The Reflector Problem and the Inverse Square Law

Newtonian Gravity

10.1093/oso/9780199658633.003.0016 ◽

2018 ◽

Author(s):

David M. Wittman

Keyword(s):

Surface Gravity ◽

Newtonian Gravity ◽

Acceleration Field ◽

Source Mass ◽

Inverse Square Law ◽

Average Acceleration ◽

Law Of Gravity ◽

Tidal Acceleration

Having developed a framework for subsuming gravity into relativity, we examine how gravity behaves as a function of the source mass (Earth, Sun, etc.) and distance from that sourcemass.We develop Newton’s inverse‐square law of gravity, and we examine the consequences in terms of acceleration fields, potentials, escape velocities, and surface gravity. Chapter 17 will build on these ideas to show how orbits are used to probe gravity throughout the universe.We also develop a tool for exposing variations in the acceleration field: the tidal acceleration field in any region is defined as the acceleration field in that region minus the average acceleration. This enables us to restate Newton’s lawof gravity as: the acceleration arrows surrounding any point show a net convergence that is proportional to the density of mass at that point. Chapter 18 will use this to develop a frame‐independent law of gravity.

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Inverse-square law between time and amplitude for crossing tipping thresholds

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2018.0504 ◽

2019 ◽

Vol 475 (2222) ◽

pp. 20180504 ◽

Cited By ~ 1

Author(s):

Paul Ritchie ◽

Özkan Karabacak ◽

Jan Sieber

Keyword(s):

Dynamical System ◽

Feedback Loop ◽

Tipping Point ◽

Dimensional System ◽

Stochastic Forcing ◽

Inverse Square Law ◽

System A ◽

Asymptotic Expressions ◽

Higher Dimensional ◽

Random Disturbances

A classical scenario for tipping is that a dynamical system experiences a slow parameter drift across a fold tipping point, caused by a run-away positive feedback loop. We study what happens if one turns around after one has crossed the threshold. We derive a simple criterion that relates how far the parameter exceeds the tipping threshold maximally and how long the parameter stays above the threshold to avoid tipping in an inverse-square law to observable properties of the dynamical system near the fold. For the case when the dynamical system is subject to stochastic forcing we give an approximation to the probability of tipping if a parameter changing in time reverses near the tipping point. The derived approximations are valid if the parameter change in time is sufficiently slow. We demonstrate for a higher-dimensional system, a model for the Indian summer monsoon, how numerically observed escape from the equilibrium converge to our asymptotic expressions. The inverse-square law between peak of the parameter forcing and the time the parameter spends above a given threshold is also visible in the level curves of equal probability when the system is subject to random disturbances.

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EXPLORING FIFTH FORCE INTERACTIONS WITH 18TH CENTURY TECHNOLOGY

International Journal of Modern Physics D ◽

10.1142/s0218271804006280 ◽

2004 ◽

Vol 13 (10) ◽

pp. 2249-2254

Author(s):

JASON H. STEFFEN

Keyword(s):

18Th Century ◽

The Other ◽

Newtonian Gravity ◽

Torsion Pendulum ◽

Source Mass ◽

Intermediate Range ◽

Inverse Square Law ◽

Fifth Force

Many theories which unify gravity with the other known forces of nature predict the existence of an intermediate-range "fifth force" similar to gravity. Such a force could be manifest as a deviation from the gravitational inverse-square law. Currently, at distances near 10-1 m, the inverse-square law is known to be correct to about one part per thousand. I present the design of an experiment that will improve this limit by two orders of magnitude. This is accomplished by constructing a torsion pendulum and source mass apparatus that are particularly insensitive to Newtonian gravity and, simultaneously, maximally sensitive to violations of the same.

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Accuracy evaluation of distance inverse square law in determining virtual electron source location in Siemens Primus linac

Reports of Practical Oncology & Radiotherapy ◽

10.1016/j.rpor.2018.01.002 ◽

2018 ◽

Vol 23 (2) ◽

pp. 105-113 ◽

Cited By ~ 1

Author(s):

Hamid Shafaei Douk ◽

Mahmoud Reza Aghamiri ◽

Mahdi Ghorbani ◽

Bagher Farhood ◽

Mohsen Bakhshandeh ◽

...

Keyword(s):

Source Location ◽

Electron Source ◽

Accuracy Evaluation ◽

Inverse Square Law

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The Buckling of a Circular Plate With a Concentric Circular Hot-Spot

Journal of the Royal Aeronautical Society ◽

10.1017/s0368393100072114 ◽

1960 ◽

Vol 64 (590) ◽

pp. 105-106 ◽

Cited By ~ 1

Author(s):

K. I. McKenzie

Keyword(s):

Critical Temperature ◽

Circular Plate ◽

Radial Stress ◽

Hot Spot ◽

Clamped Plate ◽

Inverse Square Law ◽

Cold Part

If a circular plate has a concentric circular hot area, there is a critical temperature for this area at which the plate buckles. This temperature is calculated in this note for the case of a clamped plate supported in such a way that the radial stress in the cold part obeys the inverse square law.

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