Newsgroups: sci.space.history
From: Henry Spencer <henry@zoo.toronto.edu>
Subject: Re: Apollo polar orbit question
Date: Mon, 1 Dec 1997 00:51:08 GMT

In article <65sru2$fgt@omnifest.uwm.edu>,
Chris Roth <croth@omnifest.uwm.edu> wrote:
>Suppose one of the final Apollo flights was a nonlanding
>mission. The LM would be a remote sensing platform, and
>would have no rockets and no rocket fuel aboard.
>Could the CSM and Saturn V get that "CSM-and-LM stack" into a
>lunar polar orbit?

Yes.  To a first approximation, the spacecraft dawdles out to lunar
distance, and the Moon comes up and almost-hits-it from behind, and simply
selecting the exact position where this happens chooses the orbital
inclination -- there is no extra cost for a polar orbit.  In fact, when you
move beyond first approximations, it does cost something... but if you're
deleting the LM's fuel, or using it for orbital propulsion rather than
landing, you've got lots of margin to overcome such second-order factors.

Actually, the most plausible way to fly such a mission would have been to
delete the LM entirely, and fly a CSM-only mission like Apollo 8.  The
SM's SIM bay is quite adequate as an instrument platform unless you're
getting really ambitious.

A slightly more ambitious alternative would be to take along an unmanned
cargo LM loaded with equipment and supplies, to be landed automatically
at the planned site for the next mission.  This would increase surface
stay time, available equipment, and return payload for the landing
mission.  After LM separation, the CSM does the orbital mission.

>What would be different as compared
>to the standard equatorial-ish orbits we saw with the
>real Apollo missions?

Precious little apart from the details of the mission plan.  One detail
that might be different is stay time.  Unless you've got enough margin to
do a substantial plane change at departure time -- perhaps possible in
this case, it's not ridiculously expensive -- you need to wait until your
orbital velocity is pointed in the right direction for the escape burn.
That only happens twice a month in a lunar polar orbit, because the orbit
is roughly fixed in space (lunar orbital precession is negligible) as the
Moon goes around in *its* orbit.  So you have to choose between a short
stay, maybe a day or two, and a two-week stay.
--
If NT is the answer, you didn't                 |     Henry Spencer
understand the question.  -- Peter Blake        | henry@zoo.toronto.edu

Newsgroups: sci.space.history
From: Henry Spencer <henry@zoo.toronto.edu>
Subject: Re: Proposed Apollo follow-on landing sites (was Re: What if...?)
Date: Tue, 10 Mar 1998 15:35:48 GMT

In article <6e3bjt$51o@nrtphc11.bnr.ca>,
Cathy James <cajames@fngdev8fngdev8:0.0> wrote:
>>relay satellite.  That could have been avoided for the descent of the
>>polar landing by either doing the descent over the nearside or doing it
>>over the limb (with the orbit perpendicular to the line of sight from
>>Earth, not passing behind the Moon at all); rule-of-thumb orbital
>>mechanics suggests the latter.
>
>	I'm confused, Henry.  In the latter case, the plane
>of the approach orbit would be perpendicular to the Earth-Moon
>line.  How does the vehicle arrive in this orbit without a
>nearly 90 degree plane change (fuel cost prohibitive)?

It's the other polar orbit which would need the plane change, actually.
Intuition is deceiving here:  the Moon's motion, not the spacecraft's,
dominates the encounter (in simplified rule-of-thumb work, anyway).  The
spacecraft swings out to the vicinity of the Moon's orbit, and the Moon
comes zipping up from behind and starts to go past.

The choice of lunar orbit is determined by exactly where the spacecraft is
when the Moon arrives.  If it's in the Moon's orbital plane but slightly
outside the Moon's orbit, the lunar farside equator starts to pass under
it, at which point an insertion burn will put it into a (retrograde)
equatorial orbit.  If it's at the Moon's orbital distance but slightly
above or below the orbital plane, then one of the lunar poles will start
to pass under it, and an insertion burn will put it into a polar orbit
roughly perpendicular to the Earth-Moon line.

