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We report results on an elastic cross section measurement in proton-protoncollisions at a center-of-mass energy $\sqrt{s}=510$ GeV, obtained with theRoman Pot setup of the STAR experiment at the Relativistic Heavy Ion Collider(RHIC). The elastic differential cross section is measured in the four-momentumtransfer squared range $0.23 \leq -t \leq 0.67$~GeV$^2$. We find that aconstant slope $B$ does not fit the data in the aforementioned $t$ range, andwe obtain a much better fit using a second-order polynomial for $B(t)$. The $t$dependence of $B$ is determined using six subintervals of $t$ in the STARmeasured $t$ range, and is in good agreement with the phenomenological models.The measured elastic differential cross section $\mathrm{d}\sigma/\mathrm{dt}$agrees well with the results obtained at $\sqrt{s} = 546$~GeV forproton--antiproton collisions by the UA4 experiment. We also determine that theintegrated elastic cross section within the STAR $t$-range is$\sigma^\mathrm{fid}_\mathrm{el} = 462.1 \pm 0.9 (\mathrm{stat.}) \pm 1.1(\mathrm {syst.}) \pm 11.6 (\mathrm {scale})$~$\mu\mathrm{b}$.

Results on Elastic Cross Sections in Proton-Proton Collisions at $\sqrt{s} = 510$ GeV with the STAR Detector at RHIC