## South African Skeptics

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Question: Wich pool will catch the most meteorites?
 The equatorial pool The northern pool Equal amounts

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# Swimming pool and meteorite problem

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st0nes
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 « Reply #15 on: October 06, 2009, 09:27:40 AM »

I almost forgot another assumption: a spherical Earth.  As we all know on this forum, the Earth is NOT spherical; it is an oblate spheroid, fatter around the equator than the poles, and the Southern hemisphere is slightly heftier than the Northern. Sort of pear-shaped, actually.  Over millions of years, this shoulld have the effect of causing the equatorial pool to gather ever so slightly more meteorites.
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cyghost
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 « Reply #16 on: October 06, 2009, 10:16:06 AM »

There you go. You just *had* to bring maths into it didn't you?
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Peter Grant
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 « Reply #17 on: October 09, 2009, 20:28:33 PM »

OK, OK.  Let's assume a meteorite flux of 1 meteorite/m^2/day everywhere on the surface of the Earth (We've been told that the flux is equivalent, so meteor showers and so on are irrelevent).

Assume also that the dimensions of the swimming pool are 50m x 20m = 1000m^2
If the Earth were not rotating each pool would would be struck by 1000 meteorites per day.

Does the rotating Earth make a difference?

The area swept out by the equatorial pool during the course of the day is:-
Circumference of the Earth at the equator x 20m = 4,000,000m x 20m = 80,000,000m^2

The area swept out by the tropical pool during the course of the day is:-
Circumference of the Earth at the tropic x 20m = 3,668,200m x 20m = 73,364,805m^2

This would seem to indicate that the equatorial pool should be struck by more meteorites,

How? I don't see how you reach this conclusion.

BUT: The equatorial pool is moving faster and therefore spends proportionally less time in each â€˜sectorâ€™ of its larger area.

This I agree with.

This exactly cancels out the effect of the larger area, and each pool  will be struck by the same number of meteorites.

It's one or the other, I don't see how it can be both.
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st0nes
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 « Reply #18 on: October 15, 2009, 07:07:22 AM »

This would seem to indicate that the equatorial pool should be struck by more meteorites,

How? I don't see how you reach this conclusion.

Imagine Cameron Diaz.  She is naked save for two narrow (say, two inch wide) white belts, one about her hips and the other around her waist.  Sewn into the belts are railway tracks along which run two identical carts.  The carts move around the tracks at speeds that result in their completing their circumnavigations of Cameron in precisely the same amount of time.

Now imagine the seven dwarfs standing (evenly spaced) around Cameron, each armed with a tiny paintball gun. They open fire and continue their bombardment for the time taken for the carts to complete one orbit of Cameron, then they stop.

We now remove the belts from Cameron and lay them out.  The belt that was around her waist is an analogue of the strip swept out by the swimming pool on the tropic, the belt that was around her hips is an analogue of the strip swept out by the equatorial pool.  We would expect that--because it is longer--the hip belt will have more paintball splodges than the waist belt, but it will have the same number of splodges per unit area as the waist belt.

This exactly cancels out the effect of the larger area, and each pool  will be struck by the same number of meteorites.
It's one or the other, I don't see how it can be both.

Quite right.  So let's turn our attention to the carts.  Because they were moving for the same amount of time through an identical paintball bombardment, they will have been struck by the same number of paintballs.  Their speed is not relevant. They are the analogues of the swimming pools.
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Peter Grant
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 « Reply #19 on: October 15, 2009, 20:27:44 PM »

This would seem to indicate that the equatorial pool should be struck by more meteorites,

How? I don't see how you reach this conclusion.

Imagine Cameron Diaz.  She is naked save for two narrow (say, two inch wide) white belts, one about her hips and the other around her waist.  Sewn into the belts are railway tracks along which run two identical carts.  The carts move around the tracks at speeds that result in their completing their circumnavigations of Cameron in precisely the same amount of time.

Now imagine the seven dwarfs standing (evenly spaced) around Cameron, each armed with a tiny paintball gun. They open fire and continue their bombardment for the time taken for the carts to complete one orbit of Cameron, then they stop.

We now remove the belts from Cameron and lay them out.  The belt that was around her waist is an analogue of the strip swept out by the swimming pool on the tropic, the belt that was around her hips is an analogue of the strip swept out by the equatorial pool.  We would expect that--because it is longer--the hip belt will have more paintball splodges than the waist belt, but it will have the same number of splodges per unit area as the waist belt.

Enjoyed imagining that even more. However, if we are to assume the dwarves are firing an equal number of paint balls at her hip and waist belts and that they never miss, even when firing at her narrow little waist, then an equal number of paint balls will hit each belt and the splodges will be more spread out on the hip belt.

This exactly cancels out the effect of the larger area, and each pool  will be struck by the same number of meteorites.
It's one or the other, I don't see how it can be both.

Quite right.  So let's turn our attention to the carts.  Because they were moving for the same amount of time through an identical paintball bombardment, they will have been struck by the same number of paintballs.  Their speed is not relevant. They are the analogues of the swimming pools.

Would it be an equal bombardment? By the time a volley of seven paint balls reaches her waist their impact points will be closer together.
 « Last Edit: October 15, 2009, 21:17:23 PM by Peter Grant » Logged
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