South Africa Flag logo

South African Skeptics

September 16, 2019, 18:01:09 PM
Welcome, Guest. Please login or register.
Did you miss your activation email?

Login with username, password and session length
Go to mobile page.
News: Follow saskeptics on twitter.
   
   Skeptic Forum Board Index   Help Forum Rules Search GoogleTagged Login Register Chat Blogroll  
Poll
Question: Wich pool will catch the most meteorites?
The equatorial pool
The northern pool
Equal amounts

Pages: [1] 2  All   Go Down
  Print  
Author Topic:

Swimming pool and meteorite problem

 (Read 2816 times)
0 Members and 1 Guest are viewing this topic.
Rigil Kent
Clotting Factor
Hero Member
*****

Skeptical ability: +19/-3
Offline Offline

Posts: 2460


Three men make a tiger.


« on: September 30, 2009, 21:54:48 PM »

As you kow, there is only one way to do logic problems, and that is democratically.

Suppose there is an Olympic sized swimming pool situated directly on the earth's equator, running east to west in its length. Also, there is a second swimming pool of identical size, shape and orientation, but located on the Tropic of Cancer. If the probability of falling space debris is exactly equal around the globe, which one of the two swimming pools would you expect is more likely to catch more meteorites over a few million years?

Mintaka
Logged
cyghost
Skeptically yours
Hero Member
*****

Skeptical ability: +12/-1
Offline Offline

Posts: 1409


Carpe diem


« Reply #1 on: September 30, 2009, 22:02:53 PM »

I went with equal but feel there may be a catch  Cheesy
Logged
rwenzori
Sniper
Sr. Member
****

Skeptical ability: +7/-1
Offline Offline

Posts: 403


Merda accidit.


« Reply #2 on: October 01, 2009, 05:55:24 AM »

Oooh!  I do feel a bit out of my depth - I must be in the deep end. Here goes anyway.

1. Do pools catch meteorites? I don't know. Maybe fill it with rwenzori's patent meteorite-catching mieliepap&kevlar compound.

2. I'm not sure about your assumption about probability - it's not quite enough, as one needs to know direction. If true, then I suppose pools are equal. But...

3. Most matter in the solar system is in the plane of the planets or so, roughly, is it not? So most meteorites are coming in that plane at earth, roughly? If so...

4. The Tropic of Cancer pool represents a greater proportion of the latitude and thus is likely to trap more. But...

5. Because the meteorites coming at the Northern pool are coming in at an angle, they must pass through more atmosphere and are more likely to burn up before reaching the pool, therefore less being trapped.

So I don't know. I do have the funny feeling that by this logic there must be a shitload of meteorites at the Poles.  Huh? Huh?


Logged
Rigil Kent
Clotting Factor
Hero Member
*****

Skeptical ability: +19/-3
Offline Offline

Posts: 2460


Three men make a tiger.


« Reply #3 on: October 01, 2009, 10:13:57 AM »

Quote
5. Because the meteorites coming at the Northern pool are coming in at an angle, they must pass through more atmosphere and are more likely to burn up before reaching the pool, therefore less being trapped. (My bold)

But does it? Isn't the atmosphere, in turn, thicker at the equator?

I was thinking that, with each rotation of the globe, the equatorial pool must sweep through a larger area compared to the northern pool. Maybe it covers more square meters per hour. That would be akin to asking if you get wetter by walking or running in the rain.

Mintaka
« Last Edit: October 01, 2009, 10:36:17 AM by Mintaka » Logged
BoogieMonster
NP complete
Hero Member
*****

Skeptical ability: +19/-1
Offline Offline

Posts: 3086



« Reply #4 on: October 01, 2009, 14:14:07 PM »

Well, I'd venture to say that the majority of meteorites that enter our atmosphere do so during meteorite showers. And those occur when the earth moves through clouds of debris that lie, or have come into, it's path... Hence i'd say that the most meteorites would come at earth from a specific direction... ie, the direction that the earth is traveling along it's orbit.

Secondly, I'm reminded that the earth is tilted. Because of that, the two pools will deviate "up" and "down" as the earth rotates, with regards to the imaginary path the earth is taking. But, because of the shape of the earth, the "higher" or "lower" a pool is, the less surface area it presents to the debris sitting out there in the earth's path. With the optimum spot for presenting the most surface area being dead center (thus, when it's turned such that the pool is facing the incoming debris head on, ie, the pool is on the same plane as the earth's imaginary orbital line.). This is where it gets tricky. Sometimes the tropic of cancer pool gets rotated such that it is closer to this optimal spot than the equatorial pool. And sometimes it's the other way around. You'd have to figure out what the ratio is... Note that this position also depends on the earth's position in it's orbit, because the orientation of the earth's tilt with regards to the incoming debris changes hear round... Intuitively 1/2 the year one pool will get more exposure, and 1/2 the other. Thus I have a feeling that it cancels out....

