Moon Miners' Manifesto

#92 February 1996

Description of Clarke orbits

Why most planets and asteroids have Clarke orbits, and most moons do not.

The location of, even the very existence of, surface-synchronous orbits depends on three factors:

• The mass of the planet, moon, or asteroid in question
• Its rotation period
• Its proximity to deeper gravity wells

The more massive the body in question, the farther out will be any surface-synchronous orbit, all else being equal and the periods of the compared bodies being closely similar.

Earth and Mars have similar periods or days of 24 hours and 24 hrs. 37 minutes respectively. Earth's geosynchronous orbit lies some 23,000 miles above the surface. The synchronous orbit for Mars, with only a tenth of Earth's mass, lies 10,500 miles above the surface. In contrast, a 24 hr. orbit above Saturn (95 times more massive than Earth) would lie about 160,000 miles above its cloudtops.

The slower a body rotates, the farther out will be any surface-synchronous orbit.

If Earth rotated in 48 hrs rather than 24, its synchronous orbit would lie nearly 39,000 miles above the surface [period^2= distance^3 (from planet center)]. Conversely, if Earth rotated in just 12 hours, its geosynchronous orbit would lie just 13,000 miles above the equator.

If the theoretical surface-synchronous orbit lies beyond the closest Lagrange point of a more massive body, a synchronous orbit will not exist as any object following such an orbit would fall into the dominant gravity well of the larger object.

The moon's rotation period, locked to the period of its orbit about Earth, is a lazy 28.53 days. If the moon were an isolated body off by itself, i.e., not a satellite of Earth or some other close and more massive dominant body, its surface synchronous orbit, i.e., one with a period of 28.53 days, would lie about 55,000 miles out. In actuality, such an orbit would run over the shoulder of the moon's gravity well into Earth's gravity well on the side facing Earth.

Most natural planetary satellites or moons have had their original rotations slowed, or speeded up, by overwhelming tidal forces until their rotation is locked to their orbital period, so that they always keep the same face turned toward their planet. Io, Europa, Ganymede, and Callisto always keep the same face turned toward Jupiter, Titan and its siblings, the same face towards Saturn, etc. Likewise, their would-be surface-synchronous orbits run over the lip of the gravity well interfaces with their host planet.

For communications on tidally locked planetary moons, there are three solutions:

• a constellation of satellites in swift close-in orbits;
• fewer satellites in very eccentric "Molniya" type orbits with their apogee (at which they move slowest and near which they spend by far the most time each orbit) above the place needing communications;
• relay satellites at planet-moon L4 and L5 co-orbital Lagrange points, respectively centered some 60° ahead of and behind the moon in its orbit about its planet at the same distance from the moon as the planet.

For the moon, L4 and L5 lie 238,000 miles out, fully ten times farther out than Earth's geosynchronous orbit, meaning longer lag times and requiring more broadcast power.

On the other hand, as small as asteroids are, their shallow gravity wells are far enough removed from those of more massive planets, that they can enjoy surface-synchronous orbits. Ceres, with a period of 9.08 hrs. has a Clarke orbit just 486 miles above its equator.

Contents of this issue of Moon Miners' Manifesto