From: roberts@cmr.ncsl.nist.gov (John Roberts)
Subject: A solution to "NASA Coverup"? (long)
X-Added: Forwarded by Space Digest
Organization: National Institute of Standards and Technology formerly National Bureau of Standards
Original-Sender: isu@VACATION.VENARI.CS.CMU.EDU
Distribution: sci
Date: Sun, 8 Nov 1992 03:40:51 GMT


-From: snarfy@cruzio.santa-cruz.ca.us
-Subject: NASA Coverup
-Keywords: More sources for 43,000 mile figure
-Date: 6 Nov 92 01:18:00 GMT

-     Generally the objections fall into seven categories:
-...7.   I ,snarfy , have an impolite, beligerent,  obnoxious  and  generally
-     bad attitude, and my error in transposing terms in the equation 180/6 =
-     30 indicates that I am also stupid  and  unqualified  to  address  this
-     newsgroup.

I think the attitude is part of it. Unfortunately, it's fashionable these
days to seek glory by claiming that some revered scientist is guilty of
fraud - often these claims have little or no foundation. When you accuse
the tens of thousands of people who worked on Apollo of fraud, it's natural
that many people will tend to put you in that category, whether that's 
accurate or not. It's not necessary to be belligerent about a discrepancy
in calculations. I occasionally come up with results in my calculations
that are different from the accepted values, and when that happens, I post
a question on it and try to get independent verification. Usually it turns
out that I made a mistake or left out some important factor, but once in a
while it appears that the results are confirmed - for instance, I have not
yet found any problems with my calculations showing that a 1AU Dyson sphere
would be too hot to live on, and that for a comfortable temperature, radius
must be increased to at least 1.75 AU. (I wish someone would check that -
I've found an error in the unrelated calculation of internal photon pressure
of a reflective sphere, which still needs to be fixed.)

The other problem is the degree to which a claim varies from the accepted
state of affairs, and the degree to which people would have to change their
world view to accommodate the claim. The greater the degree of change required,
the stiffer the standards for validation. You might post an argument that
aluminum alloy would have been a better choice than titanium for the legs of 
the lunar lander (or vice versa), and you might get some replies arguing to the 
contrary, but you wouldn't expect a heated exchange over it (except perhaps
for a few crazed metallurgists), and if it turned out that your opinion
was the result of reading an article in Popular Science rather than years
of research on metal alloys, nobody would be particularly angry about it.
On the other hand, when you make the spectacular claim that the moon's
surface gravity is nearly four times the accepted value, and extrapolate
that to claims of fraud, then people are going to be very insistent on
knowing your sources and your calculations. When it turns out that your
sources are more or less popular accounts (with nary a differential
equation among them), then they will justifiably "request" that you seek
out better sources. (I occasionally make spectacular claims based on
popular accounts, but I try to make it clear that the popular accounts
are the source, and that I'm ready to accept correction from those who
know more on the subject.)

-                  Ok, back to work:

OK, let's look at the source of your dilemma:

-   Let me here define "Neutral Point" :

-   The  neutral  point  is  that  point  in a lunar spacecraft's trajectory,
-   measured by the straight line distance from the moon's center  in  miles,
-   where the force of gravitational influence in the direction of the moon ,
-   measured  in  pounds of "pull" on the spacecraft,is equal to the force of
-   influence toward the direction of the earth, also measured in  pounds  of
-   "pull".

By the way, I think you'll be much happier in the long run if you do your
calculations in SI (metric) units. I often do simple calculations in standard
units, but the tough problems are much more easily handled using SI.

-   I believe that the direct quotation from the July 25,1969  Time  magazine
-   article would be helpful here:

-   "At  a  point 43,495 from the moon, lunar gravity exerted a force [on the
-   spacecraft] equal to the gravity of the Earth , then some  200,000  miles
-   distant."

-   In "Project Apollo: Man to the Moon" by Thomas J. Alexander  (Harper  and
-   Row , 1964 ) ,the author states:

-   "At  a  point  some  40,000 miles from the Moon ,when the craft is poking
-   along at about 2000 mph, it crosses THE LINE  where  the  moon's  gravity
-   exceeds  that  of  the  earth . That's the second part of the trjectory."
-   (caps mine).

It appears that you're assuming that the spacecraft spends its journey
moving along a straight line between the center of the Earth and the center
of the moon. Orbital maneuvers are a very complex field of study, and I 
don't know most of the details (I can only do the very simple calculations),
but it seems to me that that's a very unlikely course for the spacecraft
to take. After firing to escape low earth orbit, the spacecraft is moving
in nearly a parabolic or hyperbolic (probably parabolic, but I'm not sure -
it depends on velocity) trajectory, which gradually changes to a (probably)
hyperbolic trajectory about the moon, as the moon's gravitation becomes
predominant. Remember that the moon is orbiting about the Earth at a 
velocity of around 1023 meters per second (avg) - if it takes the spacecraft 
several days to get from Earth orbit to the moon, the moon will have traveled
a tremendous distance "sideways" during that time. So it makes sense to
"lead" your shot - aim the spacecraft toward where the moon will be when
the spacecraft gets to the moon's orbit. (Actually, since the objective is 
not a lunar impact but a lunar orbit, you want the spacecraft to be where
the moon's gravity will whip it around the moon, thus minimizing the amount
of fuel you have to burn to get into lunar orbit. The calculations for that
are extremely complex, but I think this is a pretty fair simplification for
the layman.)

The net result is that as the spacecraft approaches the moon, it does so
at a very large angle with respect to the line between the Earth and the 
moon, so you can't just subtract the spacecraft-moon distance from the
earth-moon distance and use that as the spacecraft-Earth distance. Note
that your sources don't say that the two forces *cancel* (which they would
do if the spacecraft were exactly on the line between the Earth and the
moon), just that the two forces are *equal*. I think this is the main
source of your discrepancy. (If this analysis is correct, I think you
owe those poor Apollo scientists an apology.)

(There are many points in space where the gravitational influence of
the Earth and the moon are *equal*, but they don't form a line or a
plane - I believe it's a complex curve surrounding the moon.

Another pitfall that is especially important to recognize in weighing
the influence of phenomena that tend to cancel one another out is the
sensitivity of the results to errors in the initial assumptions. For
instance, suppose you're using a value of 238000 miles for the distance
from the center of the Earth to the center of the moon. Suppose the actual
distance on that day was 236000 miles or 240000 (the distance varies from
about 225700 miles to 252000 miles) - what effect would that have on the
results of your calculations? For calculations where you just multiply this
in as a factor, the effect would be fairly insignificant - less than a percent.
when you square the value to work out the inverse square, the effect is
greater - nearly two percent. When you subtract one inverse square from
another inverse square, the error can be tremendously magnified. Remember
in your earlier post when the neutral point was said to have been stated
as 22100-25200 miles from the moon? Perhaps that doesn't mean they couldn't
make a more accurate guess - perhaps that means the value actually changes
over that range as the moon moves between perigee and apogee.

So it would appear that neutral point calculations are fairly sensitive to
errors in Earth-moon distance. Other factors may be similarly sensitive.
You can write a computer program to check the sensitivity of your initial
assumptions - vary each one up and down slightly, and record the effect that
each variation has on the outcome. (That's a little bit simplistic - in some
cases you may have to try variations in *combinations* of factors, but at
least it's a start.)

I worked out some calculations of my own, that seem to be fairly consistent
with the stated neutral point range, but which are quite different for the
posted distance of the Lagrangian point. This post is already long enough,
so I'll try to put them in a followup post.

John Roberts
roberts@cmr.ncsl.nist.gov

Newsgroups: sci.space