Tag Archives: gravity

Crowdsourcing Gravity

The proliferation of smartphones with internal sensors has led to some interesting opportunities to make large-scale measurements of a variety of physical phenomena.

The iOS app ‘Gravity Meter’ and its android equivalent have been used to make  measurements of the local surface acceleration, which is nominally 9.8 meters/sec2. The apps typically report the local acceleration to 0.01 (iOS) or even 0.001 (android) meters/secaccuracy, which leads to two interesting questions: 1)How reliable are these measurements at the displayed decimal limit, and 2) Can smartphones be used to measure expected departures from the nominal surface acceleration due to Earth rotation? Here is a map showing the magnitude of this (centrifugal) rotation effect provided by The Physics Forum.

As Earth rotates, any object on its surface will feel a centrifugal force directed outward from the center of Earth and generally in the direction of local zenith. This causes Earth to be slightly bulged-out at the equator compared to the poles, which you can see from the difference between its equatorial radius of 6,378.14 km versus its polar radius of 6,356.75 km: a polar flattening difference of 21.4 kilometers. This centrifugal force also has an effect upon the local surface acceleration  by reducing it slightly at the equator compared to the poles. At the equator, one would measure a value for ‘g’ that is about 9.78 m/sec2 while at the poles it is about 9.83 m/sec2. Once again, and this is important to avoid any misconceptions, the total acceleration defined as gravity plus centrifugal is reduced, but gravity is itself not changed because from Newton’s Law of Universal Gravitation, gravity is due to mass not rotation.

Assuming that the smartphone accelerometers are sensitive enough, they may be able to detect this equator-to-pole difference by comparing the surface acceleration measurements from observers at different latitudes.


Experiment 1 – How reliable are ‘gravity’ measurements at the same location?

To check this, I looked at the data from several participating classrooms at different latitudes, and selected the more numerous iOS measurements with the ‘Gravity Meter’ app. These data were kindly provided by Ms. Melissa Montoya’s class in Hawaii (+19.9N), George Griffith’s class in Arapahoe, Nebraska (+40.3N), Ms. Sue Lamdin’s class in Brunswick, Maine (+43.9N), and Elizabeth Bianchi’s class in Waldoboro, Maine (+44.1N).

All four classrooms measurements, irrespective of latitude (19.9N, 40.3N, 43.9N or 44.1N) showed distinct ‘peaks’, but also displayed long and complicated ‘tails’, making these distributions not Gaussian as might be expected for random errors. This suggests that under classroom conditions there may be some systematic effects introduced from the specific ways in which students may be making the measurements, introducing  complicated and apparently non-random,  student-dependent corrections into the data.

A further study using the iPad data from Elizabeth Bianchi’s class, I discovered that at least for iPads using the Gravity Sensor app, there was a definite correlation between when the measurement was made and the time it was made during a 1.5-hour period. This resembles a heating effect, suggesting that the longer you leave the technology on before making the measurement, the larger will be the measured value. I will look into this at a later time.

The non-Gaussian behavior in the current data does not make it possible to assign a normal average and standard-deviation to the data.


Experiment 2 – Can the rotation of Earth be detected?

Although there is the suggestion that in the 4-classroom data we could see a nominal centrifugal effect of about the correct order-of-magnitude, we were able to get a large sample of individual observers spanning a wide latitude range, also using the iOS platform and the same ‘Gravity Meter’ app. Including the median values from the four classrooms in Experiment 1, we had a total of 41 participants: Elizabeth Abrahams, Jennifer Arsenau, Dorene Brisendine, Allen Clermont, Hillarie Davis, Thom Denholm, Heather Doyle, Steve Dryer, Diedra Falkner, Mickie Flores, Dennis Gallagher, Robert Gallagher, Rachael Gerhard, Robert Herrick, Harry Keller, Samuel Kemos, Anna Leci, Alexia Silva Mascarenhas, Alfredo Medina, Heather McHale, Patrick Morton, Stacia Odenwald, John-Paul Rattner, Pat Reiff, Ghanjah Skanby, Staley Tracy, Ravensara Travillian, and Darlene Woodman.

The scatter plot of these individual measurements is shown here:

The red squares are the individual measurements. The blue circles are the android phone values. The red dashed line shows the linear regression line for only the iOS data points assuming each point is equally-weighted. The solid line is the predicted change in the local acceleration with latitude according to the model:

G =   9.806   –  0.5*(9.832-9.78)*Cos(2*latitude)    m/sec2

where the polar acceleration is 9.806 m/sec2 and the equatorial acceleration is 9.780 m/sec2. Note: No correction for lunar and solar tidal effects have been made since these are entirely undetectable with this technology.

Each individual point has a nominal variation of +/-0.01 m/sec2 based on the minimum and maximum value recorded during a fixed interval of time. It is noteworthy that this measurement RMS is significantly smaller than the classroom variance seen in Experiment 1 due to the apparently non-Gaussian shape of the classroom sampling. When we partition the iOS smartphone data into 10-degree latitude bins and take the median value in each bin we get the following plot, which is a bit cleaner:

The solid blue line is the predicted acceleration. The dashed black line is the linear regression for the equally-weighted individual measurements. The median values of the classroom points are added to show their distribution. It is of interest that the linear regression line is parallel, and nearly coincident with, the predicted line, which again suggests that Earth’s rotation effect may have been detected in this median-sampled data set provided by a total of 37 individuals.

The classroom points clustering at ca +44N represent a total of 36 measures representing the plotted median values, which is statistically significant. Taken at face value, the classroom data would, alone, support the hypothesis that there was a detection of the rotation effect, though they are consistently 0.005 m/sec2 below the predicted value at the mid-latitudes. The intrinsic variation of the data, represented by the consistent +/-0.01 m/sec2 high-vs-low range of all of the individual samples, suggests that this is probably a reasonable measure of the instrumental accuracy of the smartphones. Error bars (thin vertical black lines) have been added to the plotted median points to indicate this accuracy.

