For making approximate estimates, the time between oppositions may be taken as roughly 2 years and 7 weeks. It can now be seen why the apparitions of Mars occur at intervals of a little over 2 years (p. 5). It is at these times that Mars and Earth are closest and the conditions are most favorable for observations of Mars. A contributory factor is that the planet is then directly opposite from the Sun and this provides the best conditions of visibility.

Because the eccentricity of the orbit of Mars is significantly greater than that of Earth's orbit, the distance between the two planets varies from one opposition to the next. This is apparent from figure 3.7 which gives the locations of Earth and Mars in their respective orbits, at several oppositions, and also shows the major axis of the orbit of Mars. The distance between the two planets ranges from somewhat less than 56 million kilometers (35 million miles) at the most favorable opposition to a little over 101 million kilometers (63 million miles) at the least favorable. The favorable oppositions, when Mars and Earth

are closest, occur when Mars is in the region of its perihelion, whereas the unfavorable ones are around aphelion. This is a consequence of the marked eccentricity of the Martian orbit. The eccentricity of Earth's orbit is too small to be significant on the scale of figure 3.7 and so it appears to be a circle with the Sun at the center.

The dates (in months) at which Earth is at various locations of its orbit are included in the figure. It is seen that the most favorable (périhélie) oppositions always take place around July, August, and early September and the least favorable (aphelic) ones are generally in January, February, and early March. Although the perihelion oppositions are best for observing Mars, intermediate oppositions, in the months of May, June, October, and November, are also quite good because the distances to Earth are never more than about 76 million kilometers (47 million miles).

For purposes of reference, the dates of the oppositions from 1969 through 1980 are given in the accompanying table, together with the respective distances between Mars and Earth. It will be observed that the opposition of August 10, 1971, is a particularly favorable one. Although it is often tacitly assumed that Earth and Mars approach most closely at the time of opposition, this is not quite true. Actually, the closest approach may occur from a few days before to a few days after the date on which Mars and the Sun are exactly oppo site as seen from Earth. The dates of closest approach for each opposition are included in the table given below.

If the orbits of Earth and Mars were exactly parallel, the time of closest approach would coincide with opposition. But the orbits are not parallel, partly because of the different eccentricities and partly because they do not lie in the same plane. The inclination of the orbital planes of the two planets will be considered shortly.

The most favorable oppositions, when Earth and Mars are within about 56 to 58 million kilometers (35 to 36 million miles) of each other, occur at intervals of 15 or 17 years. It is seen in figure 3.6 that between two successive oppositions, the planets advance by a fraction / in their orbits. The value of / is 0.134, on the average, and this is between one-seventh (0.143) and one-eighth (0.125). It follows, therefore, that it would require between seven and eight oppositions for the planets to return to a particular location in their orbits. Because oppositions must be counted in whole numbers, this means that during every seventh or eighth opposition the planets will be approximately in the same region of their orbits.

The average time between successive op positions is somewhat less than 26 months; hence, seven oppositions represent roughly 15 years and eight oppositions about 17 years. Consequently, the most favorable (perihelic) oppositions, which will, however, not be identical, will occur at intervals of either about 15 or about 17 years. The last favorable opposition, for example, occurred in 1956 (September 10), and the next will be in 1971 (August 10). The interval is close to 15 years in this case. There were similar intervals between the successive favorable oppositions of 1909, 1924, and 1939. On the other hand, the interval was 17 years between the aphelic oppositions of 1892 and 1909, and of 1939 and 1956.

An exact repetition of the dates (and orbital locations) of oppositions could occur only when a complete number of Martian (sidereal) years was exactly equal to a complete number of Earth years. After such an interval, the two planets would return to precisely the same positions in their respective orbits. A very close approximation to this situation arises every 284 Earth years (103 733 days), which is almost exactly equivalent to 151 Martian years (103 734 days). Hence, the terrestrial dates of oppositions, within a day or so, recur after a lapse of 284 years.

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