Foundations of Space Dynamics. Ashish Tewari
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1.2.2 Celestial Frame
For a motion taking place inside the solar system, any two stars (except the sun) appear to be fixed for the duration of the motion. Hence, a reference frame constructed out of three mutually perpendicular axes, each of which are pointing towards different distant stars, would appear to be fixed in space, and can serve as a sidereal reference frame. A reference frame fixed relative to distant stars is termed a celestial reference frame. For example, the rate of rotation of Earth about its own axis can be measured by an observer standing astride the North Pole by timing the rate at which a straight line joining Earth to a distant star, called a celestial meridian (see Fig. 1.3), appears to rotate. This rate gives the true rotational time period of Earth, called the stellar day, which is measured by IERS to be 23 hr., 56 min., 4.0989 s. Hence, the sidereal day is shorter than the stellar day by about
1.2.3 Synodic Frame
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
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.
1.2.4 Julian Date
Instead of the calendar year of 365 mean solar days, the tropical year of 365.242 mean solar days, and the sidereal year of 365.25636 mean solar days, it is much more convenient to use a Julian year of 365.25 mean solar days, which avoids the addition of leap years in carrying out astronomical calculations. A Julian day number (
Computation of the Julian date (JD) from a Gregorian calendar date is complicated due to the three calendar cycles used to produce the Julian calendar, namely the solar, the lunar, and the indiction cycles of 28, 19, and 15 year periods, respectively (Seidelmann, 1992). A product of these gives the Julian period of 7980 years. The Julian period begins from 4713 BC, which is chosen to be the first year of solar, lunar, and indiction cycles beginning together. The next epoch when the three cycles begin together will happen at noon UT on January 1, 3268. The following conversion formula for the JDN, truncated to the last integer, uses the numbering of the months from January to December as
(1.4)
This formula calculates the JDN for 09:25 a.m. UT on June 25, 1975, by taking
An epoch in the Julian date is designated with the prefix
Since