A Weighty Issue

(last worked on: June 10th, 2017)
(You're at: http://craigeroochi.neocities.org/weight.htm)

What happens when one weighs a given mass at the North Pole?

My take on this question: it weighs a bit more at the pole (using a spring scale) --only because it weighs a bit less when it's closer to the equator --on account of centrifugal force^.

* Unfortunately (perhaps on account of a classic SciFi story or two), no less than the Encyclopedia Britannica (2008), Microsoft's Encarta (2005), plenty of other sources and individuals --even a recent reference I've seen from Cornell --have it that an object weighs a bit more at the north or south poles because it's then a bit closer to the center of the Earth. This confusion is understandable, since objects weigh less as they're rocketed away from Planet Earth, and that's calculated on the basis of the distance from the Earth's center (of gravity).

* But gain-saying such a notion is the familiar and intuitive understanding of what happens when one mis-steps into an imaginary hole (airless, for the sake of this discussion) which passes through the Earth --and let's say it runs from the North Pole to the South Pole. You initially accelerate at the rate of one "G" (which means your downward velocity increases by 32 feet per second --each second), but that diminishes to zero acceleration/gravity when you reach Earth's center (and maximum speed). There after the growing force of gravity decelerates you --until you just reach the south pole. The whole hole to hole trip takes just under 45 minutes --about the same as an astronaut in a very low Earth orbit. (Shades of that old Firesign Theater "Rebus Kniebus" episode   :-)

More on that at this link: http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/earthole.html

So: what happens if we squash the Earth down --perhaps until it resembles an old fashioned phonograph record --and then try to explore gravity near and in the hole?

**This issue is really starting to get under my skin and it seems an appeal to authority is in order. Can someone "out there" please send me a potent opinion?

^ Hmmnnn: I'm not so sure of the centrifugal force difference either. I've read accounts of geodetic expeditions around the Earth from my copy of the 1911 edition of the Encyclopedia Britannica. Deducing the shape of the Earth was cutting edge back then and the math presented in that article is overwhelming. This is the research and analysis of scientists who personally checked out this weight difference business. No doubt there's some sort of a "gravity chip" nowadays, but I relish the pendulums, measuring chains and theodolites of those old timers.

What bothers me about the centrifugal force explanation: since the Earth's oceans and other matter can and do redistribute (which must be why the Earth is an "oblate spheroid") --I'd expect there'd be an "equal but opposite" response to the Earth's spin --such that gravity (aside from local variations due to irregularities like mineral deposits and mountains) would end up fairly the same everywhere. There's more matter in the nadir direction under your feet at our somewhat bulging equator: just enough to counter-act centrifugal force --right?

--Craig  < craig er oochi  a t  outlook dotty com >