# Limits on non-Newtonian gravity at length scales larger than 1 meter?

This answer from 2012 shows some information on an exponential term characterized by relative strength and range parameters $$\alpha$$ and $$\lambda$$,

One potential tested here is here $$V(r)=-G\frac{m_1m_2}{r}(1+\alpha\exp(-r/\lambda))$$

The below plot shows the exclusion limits for both parameters $$\alpha$$ and $$\lambda$$

but the largest length shown is only about a centimeter.

Going to the University of Washington's page The Eöt-Wash Group; Results, I can see the following plot of limits that includes range scale of 1 meter and above:

but I can not understand the physics or the units.

update: This has the unit-less expression I seek and the length scale of 1 meter and larger, but the experiment is based on a "material-composition dipole pendulum" torsional balance; one side of the dipole is four beryllium masses, and the other is four titanium masses.

That's a specific type of short-range deviation. I'm looking for a limit on all possible sources. Perhaps none exists yet?

FIG. 3: New upper limits on Yukawa interactions coupled to baryon number with 95% confidence. The uncertainties in the source integration is not included in this plot. The numbers indicate references. The shaded region is experimentally excluded. Preliminary models for 10 km < λ < 1000 km indicate that the limit on α is smaller than the dashed line.

Is there some way to know current limits on all non 1/r potential between say 1 meter and 1 AU, or at least 0.1 AU, shown as a unitless ratio to the 1/r potential?

• By "all non-1/r potentials," I assume you mean models other than the Yukawa correction that you cite? I can give you an answer without additional digging of why you're unlikely to find such parameterizations in the literature, unless you've encountered a specific example that I'm not familiar with. (That's apart from MOND, which is an approach whose details I've never followed closely.) – rob Feb 4 at 22:11
• @rob I'll welcome your answer, I don't understand this topic very well so any clarification is appreciated. I'm wondering if there are really no experimental limits on non 1/r components to the gravitational potential except for that. Wouldn't the trajectories of some spacecraft in the solar system, both far from the Sun and close to it and during planetary flybys 1 2 put some experimental limits on deviations from 1/r at least? – uhoh Feb 5 at 0:33