Re: Ideas for World Hierarchy Example

Neo wrote:

>> ... the common center of mass of the system (the barycenter)
>> is located beneath the surface of the Earth."

Think good old mechanics of levers and weights. If we assume the earth has a mass of 81, the moon has a mass of 1, and the combination of the two has a mass of 82. Now imagine that the two masses are point masses connected by a rigid rod (of zero mass). The point at which you could place a fulcrum and have the ensemble balance is 1/82 of the distance between the earth and moon starting from the centre of the earth. Taking moments about this point, we have a mass of 1 at distance 81/82 balancing a mass of 81 at distance 1/82.

All that's left to do is to determine the radius of the earth R, the (average) distance from the centre of the moon to the centre of the earth D, and decide whether D/82 is close to R. Google to the rescue: per www.factbook.com, the earth's diameter is 12756.3 km, so the radius is 6378.15 km; per Wikipedia, the average distance from earth to moon is 384399 km (though another site said 384403 km). So, the barycentre is at about 4687.8 km from the centre of the earth, which is about 1700 km below the surface.

-- 
Jonathan Leffler                   #include <disclaimer.h>
Email: jleffler_at_earthlink.net, jleffler_at_us.ibm.com
Guardian of DBD::Informix v2005.02 -- http://dbi.perl.org/