This is why the near-equatorial Apollo orbits were retrograde, and why
Lunar Prospector's first few lunar orbits didn't (as I recall) involve any
interruption of communications.

This is also the correct rough model for an economy-orbit encounter with
Mars, e.g. Mars Global Surveyor's.
--
Being the last man on the Moon                  |     Henry Spencer
is a very dubious honor. -- Gene Cernan         | henry@zoo.toronto.edu

Newsgroups: sci.space.history
From: Henry Spencer <henry@zoo.toronto.edu>
Subject: Re: Why were the lunar orbits retrograde?
Date: Thu, 12 Mar 1998 03:28:33 GMT

In article <1998Mar11.092210.48278@ludens>,
Geza Meszena <meszena@ludens.elte.hu> wrote:
>> The choice of lunar orbit is determined by exactly where the spacecraft is
>> when the Moon arrives.  If it's in the Moon's orbital plane but slightly
>> outside the Moon's orbit, the lunar farside equator starts to pass under
>> it, at which point an insertion burn will put it into a (retrograde)
>> equatorial orbit...
>
>I dont understand why this thing force a RETROGRADE orbit for Apollo. It
>the spacecraft is above the nearside at the encounter, the same
>argumentation leads to a DIRECT orbit. Did I miss something?

No, that should indeed work.  But I gather that closer study of the
numbers shows that it's somewhat easier to get into lunar orbit starting
with an encounter over the farside.
--
Being the last man on the Moon                  |     Henry Spencer
is a very dubious honor. -- Gene Cernan         | henry@zoo.toronto.edu

Newsgroups: sci.space.history
From: Henry Spencer <henry@zoo.toronto.edu>
Subject: Re: Why were the lunar orbits retrograde?
Date: Thu, 12 Mar 1998 14:34:57 GMT

In article <6e8lt3$2ub@nrtphc11.bnr.ca>,
Cathy James <cajames@fngdev8fngdev8:0.0> wrote:
>> Intuition is deceiving here:  the Moon's motion, not the spacecraft's,
>> dominates the encounter (in simplified rule-of-thumb work, anyway)...
>
>	The more I think about this, the more confused I am.
>Since the vehicle was launched at approximately Earth escape velocity,
>it will be moving at Earth escape velocity (at lunar distance, i.e.
>much less than the 7 miles/sec usually quoted for near-Earth escape)
>when it arrives at the Moon...

Actually, the Apollos typically were not quite launched to Earth escape
velocity.  To a crude first approximation, an economy trajectory to the
Moon is an elliptical orbit with its perigee as low as possible and its
apogee at roughly lunar distance.  The velocity of such an orbit at apogee
is about 175m/s, compared to the Moon's orbital velocity of about 1000m/s.

>...can be approximated as circular, meaning that it is
>moving at 1 / sqrt(2) of escape velocity, or about 71% Vesc.
>Thus the Moon is only moving at ~71% of the spacecraft's speed
>(along a different velocity vector) at encounter time.
>	What is wrong with this analysis?  ...

The difference between "Earth escape velocity" and "slightly less than
Earth escape velocity" is greatly magnified during the climb up out of the
gravity well.  The difference between the economy orbit mentioned above
and an escape trajectory starts out as a velocity difference of under 1%
(about 70m/s out of 11km/s) and ends up as an order of magnitude at lunar
distances (175m/s versus 1400m/s).
--
Being the last man on the Moon                  |     Henry Spencer
is a very dubious honor. -- Gene Cernan         | henry@zoo.toronto.edu

Newsgroups: sci.space.history
From: Henry Spencer <henry@zoo.toronto.edu>
Subject: Re: Why were the lunar orbits retrograde?
Date: Thu, 12 Mar 1998 23:30:36 GMT

I wrote:
>>I dont understand why this thing force a RETROGRADE orbit for Apollo...
>
>No, that should indeed work.  But I gather that closer study of the
>numbers shows that it's somewhat easier to get into lunar orbit starting
>with an encounter over the farside.

