On 16 October 1929 five members of the Byrd Expedition 1 observed an intermittent 35 min green flash at the Little America station (latitude -78.57°) in Antarctica. The flash was the result of strong atmospheric refraction, likely associated with a subcritical Novaya Zemlya mirage. This paper examines the constraints placed on the observation by the Earth-Sun orbital kinematics. It is found that the length of the observation cannot be explained solely by the slowness of the setting rate of the Sun, nor the time required just before the beginning of the Antarctic summer for the top of the Sun to set, reach its relative minimum position at the horizon, and then rise back up again. The observed length of the effect, however, is consistent with the Sun effectively setting twice and rising twice during the observation, with the first effective rising being the result of the observers climbing up the radio towers at the Little America station in order to keep the top of the Sun in view.