Re: Ideas for World Hierarchy Example

> > > ... the common center of mass of the system (the barycenter)
> > > is located beneath the surface of the Earth."
> >
> > I guess I am about to be learn something new here, but how does
> > something that is 1/81 the mass of earth, pull the combined center near
> > 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.

Interesting, this seems to imply that a golf ball orbiting Earth at a great enough distance could be balanced by a fulcrum point at or above the Earth's surface. If so, would this Earth/Golf Ball system be considered more of a double planet than the Earth/Moon? Received on Wed Jan 17 2007 - 06:35:38 CET