How Long is

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How Long is Long Enough?
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Give me a lever long enough, and a fulcrum on
which to place it and I shall move the
world! Archimedes, ca. 300 BCE
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A lever is a simple machine that multiplies Force.
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Selection of Fulcrum
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Experimental Design
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Mass of Archimedes
79.5 kg
MMGP
MAGP
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Experimental Design
79.5 kg
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How High the Moon?
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How High the Moon?
t 2.55 sec
v 3 x 108 m/s
2d 7.65 x 108 m
d 3.83 x 108 m
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Distance between Centers of Mass
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Radius of the Earth
Re 6371 km
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Radius of the Moon
tan (1/4o) Rm / d
Rm d tan (1/4o)
d 3.83 x 108 m
Rm 1.67 x 106 m
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Distance from Earth to Fulcrum
X2
6371 km
383 x 103 km
1670 km
X2 391 x 103 km
X2 4 x 108 m
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Experimental Design
79.5 kg
4 x 108 m
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Mass of the Earth
mv2 / r GMm / r2
M r v2 / G
M 6 x 1024 kg
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Experimental Design
79.5 kg
6 x 1024 kg
?
4 x 108 m
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MAGP X1 gt ME X2
X1 / X2 gt ME / MAGP
c 3 x 108 m/s
1 Yr p x 107 sec
1 LY 3p x 1015 m
X1 gt X2 ME / MAGP
Xt X1 X2
Xt 3 x 1031 m
Xt p x 1015 LY
79.5 kg
6 x 1024 kg
?
4 x 108 m
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Age of Universe 13.7 Billion yr
Diameter of Universe 2.7 x 1010 LY
Xt p x 1015 LY
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Xt 105 times the Diameter of Universe!
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Wall painting in the Stanzio delle Matematiche at
the Galleria degli Uffizi (Florence, Italy) by
Giulio Parigi (1571-1635)
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Eureka!