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The GRAVITY instrument at the ESO VLTI has recently detected continuous circular relativistic motion during infrared flares which has been interpreted as orbital motion near the event horizon. Here we analyze the astrometric data from these flares, taking into account the effects of out-of-plane motion and orbital shear of material near the event horizon of the black hole. We have developed a new code to predict astrometric motion and flux variability from compact emission regions following particle orbits. Our code combines semi-analytic calculations of timelike geodesics that allow for out-of-plane or elliptical motions with ray tracing of photon trajectories to compute time-dependent images and light curves. We apply our code to the three flares observed with GRAVITY in 2018. We show that all flares are consistent with a hotspot orbiting at <jats:italic>R<\/jats:italic>\u2004\u223c\u20049 gravitational radii with an inclination of <jats:italic>i<\/jats:italic>\u2004\u223c\u2004140\u00b0. The emitting region must be compact and less than \u223c5 gravitational radii in diameter. We place a further limit on the out-of-plane motion during the flare.<\/jats:p>","DOI":"10.1051\/0004-6361\/201937233","type":"journal-article","created":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T13:38:55Z","timestamp":1581946735000},"page":"A143","source":"Crossref","is-referenced-by-count":105,"title":["Modeling the orbital motion of Sgr A*\u2019s near-infrared flares"],"prefix":"10.1051","volume":"635","author":[{"name":"GRAVITY Collaboration","sequence":"first","affiliation":[]},{"given":"M.","family":"Baub\u00f6ck","sequence":"additional","affiliation":[]},{"given":"J.","family":"Dexter","sequence":"additional","affiliation":[]},{"given":"R.","family":"Abuter","sequence":"additional","affiliation":[]},{"given":"A.","family":"Amorim","sequence":"additional","affiliation":[]},{"given":"J. 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