> Only 30?  Looks something more like 10,000 to me.

10000?? A mountain, only 1.3 km high, scaled by this factor, would then
be higher than the earth's equatorial diameter!

> They say the earth, if
> shrunken down, would be more smooth than any common man-made sphere.

This shrunken earth would then be a very tiny sphere:
   Diameter of earth = 12756 km
   Height of Mt. Everest = 8.850 km
   Depth of Marianas trench = 10.924 km

Thickness of the traces of a standard printed circuit board = 0.035 mm
These traces are man-made and are *easily* felt with the fingertips.
Shrinking the earth by approx. 1/253000000 gives
   Diameter of earth = 5 cm (2")
   Height of Mt. Everest = 0.035 mm
   Depth of Marianas trench = 0.043 mm

Shrinking the earth by approx. 1/312000000 gives
   Diameter of earth = 4.1 cm
   Height of Mt. Everest = 0.028 mm
   Depth of Marianas trench = 0.035 mm

Although neither Mt. Everest nor Marianas trench have vertical walls,
even a 5-cm-earth would have a feelable Mt. Everest and Mariana trench.
But 35 micrometers are far from the smoothest man-made sphere; the
most accurate sphere probably is this:
http://www.tip.csiro.au/IMP/Optical/spheres.htm

Enlarging this to earth-size, we get
   Diameter =    9.4 cm -> 12756 km
   Total error =  50 nm -> 6.79 m (not km!)
   Roughness   = 0.2 nm -> 37.6 cm

Or the other way:
   Diameter of earth = 0.032 mm (!)
   Height of Mt. Everest + Depth of Marianas trench = 50 nm

So "more smooth than any man-made sphere" is wrong by two to three
orders of magnitude (depending on the diameter, of course).

   Sputnik

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