A spacecraft is on the Near Earth Asteroid Seneca, transmitting pulsed data to Earth. Due to the relative motion of the asteroid and the Earth around the Sun, the time it takes for a pulse to arrive varies approximately between $2$ and $39$ minutes. Assuming the Earth moves in a circular orbit and that the orbit of Seneca does not intersect the orbit of the Earth, calculate the semi-major axis, $a_S$ of Seneca’s orbit around the Sun (in AU).