As others have noted, I forgot an important issue here:  only by aiming
for a farside encounter can you get a free-return trajectory.  What you
get from a nearside encounter with no engine burn is a gravity-assist
trajectory that throws you out into the solar system (which is, in fact,
what was done with the S-IVB stages of the first few lunar missions).
Not a good failure mode...

In fact, Apollo gradually moved away from free-return trajectories, as
confidence built up and landing targets moved away from the equator (an
orbit derived from a free-return trajectory has to be nearly equatorial),
but they were still an important abort option even when it was necessary
to make a substantial engine burn to reach one.
--
Being the last man on the Moon                  |     Henry Spencer
is a very dubious honor. -- Gene Cernan         | henry@zoo.toronto.edu

Newsgroups: sci.space.history
From: Henry Spencer <henry@zoo.toronto.edu>
Subject: Re: Why were the lunar orbits retrograde?
Date: Fri, 13 Mar 1998 04:28:01 GMT

In article <6e9pb4$u23$1@bartlet.df.lth.se>,
Magnus Olsson <mol@bartlet.df.lth.se> wrote:
>As long as you launch with less than escape velocity, you get radial
>velocity zero, and as small a tangential velocity as you like, at
>apogee...

Not quite.  The size of the tangential velocity is limited by the need for
perigee above the Earth's atmosphere -- efficient ways of getting into
such an orbit generally involve doing most of the thrusting more or less
horizontally while above the atmosphere, which automatically gives you a
perigee at that altitude.
--
Being the last man on the Moon                  |     Henry Spencer
is a very dubious honor. -- Gene Cernan         | henry@zoo.toronto.edu

From: Henry Spencer <henry@zoo.toronto.edu>
Newsgroups: sci.space.tech
Subject: Re: Lunar Polar Orbits
Date: Tue, 7 Apr 1998 02:41:01 GMT

In article <3528DB03.485F@lunacorp.com>,
David Gump  <dgump@lunacorp.com> wrote:
>Can anyone tell me if a satellite can theoretically be put into a polar
>lunar orbit that always passes over the zero longitude/zero latitude
>point on the Moon's near side?  In other words, could the orbit be
>locked in the same way that near side of the Moon always points toward
>Earth?

No, not so far as is known.  The trick that's done with Earth orbits to
hold them in a (more or less) constant relationship to the Earth-Sun line
doesn't work for lunar orbits; the Moon does not have enough of an
equatorial bulge.  It is marginally possible that a carefully-chosen and
quite low orbit could exploit lunar mascons to do the same trick, given a
complete and detailed understanding of the lunar gravitational field
(which we don't have yet), but I wouldn't bet money on it.

There are the Lagrange points, and halo orbits around them, but they are
a long way from the surface and aren't well placed for polar coverage.
--
Being the last man on the Moon                  |     Henry Spencer
is a very dubious honor. -- Gene Cernan         | henry@zoo.toronto.edu

Newsgroups: sci.space.history
From: henry@spsystems.net (Henry Spencer)
Subject: Re: Does any Apollo hardware still orbit Moon?
Date: Wed, 21 Jul 1999 19:51:59 GMT

In article <3795F728.52B4BC15@earthlink.net>,
Kirk Voelcker  <anaxagoras@earthlink.net> wrote:
>I think the mascons of the Moon make for any orbit an unstable one, save
>for the libration points of the Earth-Moon system.

Even they are of questionable stability, actually, given the effects of
solar perturbations, Earth's equatorial bulge, the eccentricity of the
Moon's orbit, etc.  (The theory of the libration points would apply
exactly only if the Moon's orbit was circular.  The assumption that a
small amount of eccentricity would cause only minor deviations from the
predictions of circular-orbit theory is tempting, but it's NOT TRUE for
tricky things like libration points.)  The three colinear points are
naturally unstable, and the Trojan points, although close to being stable,
aren't trustworthy in the long term.

That said, reasonably high lunar orbits probably *are* stable for fairly
long times.  The effects of the mascons fall off quickly with altitude.
There just hasn't been very much use of high lunar orbits so far.
--
The good old days                   |  Henry Spencer   henry@spsystems.net
weren't.                            |      (aka henry@zoo.toronto.edu)