$G=1/m_P^2$. This is in contrast to linear DSR corrections, considered in [@KS], for example.

For the comparison of classical gravity and DSR in non-central scattering, considered in subsection (2.2), we assume a typical lowest-order DSR relation (for different kinds of such approximations, see [@exp]) between $p$ and $\pi$ $$\label{beta}
\pi\approx p\left[1+\kappa\left(\frac{p}{m_P}\right)^n\right]$$ with a constant $\kappa$ of order not too far from unity and some positive integer power $n$. This kind of relation is in good accordance with the leading term $\propto p^2$ in (\[pp\]), derived in connection with central collisions, if $n=2$.

Considering an almost central collision from a DSR point of view, we replace $p$ by $\pi$, the variable related to interaction proceses, in the wavelength of the virtual particle, so that $\lambda\approx1/2\pi$. Then from (\[imp\]) we obtain the modified scattering angle, $$\label{thet}
\cos\frac{\vartheta}{2}\approx\left[1+\kappa\left(\frac{p}{m_P}\right)^n\right]
\cos\frac{\vartheta_0}{2}$$ and from comparison of (\[thet\]) with (\[teta\]) it follows that (at least in the considered scattering example) the lowest order correction term of DSR can agree with Newtonian gravity, when it is quadratic in the ratio $p/m_P$. Then only the constants $\beta$ and $\kappa$ must be matched. The result is also a first order approximation in the scattering angle around $180^\circ$. To consider further 