Our previous analyses of radio Doppler and ranging data from distant spacecraft in the solar system indicated that an apparent anomalous acceleration is acting on Pioneer 10 and 11, with a magnitude ${a}_{P}\ensuremath{\sim}8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8} {\mathrm{c}\mathrm{m}/\mathrm{s}}^{2},$ directed towards the Sun. Much effort has been expended looking for possible systematic origins of the residuals, but none has been found. A detailed investigation of effects both external to and internal to the spacecraft, as well as those due to modeling and computational techniques, is provided. We also discuss the methods, theoretical models, and experimental techniques used to detect and study small forces acting on interplanetary spacecraft. These include the methods of radio Doppler data collection, data editing, and data reduction. There is now further data for the Pioneer 10 orbit determination. The extended Pioneer 10 data set spans 3 January 1987 to 22 July 1998. (For Pioneer 11 the shorter span goes from 5 January 1987 to the time of loss of coherent data on 1 October 1990.) With these data sets and more detailed studies of all the systematics, we now give a result of ${a}_{P}=(8.74\ifmmode\pm\else\textpm\fi{}1.33)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ ${\mathrm{c}\mathrm{m}/\mathrm{s}}^{2}.$ (Annual-diurnal variations on top of ${a}_{P},$ that leave ${a}_{P}$ unchanged, are also reported and discussed.)

/pdf/study-of-the-anomalous-acceleration-of-pioneer-10-and-11-1mesaeyhwz.pdf

Study of the anomalous acceleration of Pioneer 10 and 11

Torsion balance experiments: A low-energy frontier of particle physics

https://zenodo.org/record/1258483/files/article.pdf

The arguments against ``antigravity'' and the gravitational acceleration of antimatter

The enunciation of the 'fifth force' hypothesis in 1986 spawned a generation of experiments searching for deviations from newtonian gravity. Although no compelling evidence for any new weak forces has emerged in the past six years, the searches for anomalous gravitational effects have produced a large number of important experimental and theoretical results.

Six years of the fifth force

http://cds.cern.ch/record/296921/files/9602350.pdf

Macroscopic forces from supersymmetry

A vacuum balance that compares the weights of 10-kg stainless-steel masses suspended in evacuated tubes at different levels in a hydroelectric reservoir is being used to measure the gravitational attractions of layers of lake water up to 10 m in depth The mean effective distance between interacting masses in this experiment is 22 m, making it the largest-scale measurement of G using precisely controlled moving masses The experiment extends laboratory-type measurements into the range previously explored only by geophysical methods Assuming purely Newtonian physics the value of the gravitational constant determined from data obtained so far is G=6689(57)×10-11 m3 kg-1s-2, which agrees with laboratory estimates The data admit at a 06 standard deviation level the parameters of non-Newtonian gravity inferred from geophysical measurements in mines and a tower These measurements push the estimated ranges of non-Newtonian forces down to a scale accessible to our reservoir experiment, so that experimental improvements now at hand may provide a critical test of non-Newtonian effects

/pdf/determination-of-the-gravitational-constant-at-an-effective-47015gti5t.pdf

Determination of the gravitational constant at an effective mass separation of 22 m

A vacuum balance has been constructed to compare the weights of interchangeable 10 kg masses hanging in evacuated tubes at different levels in a hydroelectric reservoir and used to measure the gravitational constant on a scale of tens of metres. Balance deflections are measured capacitively relative to a reference plane (containing electrodes) that is itself maintained horizontal by capacitive reference to interconnected mercury pools activating a servoed supporting leg. When the balance is mounted on a 38 m electricity pylon in the reservoir experiment, a sensitivity of 1 part in 109 is achieved. In a laboratory situation a sensitivity of 1 part in 1010 appears possible.

A balance for precise weighing in a disturbed environment

Geophysical measurements of the gravitational constant and a recent reexamination of experiments performed early in the century on the equivalence of inertial and gravitational mass may have provided either observational clues to the unification of gravity with electroweak and strong nuclear forces or an indication of a new, previously unrecognized force. The evidence is still less than completely conclusive but it has now become difficult to find explanations of the geophysical observations other than non-Newtonian gravity. We also point to the requirements of the next generation of experiments. These include measurements of gravity or gravity gradient in the deep ocean and high above it and Von Eoetvoes-type experiments in steep terrain to test the possibility that a postulated short-range (100 to 1000 m) component of gravity depends upon fundamental particle count rather than mass.

Geophysics and the law of gravity

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Determination of the gravitational constant at an effective mass separation of 22 m

A balance for precise weighing in a disturbed environment

Geophysics and the law of gravity