[dedaNoe (OP)]

dedanoe to NASA/ESA: GRAVITY vs. THE LEVERLAW
(in attepmt to move the world with a single coin)

you know newton's gravity law right: F = GM[1]M[2]/R^2 now consider the system earth-moon. if you take any test weight and slide it along the line that connects the centers of earth and moon you'll come to a point where the pull of the two over the test weight cancel. that's the barycenter point i.e. point of equlibrium. condition for balance in the system will be F[1] = -F[2] which expands into GM[1]M[3]/R[1]^2 = -GM[2]M[3]/R[2]^2 <=> M[1]/M[2] = R[1]^2/R[2]^2. thereby, newton's condition for balance reads: MAGNITUDES ARE IN BALANCE ON SQUARE DISTANCES FROM THE CENTER PROPORTIONAL WITH THEIR MASSES.

now consider the system earth-moon as a lever with the rigid bar and the fulcrum absent. the leverlaw mentions NO RIGID BAR, NO FULCRUM & HAS NO EXCEPTIONAL CASE. then newton's barycenter would be analogy for equlibrium point in a lever i.e. the center of the lever while barycenter-to-earth will be the distance of earth (R[1]) and barycenter-to-moon will be the distance of moon (R[2]). thier forces come tangentially to their trajectories and the condition for balance is simply: F[1]/F[2] = M[1]/M[2] = R[2]/R[1]. it reads: MAGNITUDES ARE IN BALANCE ON DISTANCES RECIPROCAL TO THEIR WEIGHTS. just compare the leverian condition (M[1]/M[2] = R[2]/R[1]) with newton's condition (M[1]/M[2] = R[1]^2/R[2]^2) - obviously this two cannot be both right at the same time.

judging only by the contents of the leverlaw - MAGNITUDES ARE IN EQUILIBRIUM ON DISTANCES RECIPROCAL TO THEIR WEIGHTS - what exactly will be archimedes' definition for lever & to what exactly do we apply the leverlaw then? in my oppinion LEVER IS SYSTEM OF WEIGHTS (as bodies not as magnitudes) WHERE EVERY WEIGHT IS GLOBAL REPRESENTOR OF ITS OWN LEVER. i have a nukebook dealing with this matters. to read it, go to http://dedanoe.googlepages.com/knigata.pdf [nofollow] it is in armageddonian. you can ask for translation at www.pmf.ukim.edu.mk [nofollow]

that's all for now! dedanoe over & out...

[lyner]

We've been into this before. A lever is a rigid body - old fashioned  mechanics.
The Earth - Moon system is not rigid . You are talking about two separate things gravitational potential and the principle of moments. Why would you expect them to behave the same way?
Can you ask a sensible question next time please?