gravity - The distance square in the Newton's law of universal gravitation is really a square?

When I was in the university (in the late 90s, circa 1995) I was told there had been research investigating the $2$ (the square of distance) in the Newton's law of universal gravitation.

$$F=G\frac{m_1m_2}{r^2}.$$

Maybe a model like

$$F=G\frac{m_1m_2}{r^a}$$

with $a$ slightly different from $2$, let say $1.999$ or $2.001$, fits some experimental data better?

Is that really true? Or did I misunderstand something?

Answer

This was suggested by Asaph Hall in 1894, in an attempt to explain the anomalies in the orbit of Mercury. I retrieved the original article in http://adsabs.harvard.edu/full/1894AJ.....14...49H

Interestingly, he mentions in the introduction that Newton himself had already considered in the Principia what happens if the exponent is not exactly 2, and had concluded that the observations available to him strongly supported the exact power 2!

The story is retold, e.g., on p.356 of N.R. Hanson, Isis 53 (1962), 359-378.

See also Section 2 of http://adsabs.harvard.edu/full/2005MNRAS.358.1273V