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[en] Exclusive photoproduction of ρ(770) mesons is studied using the H1 detector at the ep collider HERA. A sample of about 900,000 events is used to measure single- and double-differential cross sections for the reaction γp → ππY. Reactions where the proton stays intact (m = m) are statistically separated from those where the proton dissociates to a low-mass hadronic system (m< m< 10 GeV). The double-differential cross sections are measured as a function of the invariant mass mππ of the decay pions and the squared 4-momentum transfer t at the proton vertex. The measurements are presented in various bins of the photon–proton collision energy W. The phase space restrictions are 0.5 ≤ m ≤ 2.2 GeV, |t| ≤ 1.5 GeV, and 20 ≤ W ≤ 80 GeV. Cross section measurements are presented for both elastic and proton-dissociative scattering. The observed cross section dependencies are described by analytic functions. Parametrising the m dependence with resonant and non-resonant contributions added at the amplitude level leads to a measurement of the ρ(770) meson mass and width at m = 770.8 (tot.) MeV and Γ = 151.3 (tot.) MeV, respectively. The model is used to extract the ρ(770) contribution to the ππ cross sections and measure it as a function of t and W. In a Regge asymptotic limit in which one Regge trajectory α(t) dominates, the intercept α(t=0)=1.0654 (tot.) and the slope α′(t=0)=0.233 (tot.) GeV of the t dependence are extracted for the case m = m.