Much could be learned about space if only it were possible to suspend a satellite motionless in space, observing changes of magnetic fields and particle flows at one fixed spot. It cannot be done. To stay up and resist gravity, a satellite must be constantly on the move and must follow its prescribed orbit.

    The best we can do is station-keeping: for instance, the motion of a satellite in a synchronous orbit around the equator is matched by the rotation of the Earth below it, allowing it to permanently stay above the same equatorial spot.

Station-keeping in orbits around the Sun

    With enough velocity, a spacecraft can break loose from the Earth's gravity and enter an orbit around the Sun, like that of a planet. If it then orbits the Sun with the same period as the Earth--one year--it may keep a fixed position relative to Earth. In particular, if that position is between the Sun and the Earth, the spacecraft can be an "early warning station", intercepting any changes in the solar wind before they reach Earth.

    However, orbital laws require planets closer to the Sun to move faster, by a formula found in 1619 by Johannes Kepler. While the Earth goes around the Sun in 365 days, Venus which is closer only needs 225 days and Mercury, closer still, only 88. Thus any spacecraft going around the Sun in an orbit smaller than the Earth's will soon overtake it and move away, and will not keep a fixed station relative to Earth.

    If the distance is just right--about 4 times the distance to the Moon or 1/100 the distance to the Sun--the spacecraft, too, will need just one year to go around the Sun, and will keep its position between the Sun and the Earth. That position is the Lagrangian Point L1, so called after the Italian-French mathematician who pointed it out, Joseph Louis Lagrange (1736-1813).

    The sister-site From Stargazers to Starships discusses Lagrangian points in more detail than is done here, among other things deriving the distance of L1 (the derivation of L2 is almost identical) and also the equilibrium points L4 and L5. While neither calculation requires calculus, both are somewhat lengthy and assume familiarity with basic principles of Newtonian mechanics, covered in preceding sections of the "Stargazers" site.

Spacecraft Observatories at L1

    Such a spacecraft must have its own rocket engine. First, the position is unstable: if the spacecraft slips off it, it will slowly drift away, and sooner or later some correcting action is needed. In fact, the preferred position is actually some distance to the side of L1, for if the spacecraft is right on the Sun-Earth line, the antennas which track it from Earth are also aimed at the Sun, a source of interfering radio waves. Thus corrections are in fact needed quite regularly. Furthermore, the most economic way of getting to L1 is letting the spacecraft pass close to the Moon and using the moon's gravity to extract an extra boost from the Moon's orbital motion. Those maneuvers too require on-board propulsion, as does the final approach to L1.

Other Lagrangian Points

    There exist altogether 5 Lagrangian points in the Sun-Earth system and such points also exist in the Earth-Moon system. Among these, the most attention has been given to the two stable points L4 and L5, located in the Moon's orbit but off the position of the Moon (see picture). These positions have been studied as possible sites for artificial space colonies in some (very!) distant future.

For those interested in space colonies at the Lagrangian points:

• Gerald K. O'Neill, "The Colonization of Space", Physics Today September 1974, p. 32.

• Gerard K. O'Neill, "The High Frontier", William Morrow and Co., NY, 1977; Anchor Books (Doubleday) 1982.