May 17, 2016 report

# Deep space experiment could measure the gravitational constant with nearly 1,000 times improvement in accuracy (Update)

(Phys.org)—Scientists have proposed an experiment that could measure the value of Newton's gravitational constant, *G*, from deep space instead of an Earth-based laboratory. The researchers predict that the deep space experiment could estimate *G* with an improvement in precision of nearly three orders of magnitude, since it would avoid the influence of Earth's gravity.

The researchers, Michael Feldman *et al.*, have published a paper on the proposed experiment in a recent issue of *Classical and Quantum Gravity*.

**Uncertainty with Big G**

Newton's gravitational constant, *G*, determines the strength of the gravitational force between any two objects anywhere in the universe. Over the past century, a dozen or so Earth-based experiments have used torsion balances, atom interferometers, and other tools to measure the value of *G* to be approximately 6.67408 x 10^{-11}, with an uncertainty of 4.7 × 10^{−5}.

Although this may sound precise, it is not very precise at all compared to many other physical constants, which have uncertainties that are many orders of magnitude smaller than this. In recent years, the large variations in the measured values of *G* have caused scientists to question if *G* is truly constant at all. (Currently, the overwhelming consensus is that *G* is constant, and that the variations are due to large systematic measurement errors.)

"*G* is currently the least well known of all the fundamental physical constants, which is embarrassing," Feldman told *Phys.org*. "A more precise number, and the possibility that *G* could vary with time, location, or the type of matter involved, could link to improvements in Einstein's general relativity, including quantum gravity."

One of the main reasons that *G* is so difficult to measure accurately is that experiments must account for the influence of Earth's gravity, *g* (sometimes called "little *g*" in contrast to "big *G*"). Little *g* is the acceleration due to gravity specifically on Earth, where it has a constant value of approximately 9.8 m/s^{2}. Elsewhere in the universe, this value changes, since it depends on the Earth's mass and the distance between the Earth and another object. However, the value of big *G* does not depend on these factors, and so it remains the same everywhere in the universe.

**Deep space lab**

In the new paper, the researchers suggest that the best way to avoid the effects of Earth's gravity on measurements of *G* is to perform the experiment in deep space, which refers to space outside our solar system.

The scientists propose to launch their apparatus into deep space, likely by "piggybacking" on a major mission. Out there, where the gravity of planets and stars would be negligible, the host spacecraft would release a spherical object that has a 1-cm-wide tunnel through its center. Then (this would likely be the most difficult part), the host spacecraft—which is constantly spinning the whole time—would eject a much smaller oscillating object into the tunnel in the sphere at just the right angle and speed so that the object would move back and forth through the tunnel, without bouncing off the walls.

The host apparatus would continually shine femtosecond laser pulses on the object as it oscillates in the tunnel, and the object (a retroreflector) would reflect these pulses back to the host spacecraft. These pulses would provide data on the period of the object's harmonic motion, which is directly dependent on the value of *G*. The data would then be sent back to Earth via radio communication for interpretation.

If everything goes as expected, the researchers' simulations showed that this experiment could measure *G* with an uncertainty of 6.3 x 10^{-8}, which is nearly three orders of magnitude more precise than the current best measurement.

Even though the deep-space experiment wouldn't have to deal with the Earth's gravity, it would still have to contend with other, smaller non-gravitational accelerations that would also affect the retroreflector's motion. These influences include solar radiation pressure, solar tidal effects, cosmic rays, and the momentum from the laser pulses. Some of these effects could be dealt with through careful design—for example, the sphere could be shielded from solar radiation pressure by positioning it in the shadow of the host spacecraft. But the researchers explain that any acceleration greater than 10^{-17} m/s^{2} must be modeled and accounted for when interpreting the data.

**Why measure G?**

The National Science Foundation in the US recently issued a solicitation for new approaches for measuring *G* (Ideas Lab: Measuring "Big G" Challenge). The NSF webpage says that measuring a more precise value of *G* will benefit many fields of physics and metrology, such as understanding the Casimir effect, improving the spring constants that are used to calibrate atomic force microscopy cantilevers, and understanding intermolecular forces in DNA. A precise value of *G* might also be used to test proposed theories that unify gravity with quantum electrodynamics.

Explore further

**More information:**Michael R. Feldman

*et al.*"Deep space experiment to measure

*G*."

*Classical and Quantum Gravity*. DOI: 10.1088/0264-9381/33/12/125013

Also at arXiv:1605.02126 [gr-qc]

© 2016 Phys.org

**Citation**: Deep space experiment could measure the gravitational constant with nearly 1,000 times improvement in accuracy (Update) (2016, May 17) retrieved 20 August 2019 from https://phys.org/news/2016-05-deep-space-gravitational-constant-accuracy.html

## User comments

notalltheglitterisgoldcomposecomposeshavera"G-force" isn't really a scientific concept, but can be a useful one. It's just a measure of how strong a force is. Is the force equivalent to the force of gravitation at sea level? It's a 1-G force. Twice as strong: 2-G.

