A flying object position measuring apparatus includes an optical sensor, a storage, an orientation calculator, and a position calculator. The optical sensor obtains an image of a flying object. The flying object performs flight along a ballistic trajectory. The storage stores, in advance, basic trajectory information regarding a basic trajectory of the flying object. The basic trajectory information includes position information of a start point at which the flying object starts the flight. The orientation calculator calculates an orientation of the flying object as viewed from the optical sensor on the basis of the image obtained by the optical sensor. The position calculator calculates, as a position of the flying object, an intersection of a plane of rotation with the orientation of the flying object. The plane of rotation is a plane based on a rotation of the basic trajectory around a vertical axis that travels through the start point.