http://science.nasa.gov/headlines/y2006/30nov_highorbit.htm
A New Paradigm for Lunar Orbits
NASA Science News
November 30, 2006
November 30, 2006: It’s 2015. You’re NASA’s chief engineer designing a
moonbase for Shackleton Crater at the Moon’s south pole. You’re also
designing a com-system that will allow astronauts constant radio
contact
with Earth.
But you know that direct transmissions won’t work–not always. As seen
from
Shackleton Crater, Earth is below the horizon for two to three weeks
each month (depending on the base’s location). This blocks all radio
signals, which travel line of sight.
The solution seems obvious. Simply place a satellite in a high,
circular
orbit going almost over the Moon’s poles. Better yet, place three
satellites into the same orbit 120 degrees apart. Two would always be
above the lunar horizon to relay messages to and from Earth.
There’s just one problem.
“High-altitude circular orbits around the Moon are unstable,” says Todd
A. Ely, senior engineer for guidance, navigation, and control at NASA’s
Jet Propulsion Laboratory. “Put a satellite into a circular lunar orbit
above an altitude of about 430 miles (1,200 km) and it’ll either crash
into the lunar surface or it’ll be flung away from the Moon altogether
in a hyperbolic orbit.” Depending on the specific orbit, this can
happen
fast: within tens of days.
Why? Earth is responsible. The gravity of massive Earth only 240,000
miles from the Moon constantly tugs on lunar satellites. For a lunar
orbit higher than 430 miles, Earth’s pull is actually strong enough to
whisk a spacecraft out of the game.
Satellites in Earth orbit don’t experience this sort of interference
from the Moon. The Moon has just 1/80th Earth’s mass - scarcely more
than
1%. Relatively speaking, the Moon is a gravitational pipsqueak. Indeed,
to any satellite in Earth orbit, the gravitational pull of the Sun is
160 times stronger than any lunar influence.
Any satellite in orbit around the Moon higher than about 430 miles,
however, finds itself in a kind of celestial tug-of-war between Moon
and
Earth. Earth’s pull can actually change the shape of an orbit from a
circle to an elongated ellipse.
Stable circular lunar orbits do exist below an inclination of
39.6??,
says Ely, but they spend so much time near the equator that “they are
terrible orbits for covering the poles.”
NASA wants to explore the Moon’s polar regions for many reasons–not
least is that deep polar craters may contain ice, which astronauts
could
harvest and melt for drinking or split into hydrogen and oxygen for
rocket fuel and other uses. The instability of polar orbits poses a
real
problem for exploration.
[An elliptical orbit around the moon]
Now for the good news. Ely and
several colleagues have discovered a whole new class of “frozen” or
stable high-altitude lunar orbits. Pictured right, they are all
inclined
at steep angles to the Moon’s equatorial plane so they get far above
the
horizon at the lunar poles, and–surprise–they are all also quite
elliptical.
“For better South Pole coverage, you want an ellipse with an
eccentricity of about 0.6, which is pretty oval,” Ely says. An
eccentricity of 0 is a circle, along which a satellite travels at a
constant speed around a primary body (say, the Moon) at its center.
With
Earth nearby, that’s out of the question: “An inclined circular orbit
is
kind of a blank canvas where Earth can quickly work its will,” Ely
says.
In contrast, an eccentricity of 0.6 is an ellipse about as oval as an
American football minus the pointed ends; the Moon would be at one
focus
of the ellipse. “The ellipse effectively ‘locks in’ the satellite’s
behavior to make it tougher for Earth to change,” Ely explains. [See
the
appendix below for details.] How stable are they? Ely and his
colleagues
calculate that certain elliptical, high-inclination, high-altitude
lunar
orbits may remain stable for periods of at least a century. Indeed, Ely
hypothesizes the orbits could last indefinitely.
For lunar communications and navigation, Ely recommends spacing three
satellites 120?? apart in the same elliptical orbit at an
inclination of
51??. Each satellite in turn would go screaming down past periapsis
(closest approach to the lunar surface) only 320 miles (700 km) above
the north lunar pole, but would each linger fully 8 hours of its
12-hour
orbit at 4,800 miles (8,000 km) above the horizon over the south lunar
pole. In this configuration, two of the three satellites would always
be
in radio line-of-sight from a South Pole moonbase.
High-inclination, highly elliptical orbits being cheapest and most
stable for communications satellites around the Moon? To Earth-centered
satellite engineers used to thinking in terms of circular equatorial
orbits, “it’s a new paradigm,” Ely declares.
risolto il problema!
molto interessante…