The "G" here isn't the same as the "G" in "G-force." At the very simplest explanation, it's just a way to tell us how strongly two masses will attract each other at some distance apart. More specifically, it's a constant that tells us how strongly energy changes measures of space and time around it, which indirectly leads to the effect we call gravity.

shaveracomposecomposecomposeantigoraclecomposeTechnoCreedThank you Zephir. I was not aware that the sun was so close to be a perfect sphere. Here is the link to the paper related to the Guardian article https://www.resea...iability

composeWhydening Gyrecomposeadam_russell_9615composeWhydening GyreI'm stickin' to Highly Improbable...

Whydening GyreYeah, but...

Isn't the gravitational constant derived from Newton, that heim requires to use his method, in the first place?

axemastercomposeKedasbecause that would be very interesting for anti-gravity.

composeindio007composeGustavTektrixWhydening GyreJust read about it. Amazingly accurate considering the experimental setup he had. Even more amazing was the elegant math that interpreted its actions....

baraknantigoracleDa SchneibIt is an empirical value in both Newtonian TUG and Einsteinian GRT. If we had a quantum gravity theory we might be able to get a theoretical value. Note "might;" it's possible to imagine quantum gravity that still had the gravitational constant (or some constant it's dependent upon) be an empirical value, too. Remember the 23 free parameters of the Standard Model.

Whydening GyreAre you intimating it might be variable according to mass variations in any given locality locality?

Da SchneibMore later if the article isn't paywalled or is on arXiv.

Da SchneibNo, but the measurements might. Too many variables; these guys are over a masscon in the mantle, those guys are over a batholith, them guys over there have a lot of mountains close by. Each one is at a different altitude, and that's relative to sea level which is different in different places because the Earth is pear-shaped. Then there are systematic errors due to things like air currents. Somebody forgets to subtract the gravity of the Moon or daily errors from the gravity of the Sun creep in. Out in space you don't have to worry about a lot of these things.

BongThePuffinWhydening GyreBut, like the Terminator - He'll be back...:-)

Ryan1981antialias_physorgErm...Whut? Please look up what G is and then what the LHC does. Then you can likely answer this for yourself.

torbjorn_b_g_larsson@not: No, the concept of gravity as force (for weakly curved spacetime) isn't wrong. Magnetism is included as all energies as soon as you use general relativity as your description of gravity.

torbjorn_b_g_larssonWhen you naively quantize gravity you find you can do that for weak fields. That is summed up in Core Theory, "the Feynman path-integral formulation of an amplitude for going from one field configuration to another one, in the effective field theory consisting of Einstein's general theory of relativity plus the Standard Model of particle physics", the theory behind everyday physics. [ ]http://www.preposterousuniverse.com/blog/2015/09/29/core-theory-t-shirts/

But you also find that without a quantum gravity theory for high energies we have to use empirical fits for gravity field theory parameters, which then goes into G of the general relativity theory. [ https://golem.ph....639.html ]

Da SchneibGRT does include a magnetic field that's attracting an object that does not move; this is potential energy and thus goes into the first and second terms of the EFE. But that's pretty esoteric for someone who's perhaps a bit unclear on the difference between gravity and magnetism.

torbjorn_b_g_larssonMaybe "included as all energies" was a bit cryptic. The stress-energy tensor makes the inclusion, and "tells spacetime how to curve". In the linearized EFE, but not in the Newtonian gravity approximation, a slowly changing stress-energy (small velocities) can accommodate some magnetic fields, I think. (But I haven't studied GR, so I can't estimate the effects.)

lupusTechnoCreedRight on

In consise form 6.674 08(31) x 10-11 m³ / kg s²

It means that the true value of G is somewhere between 6.67377 x 10-11 m3 / kg s² and 6.67439 x 10-11 m³ / kg s² http://physics.ni...Value?bg

Da SchneibYep. A little bit of calculation shows the absolute uncertainty would be 3.1 x 10^-15. Exactly what @Techno said.

JackBidnikthat the same equation can describe both the gravitational force on planets, and the electrostatic force between proton and electron in the Bohr hydrogen atom.

The equation is: F =Gs* M*m/r ^ 2, where

Gs = (1/ (M+m))*r*Vo^2*c^4/(Vo^2 +c^2)^2

and where Vo is orbital velocity, c is speed of light, and Gs is what I call Special G.

The surprising corollary is that this equation also applies to stars in orbit about galaxies,

thus indicating there is no need to postulate dark matter, as the equation dispels the problem of

insufficient force using the Newtonian constant.

Check last page of Susskind's blog for more info.

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