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Newton’s Gravitational Constant ‚Big‘ G – A proposed Free-fall Measurement
CODATA Fundamental Constants Meeting Eltville – 5 February, 2015
projected and presented by
Christian Rothleitner
(currently working at PTB)
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Acceleration due to gravity:
g = 9.806 65 m s-2
m
z g
g
Newtonian constant of gravitation:
G= 6.673 84 x 10-11 m3 kg-1 s-2
Free-fall experiments to determine ‚Big‘ G
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Free-fall absolute gravimeter
FG5-X
Microg-LaCoste (Lafayette, CO, USA)
FG5-X : Precision : 15 µGal/√(Hz)* Accuracy: 2 µGal*
(*from http://www.microglacoste.com/absolutemeters.php)
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Principle of measurement
acceleration due to gravity
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Earth as source mass ME
Measurement of G with a gravimeter
ME
Calculate g with theoretical model
Measure g
Determine G
Problem: Mass, geometry and density distribution of Earth are not well known!
r
mt g
ME=m1
mt=m2
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Use of well defined source mass, MS
ME
Ms produces perturbing acceleration P(z,G)
Total signal is
Ms
gravity gradient
configuration 1
masssourceEarth
GzPzgg ),(01
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masssourceEarth
GzPzgg ),(02
Use of well defined source mass MS
ME
Ms produces perturbing acceleration P(z,G)
Total signal is
Ms
configuration 2
Differential signal
masssource
GzPgg ),(212
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Schwarz et al., 1998, University of Colorado – Free-Fall Gravimeter
JP Schwarz, DS Robertson, TM Niebauer & JE Faller (1998). A free-fall determination of the universal constant of gravity. Science, 18, 2230-2234
FG5 gravimeter
source mass:
~500 kg
Result: DG/G = 1.4·10-3
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Free-fall Gradiometer
BS: Beam splitter
Det.: Detector
height 1: gT
height 2: gB
Dz
reference mirror also in free-fall
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M
M
Measurement of G with a gravity gradiometer
Configuration 1
top
bottom
acceleration due to external mass
acceleration due to Earth
equivalent to
second source mass to increase signal
however, cancels tides, ocean loading, etc.
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Measurement of G with a gravity gradiometer
top
bottom
Config. 2 – Config. 1:
Configuration 2
M
M
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University of Florence – Atom interferometer (Raman interferometry)
Result: DG/G = 1.5.10-4
Test mass:
Rubidium atoms
Source mass:
~516 kg tungsten
G Rosi et al. (2014). Precision measurement of the Newtonian gravitational constant using cold atoms. Nature, 510, 518–521.
source: http://www.nist.gov/pml/div684/fcdc/newtonian-constant.cfm
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Differential gradiometer
merge
3 simultaneously dropped masses
M
M
M
M
M
M
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height 1: gT
height 2: gM
D z
height 3: gB
D z
Second Vertical Derivative of g (SVD)
2
Null instrument (no g or )
Differential gradiometer
Rothleitner Ch & Francis O. (2014). Measuring the Newtonian constant of gravitation with a differential free-fall gradiometer: A feasibility study. Rev. Sci. Instrum, 85, 044501. Rothleitner, C. (2010). Interferometric differential free-fall gradiometer. EP2348338B1, US20130205894.
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Separation of inertial from gravitational forces
Measured force in a non-inertial frame:
see e.g. Hofmann-Wellenhof, B & Moritz, H (2005). Physical Geodesy. Springer Wien New York.
Coriolis force
Euler and centrifugal force
Linear acceleration
Gravitat. force
• Inertial forces disappear; only gravitational signal measured
• No inertial stabilization necessary
• Applications: fundamental physics, gravimetry, navigation
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Proposal
Perform a Big G measurement by
• Using an atom and a classical gradiometer
• Using the same source mass
• Comparing uncertainty budgets
• Identifying and eliminating systematic errors if present
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• Same physical sizes of classical and atom gravimeter
• same source masses can be used
• Two different technologies / physical laws for same experiment
• Test of physical theories
• Detection of systematic errors
Advantages of free-fall experiments
Atom gradiometer, Tino group, Florence University**
Differential gradiometer @ Univ. Luxembourg
10
0 c
m
*See also ‘G Rosi et al. (2015). Measurement of the Gravity-Field Curvature by Atom Interferometry. PRL, 114.‘ for differential gradiometer. **Picture from Lamporesi, 2006, PhD thesis
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• Both technologies are under intense research
• good know-how; immediate start possible
• Benefit for industry
• use in other areas of science and technology
• Reflects the popular story about Newton´s apple
• Attractive for popular readership
Advantages of free-fall experiments
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Acknowledgements
Geophysics laboratory @ University of Luxembourg
Prof. Olivier Francis, Gilbert Klein, Marc Seil, Ed Weyer, André Stemper
Micro-g LaCoste Inc., Lafayette (CO), USA
Dr. Timothy M. Niebauer and the team of Micro-g LaCoste
Physikalisch-Technische Bundesanstalt
Braunschweig und Berlin
Bundesallee 100
38116 Braunschweig
Dr. rer. nat. Christian Rothleitner
Arbeitsgruppe 5.34 Multisensor-Koordinatenmesstechnik
(Working Group 5.34 Multisensor Coordinate Metrology)
Telefon: +49 (0)531 592-5348
E-Mail: [email protected]
www.ptb.de
Stand: 02/15