Note that this also holds for the amount of atmosphere that debris must travel through. Sometimes one pool has the upper hand, sometimes the other....

Nope, I'm lost. If there's a difference it'll take quite a bit of math to arrive at the answer. There's lots of motion going on here...

If anything, I'm going with, too close to call, probably the same.

Logged
Tweefo
Hero Member
*****

Skeptical ability: +10/-0
Offline Offline

Posts: 1534



WWW
« Reply #5 on: October 01, 2009, 17:14:03 PM »

Most meteorites found on earth was picked up in Antarctica. It is easier to spot them against the white snow and ice but that also covers a lot. So I think the futher north or south you go the better you chance.
Logged
Jane of the Jungle
Full Member
***

Skeptical ability: +4/-0
Offline Offline

Posts: 235



« Reply #6 on: October 01, 2009, 17:22:10 PM »

Mintaka, it seems like you're going to raise more questions than answers on this Topic Wink
(from my side in anyway) Grin

Whilst pondering about this one, I drove right passed a offramp today Grin

Ok, so here I'm going:

Quote
According to geology.com:

"Each day Earth is believed to gain over 1000 tons of mass from the infall of tiny meteorites. Most of these meteorites are the size of a dust particle or sand grain. Rarely a meteoroid large enough to be witnessed falls all the way to Earth. Several hundred meteorites larger than marbles are thought to reach Earth's surface each year."

I would say the two pools would fill up at the same rate, even though earth is tillted, debris don't enter Earths atmosphere only at a certain point. If debris were to fall more on certain areas than others, wouldn't earth be oval shaped after 4.5 billion years of debris? 4.5 billion x 365 x 1000 tons Shocked

Quote
According to josleys.com
We know also that it is not a perfect sphere: the diameter from pole to pole is shorter than the diameter at the equator. The difference is small: the equatorial diameter is about 12,700 kilometers, and the pole to pole diameter is only about 40 km shorter.

After 4.5 million years, a 40km difference OK OK maybe someone are prepared to do some calculations for us? Roll Eyes
But what if ......earth were shaped like this 4.5 bil years ago, only with a smaller diameter, and debris
caused it to grow to 12, 700 kms?Roll Eyes Which would mean your pool levels would uuuuhhhhmmm darn Huh?


 Grin
Logged
Rigil Kent
Clotting Factor
Hero Member
*****

Skeptical ability: +19/-3
Offline Offline

Posts: 2460


Three men make a tiger.


« Reply #7 on: October 01, 2009, 17:57:13 PM »

This is where it gets tricky. Sometimes the tropic of cancer pool gets rotated such that it is closer to this optimal spot than the equatorial pool. And sometimes it's the other way around. You'd have to figure out what the ratio is... Note that this position also depends on the earth's position in it's orbit, because the orientation of the earth's tilt with regards to the incoming debris changes hear round... Intuitively 1/2 the year one pool will get more exposure, and 1/2 the other. Thus I have a feeling that it cancels out....

Each year the ecliptic (the plane in which the earth orbits the sun) will intersect the equator twice, while each tropic will be brushed by the ecliptic only once. So going with your argument, the equator should spend more time at the "optimal" position, i.e. right in the midde at the front of spaceship earth as it hurtles into space debris. Interesting idea.


But what if ......earth were shaped like this 4.5 bil years ago, only with a smaller diameter, and debris caused it to grow to 12, 700 kms?Roll Eyes Which would mean your pool levels would uuuuhhhhmmm darn Huh?

The slight bulge at the equator is usually blamed on the centrifugal force due to the earth's rotation.

Quote
Whilst pondering about this one, I drove right passed a offramp today


Oh-oh! Hope you didn't end up anywhere nasty.

Quote
If debris were to fall more on certain areas than others, wouldn't earth be oval shaped after 4.5 billion years of debris? 4.5 billion x 365 x 1000 tons


Probably not. Gravity will soon suck everything back into a sphere. Its interesting to look at pics of the gazillion moons of the gas giants, and the larger asteroids. It seems that the bigger they are, the closer they become to ball shape. The Earth, I would imagine, is well within the mass range that will render it perfectly spherical should it stop spinning.

