app-a

SP-4212: On Mars: Exploration of the Red Planet. 1958-1978




Appendix A
Orbital Relationships of Earth and Mars

[427] The following is a brief explanation of planetary motions and, in particular, the relationships of the orbits of Earth and Mars. Mercury is the planet closest to the sun. Venus, Earth, Mars, the asteroids, Jupiter, Saturn, Neptune, and Pluto, in that order, are farther out, All move around the sun in the same direction, If the solar system were viewed from far above Earth's northern hemisphere, the planetary motion would appear to be counterclockwise, The planetary orbits lie in very nearly the same plane. The paths of the planets, if seen from the sun, would all describe the same circle, except for Mercury and Pluto, which have tilted orbits- the innermost and outermost of the sun's satellites.

The planets move in the same direction and most of them occupy a common plane, but the distance between any two planets varies considerably with time, Figure l illustrates the perihelia (points of closest approach to the sun) and aphelia (farthest points from the sun) of Mercury and Mars. Earth and Venus have more nearly circular orbits. Since Earth and Mars travel around the sun in orbits of different lengths with different velocities, the distance between the planets varies constantly. About every 780 days (the actual interval ranges from 765 to 810 days), Earth overtakes its slower neighbor in their unending orbiting of the sun. (Kepler pointed out in his third law: The square of the period of a planet's complete revolution around the sun is proportional to the cube of its mean distance from the sun.) Seen from the sun, the two planets momentarily lie along a straight line. Seen from Earth, Mars is in a...


Fig. 1. Orbits of the inner planets of the solar system are drawn to scale (although the sizes of the planets are not). Orbits of Venus and Earth are nearly circular. Mercury and Mars orbits are eccentric. Perihelion points of Mercury and Mars are indicated by [Greek letter pi] and apelion by a (Greek letter alpha).



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Fig. 2. At conjunction of Mars and Earth, Mars becomes invisible in the sun's rays. Best observation period is from quadrature to quadrature, Samuel Glasstone, The Book of Mars, NASA SP-179,1968.

...direction directly opposite that of the sun; Mars and the sun cannot be seen at the same time because they are on opposite sides of the Earth. This positioning, illustrated in figure 2, is called opposition. During opposition, Mars and Earth come closest together- between 55 and 102 million kilometers.

Distances between the Two Planets
.
Date	Kilometers
.
30 Dec. 1960	90 606 067
4 Feb. 1963	100 101 196
9 Mar. 1965	99 779 328
15 Apr. 1967	89 801 395
31 May 1968	89 801 395
10 Aug. 1971	56 166 105
25 Oct. 1973	65 017 497
15 Dec. 1975	84 329 625

As Earth keeps racing ahead and Mars falls behind, there are instances when the two planets form a straight line, with the sun interposed between them. Mars disappears from Earth's view behind the disk of the sun; the planets are in conjunction. Mars is as far away from Earth as it can be- more than 350 million kilometers.

One other position in the Earth-Mars relationship is also important. When the sun, Earth, and Mars describe a right angle, Mars is said to be in quadrature. In this position, Mars does not appear as a round disk to Earth-based observers. Instead, it looks like the gibbous moon, between half- and full-moon phases. What we do not see is the night side of Mars blending with the black sky.

If an opposition takes place along the line marked 0° on figure I, an observer on Earth would look across a shorter distance to Mars than during a 180° opposition. An opposition at Mars perihelion would offer the best opportunity for observations and spaceflight, since the distance between Earth and Mars at that point would be the shortest. Of the more recent oppositions, the one in 1924 came the closest to being at perihelion, while the 1933 opposition was almost precisely at aphelion.

For further information, see Samuel Glasstone, The Book of Mars, NASA SP-179 (Washington, 1968), and Willy Ley and Wernher von Braun, The Exploration of Mars (New York: Viking Press, 1956).

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Fig. 3. The orbits of Earth and Mars, showing the times of opposition and the separation at opposition. Samuel Glasstone, The Book of Mars, NASA SP-179, 1968.