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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.
Right:
Artist Pat Rawling's concept of a manned lunar base. [More]
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 750
miles (1200 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 (400,000 km) from the Moon constantly tugs on lunar satellites.
For a lunar orbit higher than 750 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 750
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 39.6º,
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.
 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 120º apart in the same elliptical orbit at
an inclination of 51º. Each satellite in turn would go screaming
down past periapsis (closest approach to the lunar surface)
only 450 miles (700 km) above the north lunar pole, but would
each linger fully 8 hours of its 12-hour orbit at 5,000 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.
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Editor's
note: This story describes problems keeping satellites
in high orbit around the Moon. Low-orbiting satellites have
problems, too. Lunar "mascons" tug on them and cause
them to crash into the ground. Earth affects high orbits,
mascons affect low orbits. For more information read Science@NASA's
Bizarre
Lunar Orbits.
Author: Trudy E.
Bell | Editor:
Dr. Tony Phillips | Credit: Science@NASA
| More
to the story... |
| Bizarre
Lunar Orbits (Science@NASA) -- Mysterious concentrations
of mass in the Moon's ancient lava seas disturb the
orbits of Moon-circling spacecraft.
Two
recent papers by Ely describe stable high-altitude
lunar orbits and their challenges:
APPENDIX:
THE STABILITY OF HIGH LUNAR ORBITS
The
stability of high lunar orbits (as well as of stars
and black holes) is all about angular momentum—the force
that keeps a top or gyroscope or ice skater spinning
upright, even if perturbed slightly from the side.
For
anything that's spinning, physicists use the right hand
rule. Curl the fingers of your right hand to point in
the direction of the spin. Then your thumb will point
along the axis of spin. More importantly, it will point
in the direction of what physicists call the angular
momentum vector, which has one absolute direction in
space.
You
can actually feel the angular momentum vector. Try this.
Take off the front wheel of a bicycle. Hold it horizontally
by the axle, with one arm above and one arm below, leaving
the wheel free to spin. Have a friend get the wheel
spinning as fast as possible. Once the wheel is spinning,
try to tilt it at a different angle or even to turn
it over. You will find that the spinning wheel resists
you with surprising force. Indeed, the angular momentum
of bicycle wheels is what makes it easier to balance
a bicycle when riding fast than when riding slowly.
One
last brief primer before turning to orbits: The magnitude
of the angular momentum vector depends on three quantities:
the rate of spin, the mass of the spinning object, and
the distance of the mass from the axis (the lever arm
distance). Moreover, angular momentum is conserved—that
is, absent any losses such as friction or applied external
torques (twisting motions), the angular momentum vector
will remain constant. Thus, if rate of spin, mass, or
lever arm changes, then the remaining quantities must
change in some compensating way to keep angular momentum
constant. Example: if a spinning skater brings her arms
in close to her body (shortens the lever arm distance),
she starts spinning faster. The constancy of the angular
momentum vector is also why gyroscopes are used to stabilize
the orientation of spacecraft (such as the Hubble Space
Telescope) in space.
What
does all this have to do with lunar orbits? Every orbit
has angular momentum. Satellites can be fairly massive
(kilograms), and the lever arms can be hundreds or thousands
of kilometers long. Now, if a lunar orbit is circular
with the Moon at the center, the satellite travels with
constant velocity—a situation that makes it vulnerable
to Earth's gravitational pull.
The
effect of all these fascinating dynamics is not to speed
the satellite up in its orbit, but to apply a torque
(twisting motion) that alters the inclination (tilt)
of the plane of the satellite’s orbit. Such a change
in tilt is resisted by the angular momentum vector,
just as the spinning bicycle wheel resisted your attempts
to change its tilt. The only way the orbit can compensate
to conserve angular momentum is to change its shape
or eccentricity: specifically, to become less circular
(eccentricity = 0) and more elliptical (eccentricity
> 0 but < 1). If the original circular orbit was
steeply inclined, however, the change in shape can be
so radical that the satellite is thrown into a hyperbola
(eccentricity > 1) and flies completely away from
the Moon.
Below
a critical inclination of 39.6º, the orbital plane of
a lunar satellite wobbles up and down with the line
joining the ellipse’s apoapsis (farthest point from
the Moon) and periapsis (closest point to the Moon)
being dragged around by Earth as if it were attached
by a leash. Such low-inclination elliptical orbits circulate
around the Moon. Above that critical inclination of
39.6º, the line joining the orbit's periapsis and apoapsis
stays relatively fixed in space, providing a stable
orbit for communications and navigation satellites with
minimum fuel needed for periodic course corrections.
The
Vision for Space Exploration |
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