MMM Classics Year 10: MMM #s 91-100 - Moon Society

Why most planets and asteroids have
Clarke orbits, and most moons do not.
from the MMM Info Bank
The location of , even the very existence of surfacesynchronous
orbits depends on three factors:
◊ The mass of the planet, Moon, or asteroid in question
◊ Its rotation period
◊ Its proximity to deeper gravity wells
fi The more massive the body in question, the further out
will be any surface-synchronous orbit, all else being equal the
periods of the 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.
fi The slower a body rotates, the further 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.
fi If the theoretical surface-synchronous orbit lies
beyond the closest Lagrange point of a more massive body, a
synchro-nous 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 they 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. a constellation of satellites in swift close-in orbits;
b. 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;
c. 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 further out
than Earth’s geosynchronous orbit, meaning longer lag
times and requiring more broadcast power.
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
[Continuing a Special MMM Series of Articles]
This month, we continue our series of essays on the
early days of a hopefully permanent manned lunar occupation,
looking at “Pioneer Holidays”, the self-selection drivers of
lunan pioneers with the “right stuff”, and what it takes to make
a “permanent” outpost deserving of the name.
After a break next month to turn our attention to Mars,
we’ll resume this discussion of the first roots of what is sure to
be a uniquely lunan culture in the April issue.
Meanwhile: !!!
Last month, in Moon Miners’ Review #18, we were
treated to a glimpse of an exciting new propulsion concept by
NASA Lewis propulsion whiz Stan Borowski. “LANTR”
promises to make the opening of the lunar frontier easier, more
economic, and faster developing. Immediately below are the
illustrations that should have accompanied that article.
Moon Miners’ Manifesto Classics - Year 10 - Republished January 2006 - Page 15