🚀 go-pugleaf

Note followup ... Since this involves claiming everyone is lying, the
discussion should take place off in a group dedicated to that purpose.
Alt.sci.physics.new-theories seems to fit the bill.

In article <4578@cruzio.santa-cruz.ca.us>, snarfy@cruzio.santa-cruz.ca.us writes:
> [...]
>      This calculation is apparently based on the observed distance  of  2903
>    miles  of  the  earth's  distance  from the earth-moon barycenter as that
> [...]
>    the  gravitational forces of the earth-moon system balance,was given over
>    and over again as being between 22,100 and 25,200 miles from the  surface
>    of the moon in the direction of the earth.
> [...]
>    The figure of 43,495 miles from the moon's center  for the neutral point

You seem to have some confusion of what "Neutral Point" means. The Barycenter
(center of mass between earth and moon) is directly observable by the motion
of the earth. It lies about 4700 km from the earth's center, or about 2000km
under your feet. The Lagrange L2 point (between earth and moon, where
gravitational acceleration between earth and moon balance) is 43,000 km from
the center of the moon.

These numbers agree with the first two quotes. The third quote is clearly
a typo where someone meant to say "kilometers" and said miles. Given that
this was from Time Magazine, it's clear where the fuckup was.

As for the derivation of these numbers; the barycenter is directly observable
due to the earth's motion. If you feel that the measurement was incorrect,
please submit new observations that show a different value. From that one
value (4728 km from center of the earth), we'll derive all the rest of the
numbers. If you want specific explanations, send me email or followup in
alt.sci.physics.new-theories (I do read that group).

Mass of earth:               5.96e24 kg ~ (9.78 * 6.378e6^2 / 6.67e-11)
Earth-moon distance:         384,400 km (average)
Barycenter distance:         4728 km
Mass ratio Earth/moon:       81.295 (3.84e5/4.7e3)
L2 distance from moon cent.: 42589km (3.84e5/sqrt(81.295))

Mass of moon:                7.35e22 kg (5.96e24/81.295)
Radius of moon:              1.738e3 km (31 arc min at 384,400 km)
Gravity on moon:             1.62 m/s^2 (6.67e-11 * 7.35e22 / 1.738e6^2)

1.62 m/s^2 comes awful damn close to 1/6th of 9.78 m/s^2.

I notice I didn't derive the earth-moon distance. Let's do that now:
Formula for converting orbital period to distance is:

   a = (G * (M1 + M2) * T^2 / 4 pi^2) ** 1/3

siderial period of moon(T):  2360534 s (27.031 days)
M1 is Mass of Earth, and we'll ignore the moon's mass)

   a^3 = 6.67e-11 * 5.96e24 * 5.572e12 / 39.47
   a = 5.61e25 ^ 1/3 = 3.82e8 m. 

Error in third decimal induced by ignoring moon's mass, which we hadn't
derived yet.

-- 
         Tarl Neustaedter	tarl@sw.stratus.com
         Marlboro, Mass.	Stratus Computer
Disclaimer: My employer is not responsible for my opinions.