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."
> > >
> > > 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?

1. Wikipedia: Double Planet

A double planet is an informal term used to describe two planets that orbit each other about a common center of mass that is not located within the interior of either planet.

The earth-moon system does not meet that definition - but it is closer to doing so than any other planet-satellite combination in the Solar System (unless Pluto, a dwarf planet, comes close to meeting it too - Charon is big, but I've not gone looking how big).

B: Mass of (USGA) golf ball shall not exceed 1.620 oz (45.93g or 4.6E-2 kg).
C: Mass of earth 5.9742E24 kg.

You are correct - "Give me a lever and I will move the world" (no, not a quote from me - Archimedes (287 BC-212 BC) said something close to that).

However, that wouldn't make the system a double planet - the barycentre would be very close to the centre of the earth. You calculate it - the ratio of the weights is 1:1.3E26 is so extreme that if you wanted the fulcrum say 1 micrometre from the centre of the earth, the golf ball would have to be about 100,000 light years distant (give or take a factor of 10), which is about the diameter of the Milky Way galaxy - isn't Google a wonderful institution. Received on Wed Jan 17 2007 - 22:08:14 CET