Tuesday 11 December 2018

An alternative explanation for why Planet Earth bulges at the Equator

Easy explanation - the world is spinning round, so the equator gets thrown outwards slightly, like people spinning balls of pizza dough into flat pizza bases.

Or maybe not.

Here's my gloriously long winded explanation...

As top telly scientist Prof. Jim Al-Khalili, explained in his programme "Gravity and me":

Rule 1. There's not really such a thing as gravity. Time runs more slowly near large masses and smaller masses want to move to where time moves more slowly.

Rule 2. Time moves more slowly for fast moving objects.

So with GPS satellites, they have to make a net adjustment between two opposite effects - the clocks on the satellites seem to be running a bit faster (than clocks on earth) because they are further away from the mass of the planet; but the satellites are moving quickly, which means clocks on satellites seem to be running a bit slower (than clocks on earth). The two effects don't quite cancel out.

The prof realised (after some false starts to which he cheerfully 'fesses up) that the same applies if you compare a clock at the North Pole (nearer centre of earth but not rotating) with a clock at the equator (further away from centre of earth but moving at 1,000 mph). And - unlike for satellites - these two effects exactly cancel out!

This is hardly surprising, really.

If we consider the earth to be a large blob of slow moving liquid (and ignore the thin layer of rocks floating on top), it must be clear that if a drop anywhere on the surface of the blob can move to somewhere where time is passing more slowly, it will do so. (This is no different to considering a liquid that has been poured onto a flat surface). So we can safely assume that four billion years later, the clocks for all drops on the surface of the liquid part of earth are moving at the same speed.

That is ultimately why the earth bulges at the equator - if you started with a perfect sphere, a clock at the equator would run more slowly than a clock at the North Pole (same distance from the centre of the earth and moving quickly).

So liquid on the surface flows from the Poles towards the equator until the equilibrium is reached, where the extra radius means a clock on the surface at the equator is a little bit further from the centre of the earth, which speeds up the clock a bit. The clock at the North Pole is a little bit nearer the centre, so slows down a bit, and both clocks (in fact all clocks anywhere on the surface) are running at same speed.

All part of the service!

13 comments:

Sackerson said...

Alternatively, too many mince pies.

Mark Wadsworth said...

S, pies or pizzas, same thing.

Sackerson said...

Plausible; maybe the Northern Lights are a pizza-electric effect?

Mark Wadsworth said...

+1

Bayard said...

"smaller masses want to move to where time moves more slowly."

Is there an explanation for why this is, involving, say, the second law of thermodynamics (which, AFAICS explains most things)?

Mark Wadsworth said...

B, maybe so. I use the analogy of slow moving pools at the side of a river, floating objects in the main stream are likely to end in the side pools.

Mark Wadsworth said...

... or imagine a car with independent brakes on left and right hand wheels. If you apply brakes on right, the right hand side moves slower and the car turns right.

jim said...

Very interesting. You might like to look at https://physics.stackexchange.com/questions/126919/does-time-move-slower-at-the-equator

This goes into very much the same logic as Mr Wadsworth and has some interesting links to follow.

Mark Wadsworth said...

Jim, thanks, that's reassuring.

Dinero said...

The evidence available from the GPS makes the special relativity theory redundant. This is because a signal from a satellite to the east arrives at a GPS receiver earlier than a signal arrives at a GPS receiver from a satellite to the west. Two papers have been published on this.

A. G. Kelly. A new theory on the behaviour of light.

and another.

C. C. Su. A local-ether model of propagation of electromagnetic wave.

Mark Wadsworth said...

Din, thanks, I'll have a look

Sackerson said...

A complete amateur writes: the two clocks are not moving with respect to each other, so I wouldn't expect any difference in their relative experience of time; but has anyone established that we weigh the same, or differently, at N Pole vs Equator? Compared with someone at N Pole, Earth at Equator may have more material from surface to centre, but centre of gravity further away - does that explain it?

Mark Wadsworth said...

S, a quick Google search tells us you weigh more at the North Pole. You are closer to centre of earth and the spinning effect at the Equator makes you a bit lighter still at the Equator.