Is $F = G\dfrac{{m_1}{m_2}}{r^2}$ really true? My book (Concepts of Physics by H.C. Verma) writes:

It has been reported (Phys. Rev. Lett. Jan 6, 1986) that the force between two masses may be better represented by
$$F = \frac{G_{\infty} m_{1} m_{2}}{r^2} \left[1 + \left(1 + \frac{r}{\lambda} \right) \alpha e^{-\frac{r}{\lambda}}\right]$$
where $\alpha \approx - 0.007$ and $\lambda \approx 200~\mathrm{m}$.

What is this? Such a horrendous formula! So, what about Newton's? And what's the difference between $G$ & $G_{\infty}$?
 A: In principle not, because it is wrong when describing the behavior of the orbit of Mercury, but should be borne in mind that there is no absolute truth when describe the universe, they always talk about "good approximations" and Newton's law of gravitation rule! xD, (it can take you to the moon!).
A: Yes, Newton's formula is just fine. No, the formula in your book doesn't describe reality. At first this sounded like an exercise, where the next sentence is probably something like "calculate the effect this has..." These sorts of hypothetical questions are meant to show you how you could distinguish between competing physical theories.
Some more digging turns up the actual paper, though: Fischbach et al., Phys. Rev. Lett. 1986, 56, 3. Apparently another group kept getting the wrong value for $G$ -- which is, by the way, the most difficult physical constant to measure -- and so these authors proposed some extra force. This force has an extended range (the $200\ \mathrm{m}$ determines how quickly it falls off) compared to nuclear forces, but still vanishes exponentially for large distances.
The idea never really went anywhere, and it is just an example laboratory errors. The claim was countered by Keyser et al., Phys. Rev. Lett. 1986, 56, 2425, where they show how the extra force only appears when one cherry picks the data. All measurements have some error, and if you systematically only include the measurements that randomly happen to support your hypothesis, you can make your hypothesis seem true.
