At 04:55 PM 12/14/2012, Harvey Norris wrote:
When I was a kid in the Cleveland area, we
rushed home from school (in the early 60's) to
see Captain Penny and his bullwinkle show and assorted cartoons.
http://en.wikipedia.org/wiki/Captain_Penny
Captain Penny would say at the end of every
show, "You can fool some of the people all of
the time, all of the people some of the time,
but you canât fool Mom. (Actually a quote from
Little Rascals expunged from a President Lincoln saying???
Remembering this and checking the site out, I
have to agree us sheeple gets hoodwinked
everytime, and this is why no planes hit the
World Trade Center. It is positively amazing as
to what big brother can do in the terms of
manipulation of beliefs, and the underlying
scientific scandal that comes with the package.
After extra review of this problem and the following info;
Actually what this post shows is, indeed, you can
fool some of the people some of the time. Some
people are just waiting to be fooled. All it
takes is a predeliction to believe something that
seems to confirm their suspicions.
A closely related concept are the Lagrangian or
L points. Joseph-Louis Lagrange was a
mathematician who lived between Jan. 1736 and
April 1813. During this time a considerable
amount of work was done on the orbits of the
Moon and planets. One of the key concepts was
the mathematical description of the motion of a
three body problem, i.e., the Earth, the Moon
and the Sun. His work showed that there are
places 60° in front of and behind a planet in
its orbit where the gravitational forces between
the Sun and the planet cancel each other out.
That is an inaccurate description of a Lagrange
point. The points are not where the gravitational
forces "cancel each other out." While a single
such point exists (obviously along a line between
the centers of mass of the two objects), it is
not one of the Langrangian points. L1 is the
point that is along the central axis. It is a
point such that the orbital velocity of the obect
around the earth has been lengthened by the
reduction in net force toward the earth, such
that the orbital period is that of the moon. So
the object stays in the same relationship to the
earth and moon, if it were at this exact point.
However, that point has negative stability. L4
and L5 have positive stability, that's why they
are proposed as sites for space colonies. Minimal
station-keeping would be necessary.
These became known as the Lagrangian or L
points. While Lagrange did not believe these
points had any special significance in the
Solar System, astronomers have since discovered
several asteroids in the Lagrangian points for
the Earth and Jupiter. The ones for Jupiter are
called the Trojan asteroids. Achilles was the first one discovered in 1908.
The Lagrangian points also exist in the
Earth-Moon system as well. They move about a
central point as the Earth and Moon orbit one
another and rotate on their axes. The Lagrangian
points may become important in the future as
they are excellent places to build communication
satellites and potentially even space colonies.
Several of the L5 Societies and related
organizations can be accessed through the National Space Society.
I was the Administrator of the L-5 Society in
something like 1979 or so, I forget exactly when.
Knowing that the ratio of the masses of the
Earth and Moon is approximately 81:1 and the
gravitational forces vary inversely with the
square of the distance, the approximate neutral point can be calculated.
The spacecraft, in general, followed an orbit
that was not through a "neutral point." What is
needed to understand the issue is a stody of
orbital motion. If one looks at the net
gravitational vector operating on a space
vehicle, that vector will cause acceleration in
its direction. As the object separates from the
earth and begins to approach the moon, there will
be a point where the decline in velocity,
produced when the vehicle is near the earth,
turns around and the velocity begins to increase,
as the vector begins to point more toward the
moon. That is a kind of turnaround point, and the
comments refer to it. If the Apollo spacecraft
had any kind of velocity read-out (I'd doubt it,
this is a very complex problem), they would see
the decline in velocity slow to zero and then
start to increase (in absolute value) from there,
until they actually enter moon orbit and their
velocity becomes relatively constant.
Descriptions of the spacecraft velocity would
come from measurements of, probably,
earth-reference effect, such as doppler shift of radio signals.
So the gravity on the moon is approximately .64
that of earths gravity or almost two thirds. Now
we understand why the Apollo astronauts were
making those pitiful 6 inch hops on the moon.
Very unlikely. See, by the way,
http://en.wikipedia.org/wiki/Apollo_hoax -- but
this does not deal with the gravity issue. Look at the Moon article.
http://en.wikipedia.org/wiki/Moon
It gives the equatorial gravity as about one-sixth g, i.e., 0.165 g.
That the gravity on the Moon is one sixth that
of earths is one of the biggest con jobs in the history of mankind.
It sure would be. However, this idea depends on
using a very complex calculation and presuming
that this gives us information about the surface
gravity. Various figures appear to have been
cited in media about the "neutral point." Using
one of them might lead to some conclusion as
described, but I'm not going there. Basically,
people make off-hand comments or make mistakes,
which proves absolutely nothing. Even serious
experts can make mistakes, or what they say can be misinterpreted.
The calculation of surface gravity depends on the
mass of the object and the radius of the object (neglecting tidal effects).
The question was actually asked at
http://curious.astro.cornell.edu/question.php?number=207.
The answer there depends on the easy way:
measuring surface gravity directly, which one
would need to be on the moon -- or have
instruments there -- to do. However, there is
another approach. The mass of the moon was known
before Apollo, and the basic method of measuring
it, I expect, was to observe the orbit of the
moon. The moon does not orbit around the earth,
but around the center of mass of the system. We
know the mass of the earth, from the gravity at a
known distance from the center. The center of
mass, therefore, will reveal the relative masses of the earth and moon.
So if you actually want to know the mass of the
moon -- and from that the surface gravity --, and
without depending on NASA, you need to look at
old astronomy texts, pre-Apollo. Consider this:
to predict the orbits of spacecraft in earth
orbit, it's necessary to know the mass of the
moon. Even more it is necessary to approach the
moon and know how to plan spacecraft maneuvers.
Of course, the conspiracy theorists can simply
believe the *whole thing* was bogus. And that conspiracy must be *very* wide.
http://curious.astro.cornell.edu/question.php?number=452
The mass of a large object in space is primarily
measured by the orbits it causes in smaller
objects. The method mentioned above would require
more careful and more accuate observation over a
substantial period. But the motion of the moon
was very well studied, centuries ago.
Here is a detailed study. http://adsabs.harvard.edu/full/2002Obs...122...61H
If someone doubts what is in it (Harvard must be
in on the conspiracy! They are rewriting
history!) check the old sources, if NASA has not
already found and removed them all from libraries or replaced them with fakes!
Newcomb, improving on prior efforts, in 1895,
found the ratio of mass to be 81.48 +/- 0.2, very close to the present value.
Give it up, Harvey.
