  The process of $e^+e^- \rightarrow p\bar{p}$ is studied at 22 center-of-mass
energy points ($\sqrt{s}$) from 2.00 to 3.08 GeV, exploiting 688.5~pb$^{-1}$ of
data collected with the BESIII detector operating at the BEPCII collider. The
Born cross section~($\sigma_{p\bar{p}}$) of $e^+e^- \rightarrow p\bar{p}$ is
measured with the energy-scan technique and it is found to be consistent with
previously published data, but with much improved accuracy. In addition, the
electromagnetic form-factor ratio ($|G_{E}/G_{M}|$) and the value of the
effective ($|G_{\rm{eff}}|$), electric ($|G_E|$) and magnetic ($|G_M|$) form
factors are measured by studying the helicity angle of the proton at 16
center-of-mass energy points. $|G_{E}/G_{M}|$ and $|G_M|$ are determined with
high accuracy, providing uncertainties comparable to data in the space-like
region, and $|G_E|$ is measured for the first time. We reach unprecedented
accuracy, and precision results in the time-like region provide information to
improve our understanding of the proton inner structure and to test theoretical
models which depend on non-perturbative Quantum Chromodynamics.
