I just thought of a problem with the circular HEO orbit as the staging location between Earth and Luna.
The HEO orbit plane will also precess at a different
rate (faster) than the lunar orbit, so most of the time they will not be coplanar. This results in very restrictive launch window opportunities.
This in turns makes the L-4/5 orbital region more attractive - those orbits are always in the same plane as Luna's (right?).
CFR
All I know to tell you is that the last word O'Neill heard out of the guys who work these things out with computer simulations was that the circular 2 week orbit was considered preferable to either the original L-5 proposal, or the later 2:1 resonance orbit.
Mike Combs
I just thought of a problem with the circular HEO orbit as the staging location between Earth and Luna.
The plane of the Moon's orbit is not fixed. It precesses. I forget what the precession period is, several years I think.
The HEO orbit plane will also precess at a different
rate (faster) than the lunar orbit, so most of the time they will not be coplanar. This results in very restrictive launch window opportunities.
This in turns makes the L-4/5 orbital region more attractive - those orbits are always in the same plane as Luna's (right?).
CFR
Not sure what would cause a precession such as you are suggesting. The
Moon's orbit is within 5 degrees of the Ecliptic, so a HEO orbit that
matched the Ecliptic would never have much trouble getting into the
lunar orbit plane, even if it did precess. Relative to Earth's rotation
the Moon's orbit certainly precesses, but that's because the Earth is
tilted 23 degrees to the Ecliptic. The Moon's rotation axis relative to
the Ecliptic is also almost just enough to compensate for its orbital
plane's slight misalignment, which is why those always-light peaks and
always-dark craters at the poles are actually possible.
in regard to "All I know to tell you is that the last word O'Neill heard out of the guys who work these things out with computer simulations was that the circular 2 week orbit was considered preferable to either the original L-5 proposal, or the later 2:1 resonance orbit." Since the Moon's orbit is about 4 weeks, how would a two week orbit stay out of resonance? Wouldn't it drift towards resonance? I don't know enough about mechanics to understand this myself. Sincerely, Jay Huebner at jhuebn@...
By no means am I an expert in orbital mechanics, but it seems to me that a
HEO orbit with a period of two weeks is indeed itself a 2:1 resonant
orbit. An object in such an orbit would circle the Earth twice as fast
as does the Moon. If a conjunction of Luna and an object in such an
orbit and star X happened this lunar month, then the same conjunction of
these objects would happen next lunar month, too; is that correct? What
am I missing?
"Huebner, Jay" jhuebn@...
10/18/01 10:39 AM
in regard to "All I know to tell you is that the last word O'Neill heard
out of the guys who work these things out with computer simulations was
that the circular 2 week orbit was considered preferable to either the
original L-5 proposal, or the later 2:1 resonance orbit."
Since the Moon's orbit is about 4 weeks, how would a two week orbit stay
out of resonance? Wouldn't it drift towards resonance? I don't know
enough about mechanics to understand this myself.
Sincerely, Jay Huebner at jhuebn@...
By no means am I an expert in orbital mechanics, but it seems to me that a
HEO orbit with a period of two weeks is indeed itself a 2:1 resonant
orbit. An object in such an orbit would circle the Earth twice as fast
as does the Moon. The "2:1" referred not to the resonance factor of the orbit, but to its eccentricity. IIRC, it came in to around 100,000 miles, and out to 200,000 miles.
Mike Combs
The "2:1" referred not to the resonance factor of the orbit, but to its eccentricity. IIRC, it came in to around 100,000 miles, and out to 200,000 miles. Wait, when the object comes around Earth on the side the Moon is on, the Moon's gravity will pull the orbit out towards the Moon, and when it is on the opposite side, the Moon's gravity will keep it closer to Earth, so the two week orbit in the plane of the Moon will be eccentric. It would be less so, if it were closer to Earth, so Earth's gravity would always be stronger than the Moon's, but not with a two week period. The only other choice, it seems to me, is for the two week orbit to be out of the plane of the Moon's orbit. Have I missed something here? Sincerely, Jay Huebner at jhuebn@...
> Not sure what would cause a precession such as you are suggesting. The
precession (aka nodal regression) as a result of the
non-symmetry of the Earth's gravitational field.
The closer to Earth, the faster the rate of precession.
> Moon's orbit is within 5 degrees of the Ecliptic, so a HEO orbit that
> matched the Ecliptic would never have much trouble getting into the
> lunar orbit plane, even if it did precess. Relative to Earth's rotation
>
First let us consider a LEO plane:
It is not possible for a LEO to "match the ecliptic".
The LEO plane could start being coplanar with the
ecliptic, but nodal regression occurs relative to the
Earth's equator. The LEO at 23 degrees inclination to Earth's equator would eventually be inclined at 23+23 = 46 degrees to the ecliptic, once its node has regressed by 180 degrees of terrestrial longitude.
This is an extremely expensive plane change, it would be cheaper to start from the surface of the Earth than to change the plane of such an orbit.
Add 5 degrees for luna's ecliptic means it could be
as much as 51 degrees to the lunar orbit.
> the Moon's orbit certainly precesses, but that's because the Earth is
> tilted 23 degrees to the Ecliptic.
No, I don't think so.
The Moon is heavily influenced by the Sun, that is why it stays so close to the ecliptic. As you get closer to Earth the terrestrial gravity dominates more, and
the satellite ceases to be synchronized with the ecliptic at all.
===
The precession vector of HEO comes somehwere in between LEO and Luna, it is more influenced by Earth gravity and less by the Sun than Luna.
It would be interesting to determine the precise precession for such an orbit.
A HEO could not match the ecliptic. It could easily be
inclined more than 15 degrees to the lunar orbit. Plane changes are very expensive, a 30deg plane change needs
about 50% of the delta-vee it took you to get there from Earth.
CFR.
> All objects which orbit the Earth experience orbital
> precession (aka nodal regression) as a result of the
> non-symmetry of the Earth's gravitational field.
>
you're absolutely right. I had thought all those effects had much longer
periods - 26,000 years or whatever. But the lunar precession (caused by
interaction with sun and Earth as you said) has a period of only 18.6
years - there's a corresponding minor 18.6 year motion in the Earth's
rotation axis (the "nutation" period).
So you could use a High Earth Orbit that had some correspondence to the
Moon's orbit for a year or two, but after that they would start to get
out of sync...
I do suspect there's some way to do this with a resonance, taking all
the gravitational effects into account. But it's definitely not as
simple a problem as I had thought...
Arthur