The bottom-line seems to be that it may be marginally possible to detect the Earth rotation effect, but precise measurements at the 0.01 m/sec2 level are required against what appears to be a significant non-Gaussian measurement background. Once again, some of the variation seen at each latitude may be due to how warm the smartphones were at the time of the measurement. The android and iOS measurements do seem to be discrepant with the android measurements leading to a larger measurement variation.

Check back here on Wednesday, March 29 for the next topic!

The Mystery of Gravity

In grade school we learned that gravity is an always-attractive force that acts between particles of matter. Later on, we learn that it has an infinite range through space, weakens as the inverse-square of the distance between bodies, and travels exactly at the speed of light.

But wait….there’s more!


It doesn’t take a rocket scientist to remind you that humans have always known about gravity! Its first mathematical description as a ‘universal’ force was by Sir Isaac Newton in 1666. Newton’s description remained unchanged until Albert Einstein published his General Theory of Relativity in 1915. Ninety years later, physicists, such as Edward Witten, Steven Hawkings, Brian Greene and Lee Smolin among others, are finding ways to improve our description of ‘GR’ to accommodate the strange rules of quantum mechanics. Ironically, although gravity is produced by matter, General Relativity does not really describe matter in any detail – certainly not with the detail of the modern quantum theory of atomic structure. In the mathematics, all of the details of a planet or a star are hidden in a single variable, m, representing its total mass.


The most amazing thing about gravity is that is a force like no other known in Nature. It is a property of the curvature of space-time and how particles react to this distorted space. Even more bizarrely, space and time are described by the mathematics of  GR as qualities of the gravitational field of the cosmos that have no independent existence. Gravity does not exist like the frosting on a cake, embedded in some larger arena of space and time. Instead, the ‘frosting’ is everything, and matter is embedded and intimately and indivisibly connected to it. If you could turn off gravity, it is mathematically predicted that space and time would also vanish! You can turn off electromagnetic forces by neutralizing the charges on material particles, but you cannot neutralize gravity without eliminating spacetime itself.  Its geometric relationship to space and time is the single most challenging aspect of gravity that has prevented generations of physicists from mathematically describing it in the same way we do the other three forces in the Standard Model.

Einstein’s General Relativity, published in 1915, is our most detailed mathematical theory for how gravity works. With it, astronomers and physicists have explored the origin and evolution of the universe, its future destiny, and the mysterious landscape of black holes and neutron stars. General Relativity has survived many different tests, and it has made many predictions that have been confirmed. So far, after 90 years of detailed study, no error has yet been discovered in Einstein’s original, simple theory.

Currently, physicists have explored two of its most fundamental and exotic predictions: The first is that gravity waves exist and behave as the theory predicts. The second is that a phenomenon called ‘frame-dragging’ exists around rotating massive objects.

Theoretically, gravity waves must exist in order for Einstein’s theory to be correct. They are distortions in the curvature of spacetime caused by accelerating matter, just as electromagnetic waves are distortions in the electromagnetic field of a charged particle produced by its acceleration. Gravity waves carry energy and travel at light-speed. At first they were detected indirectly. By 2004, astronomical bodies such as the  Hulse-Taylor orbiting pulsars were found to be losing energy by gravity waves emission at exactly the predicted rates. Then  in 2016, the  twin  LIGO gravity wave detectors detected the unmistakable and nearly simultaneous pulses of geometry distortion created by colliding black holes billions of light years away.

Astronomers also detected by 1997 the ‘frame-dragging’ phenomenon in  X-ray studies of distant black holes. As a black hole (or any other body) rotates, it actually ‘drags’ space around with it. This means that you cannot have stable orbits around a rotating body, which is something totally unexpected in Newton’s theory of gravity. The  Gravity Probe-B satellite orbiting Earth also confirmed in 2011 this exotic spacetime effect at precisely the magnitude expected by the theory for the rotating Earth.

Gravity also doesn’t care if you have matter or anti-matter; both will behave identically as they fall and move under gravity’s influence. This quantum-scale phenomenon was searched for at the Large Hadron Collider ALPHA experiment, and in 2013 researchers placed the first limits on how matter and antimatter ‘fall’ in Earth’s gravity. Future experiments will place even more stringent limits on just how gravitationally similar matter and antimatter are. Well, at least we know that antimatter doesn’t ‘fall up’!

There is only one possible problem with our understanding of gravity known at this time.

Applying general relativity, and even Newton’s Universal Gravitation, to large systems like galaxies and the universe leads to the discovery of a new ingredient called Dark Matter. There do not seem to be any verifiable elementary particles that account for this gravitating substance. Lacking a particle, some physicists have proposed modifying Newtonian gravity and general relativity themselves to account for this phenomenon without introducing a new form of matter. But none of the proposed theories leave the other verified predictions of general relativity experimentally intact. So is Dark Matter a figment of an incomplete theory of gravity, or is it a here-to-fore undiscovered fundamental particle of nature? It took 50 years for physicists to discover the lynchpin particle called the Higgs boson. This is definitely a story we will hear more about in the decades to come!

There is much that we now know about gravity, yet as we strive to unify it with the other elementary forces and particles in nature, it still remains an enigma. But then, even the briefest glance across the landscape of the quantum world fills you with a sense of awe and wonderment at the improbability of it all. At its root, our physical world is filled with improbable and logic-twisting phenomena and it simply amazing that they have lent themselves to human logic to the extent that they have!


Return here on Monday, March 13 for my next blog!