  The possibility of measuring the proton electromagnetic form factors in the
time-like region at FAIR with the \PANDA detector is discussed. Detailed
simulations on signal efficiency for the annihilation of $\bar p +p $ into a
lepton pair as well as for the most important background channels have been
performed. It is shown that precision measurements of the differential cross
section of the reaction $\bar p +p \to e^++ e^-$ can be obtained in a wide
angular and kinematical range. The individual determination of the moduli of
the electric and magnetic proton form factors will be possible up to a value of
momentum transfer squared of $q^2\simeq 14$ (GeV/c)$^2$. The total $\bar p
+p\to e^++e^-$ cross section will be measured up to $q^2\simeq 28$ (GeV/c)$^2$.
The results obtained from simulated events are compared to the existing data.
Sensitivity to the two photons exchange mechanism is also investigated.
