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 $q^2simeq 14$ (GeV/c)$^2$. The total $bar p +pto e^++e^-$ cross section will be measured up to $q^2simeq 28$ (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.
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