see that $ |f_2(r_1)|>|f_2(r_+)|$.

![ The black surface corresponds to the plot of $|f_2(r_1)|$, which has been treated as a function of $S$ and $v$. The other surface corresponds to $|f_2(r_+)|$. In this figure, we have set $c=M=1$, $v\in [0,0.5]$, and $S\in [1,3]$. As this figure suggests, we have $|f_2(r_1)|>|f_2(r_+)|$. The qualitative behavior of the surfaces does not change for a wider range of values of $v$ and $S$.[]{data-label="09012014d"}](f2.jpg)

In addition, we also have $|f_2(r_2)| <|f_2(r_1)|$ [^3]. Therefore, the maximum value of the left-hand side of Eq. (\[9082013m\]) during the trip occurs at $r_1$ and is given by (\[08012014i\]).

A natural question we may ask ourselves is what the values of $S$ and $v$ that minimize $|f_2(r_1)|$ are. Figure \[09012014d\] can be used to answer this question. As it suggests, the minimum of $|f_2(r_1)|$ happens when $S \to \infty$ and $v\to 0$. Substituting these values in Eq. (\[08012014i\]), one finds that $$\frac{8}{M^2e^4} { \put(2,0){$<$} \put(2,-5){$\sim$}\quad \ }10^{-16}/m^2,   \label{08012014j}$$ which yields $M{ \put(2,0){$>$} \put(2,-5){$\sim$}\quad \ }4\times 10^7\ m$. This is basically the same result yielded by the condition (\[9082013l\]).

Condition \[9082013n\]
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The condition \[9082013n\] is clearly problematic. If we image that $M$ is the mass of a body such as 