National Affairs: Celestial Mechanics

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The moon-probe Pioneer is man's first triumph in applied celestial mechanics. Earth satellites, like bullets, baseballs or missiles, need to contend with the earth's gravitation only. Pioneer was born on a higher level of technical evolution. Its projected course toward the moon took into account three of the overlapping gravitational fields (the earth's, the sun's, the moon's) that govern the solar system. To set it on its trajectory called on theoretical astronomical and mathematical lore that man has painstakingly been accumulating without practical employment since the birth of science.

Drawing a bead on the moon is something like shooting a duck from a spinning merry-go-round, using a bullet that takes two days to creep near its target. The moon has its own motion; it speeds around the earth on a somewhat elliptical orbit at 2,300 m.p.h.*Even more disturbing to the moon-marksmen is the rotation of the earth. In every minute, the earth rotates enough to make a 1,000-mile difference in the rocket's position when and if it reaches the moon's orbit.

Escape. To escape from the jealous clutch of the earth's gravitation, a departing object must move faster than any bullet ever fired from any gun. Escape velocity is given theoretically as about 25,000 m.p.h.—the speed that an object would reach if it fell from an infinite distance to the earth's surface under the exclusive influence of the earth's gravitation. Since this speed is impossible in the earth's dense lower atmosphere, a rocket headed into space must start slowly and speed up to escape velocity only after it has climbed above nearly all of the atmosphere. At high altitude the necessary speed is somewhat less than 25,000 m.p.h. because the earth's gravitational pull grows weaker with distance. To reach the moon requires slightly less speed than to escape entirely, since the moon is not at an infinite distance and because its own gravitational pull can offset the earth's diminishing pull if the rocket gets close enough. When Pioneer had risen above the atmosphere, it was moving at 23,500 m.p.h. This was not quite enough.

The trouble came in the first stage, a military Thor rocket whose gyroscopic guidance system misfunctioned just enough to make the trajectory 3.5° steeper than it should have been. This steepness reduced the advantage that was obtained from the slingshot effect of the earth's eastward rotation. Air Force experts say that a loss of speed less than 600 m.p.h. was enough to make the probe fall far short of the moon's orbit.

Spin-Stabilization. All other hardware seems to have functioned perfectly. The second stage, a considerably modified second stage of the ill-starred Vanguard, pushed the vehicle to 188 miles above the earth while small vernier rockets, set askew, made it spin on its axis at no r.p.m. The function of this spin-stabilization, like the spin of a rifle bullet, was to keep the vehicle from tumbling on its journey through space.