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- From: roberts@cmr.ncsl.nist.gov (John Roberts)
- Subject: A solution to "NASA Coverup"? (long)
- Message-ID: <BxDoxB.5u0.1@cs.cmu.edu>
- X-Added: Forwarded by Space Digest
- Sender: news+@cs.cmu.edu
- 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
- Approved: bboard-news_gateway
- Lines: 150
-
-
- -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
-
-