Читать книгу Foundations of Space Dynamics - Ashish Tewari - Страница 20

When two objects orbit one another at nearly constant rates on a fixed plane, a reference frame can be defined by two of its axes on the plane of rotation and rotating at the constant rate, and the third axis normal to the plane. Such a rotating reference frame is called a synodic frame. An example of a synodic frame is the ecliptic frame, which is a reference frame constructed out of the ecliptic plane, such as the frame in Fig. 1.3. The motion of an object measured relative to a synodic frame must be corrected by a vector subtraction of the motion of the frame itself, as exemplified by the calculation of the sidereal day from the observed rotation in the ecliptic frame. The ecliptic frame has been used as a reference since the earliest days of astronomical observations. The division of the circle into arose out of the apparent motion of the sun per day, which subtends an arc of one diameter every 12 hours when seen from Earth. Since the moon's apparent diameter from Earth is roughly the same as that of the sun, the eclipses of the sun and the moon are observed in the ecliptic (thus the name). However, since the moon's orbital plane around Earth is tilted relative to the ecliptic, the eclipses happen only along the intersection (i.e., the line of nodes) of the two planes.

The Earth‐moon line provides another synodic reference frame for space flight. The Earth and the moon describe coplanar circles about the common centre of mass (called the barycentre) every 27.32 mean solar days relative to the vernal equinox (called a sidereal month). This rotational period appears in the synodic frame to be 29.53 mean solar days (a synodic month) from one new moon to the next, which is obtained from the sidereal month by subtracting the rate of revolution of Earth‐moon system around the sun.