Fig. 3-10. Standard Astronomical Symbc

Fig. 3-10. Standard Astronomical Symbc

The interval between successive oppositions of a superior planet or successive inferior conjunctions of an inferior planet is known as the synodic period, S. The relation between the synodic period and the sidereal period, P, relative to the fixed stars is shown in Fig. 3-11. If P, and P2 are the periods of the inner and outer planets respectively, then, in general:

For an observer on the Earth, if S and P are both exprer«ed in years, then for <t superior planet the average synodic period is given by

and for an inferior planet by

Thus, for Mars, opposition will occur approximately every 780 days. Because planetary orbits are not circular, the actual synodic periods vary by several weeks. Recent and future oppositions of Mars are listed in Table 3-3. Note that the

Fig. 3-11. Determining the Synodic Period (see text for explanation)

synodic period is longest for Mars and Venus (780 and 584 days), shortest for Mercury (116 days), and approaches 1 year for the other planets.

Planetary configurations are important for interplanetary flight as well as for observations because they define the opportunities for planetary travel. For example, as shown in Section 3.3, trips to Mars along a minimum energy trajectory will leave the Earth about 97 days before opposition and arrive at Mars about 162 days after opposition, although various, factors may cause the actual flight times, particularly the arrival time, to vary by several weeks. Because an opposition of Mars occurred on December 15, 1975, we would expect flights to leave Earth on about September 10, 1975, and arrive at Mars on about May 27, 1976. The two spacecraft flown during this launch opportunity, Viking I and II, were launched on August 20 and September 9, 1975, and arrived at Mars on June 19 and August 7, 1976.

The orbits of the natural satellites of the solar system are generally less uniform than the orbits of the planets, primarily because perturbations cause substantial variations in satellite orbits. For example, the perigee location for the Moon makes one complete revolution about the Moon's orbit in only 8.85 years and the line of nodes rotates fully around the orbit in 18.6 years. Thus, in analogy

Table 3-3. Oppositions of Mars

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