN
1386:2009
1211:ISBN
1186:2012
1035:The
1022:GOCE
999:GOCE
973:and
915:GOCE
836:) =
192:gals
1626:doi
1577:PMC
1569:doi
1523:hdl
1513:doi
1464:doi
1431:doi
378:ppb
360:of
86:gal
83:cgs
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