Mintaka
« Last Edit: October 01, 2009, 18:11:14 PM by Mintaka » Logged
rwenzori
Sniper
Sr. Member
****

Skeptical ability: +7/-1
Offline Offline

Posts: 403


Merda accidit.


« Reply #8 on: October 01, 2009, 18:07:12 PM »

But does it? Isn't the atmosphere, in turn, thicker at the equator?

I was thinking that, with each rotation of the globe, the equatorial pool must sweep through a larger area compared to the northern pool. Maybe it covers more square meters per hour. That would be akin to asking if you get wetter by walking or running in the rain.


On the rain bit - does an object moving in the rain get wetter if it is not acting as a scoop? If you had two perfectly flat horizontal rectangles of glass out in the rain, one still and one moving, does the moving one gather more moss, as it were?  Huh?

On the thicker bit, there is more water vapour closer to the equator, to cool the meteor, giving it a better chance of surviving to the pool LOL! But again, the air is warmer at the equator. You seem to be right about the thickness:

Quote
The troposphere begins at the surface and extends to between 7 km (23,000 ft) at the poles and 17 km (56,000 ft) at the equator, with some variation due to weather. The troposphere is mostly heated by transfer of energy from the surface, so on average the lowest part of the troposphere is warmest and temperature decreases with altitude. ... The troposphere contains roughly 80% of the mass of the atmosphere.

http://en.wikipedia.org/wiki/Earth's_atmosphere

That said, it does seem that there are loads in the polar regions, so my original guess is looking good!

Logged
Peter Grant
Hero Member
*****

Skeptical ability: +5/-9
Offline Offline

Posts: 845


a fully caused agent


AtheistStoned AtheistStoned
WWW
« Reply #9 on: October 01, 2009, 18:53:27 PM »

Considering this is a logic problem, would I be correct in assuming we are not allowed to use anything other than what we can directly deduce from the question?
Logged
Rigil Kent
Clotting Factor
Hero Member
*****

Skeptical ability: +19/-3
Offline Offline

Posts: 2460


Three men make a tiger.


« Reply #10 on: October 01, 2009, 19:35:05 PM »

Quote
Considering this is a logic problem, would I be correct in assuming we are not allowed to use anything other than what we can directly deduce from the question?

Peter, you are of course correct - logic problems strictly speaking should contain all the info required, and the answer is known (at least by someone else). If there is a definite answer to this, I don't know what it is. Perhaps calling it a logic problem, was incorrect. Maybe its more of a speculative exercise, and some information outside that given would be useful, if not essential. Thanks for pointing that out! Embarrassed

Mintaka
Logged
Peter Grant
Hero Member
*****

Skeptical ability: +5/-9
Offline Offline

Posts: 845


a fully caused agent


AtheistStoned AtheistStoned
WWW
« Reply #11 on: October 01, 2009, 20:12:26 PM »

No worries, I'm just considering how to think about the problem.

How did you come up with it?
Logged
Peter Grant
Hero Member
*****

Skeptical ability: +5/-9
Offline Offline

Posts: 845


a fully caused agent


AtheistStoned AtheistStoned
WWW
« Reply #12 on: October 01, 2009, 21:34:32 PM »

OK, here's how I imagine it:

You're in orbit around the earth and you fire off meteors, every second, at both the equator and at the Tropic of Cancer simultaneously. The meteorites don't all land on the same spot because the earth is rotating, but are spread out evenly along the two lines of latitude. Meteorites on the equator are more widely spaced because the earth is rotating faster there. Meteorites at the Tropic of Cancer are more densely clustered and the pool will fill more quickly.
Logged
Peter Grant
Hero Member
*****

Skeptical ability: +5/-9
Offline Offline

Posts: 845


a fully caused agent


AtheistStoned AtheistStoned
WWW
« Reply #13 on: October 05, 2009, 20:51:29 PM »

Voting without posting shouldn't be allowed.  Angry
Logged
st0nes
Hero Member
*****

Skeptical ability: +10/-1
Offline Offline

Posts: 942



mark.widdicombe1
WWW
« Reply #14 on: October 06, 2009, 09:15:57 AM »

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, BUT: The equatorial pool is moving faster and therefore spends proportionally less time in each ‘sector’ of its larger area.  This exactly cancels out the effect of the larger area, and each pool  will be struck by the same number of meteorites.
Logged
Pages: [1] 2  All   Go Up
  Print  


 
Jump to:  

Powered by SMF 1.1.11 | SMF © 2006-2009, Simple Machines LLC
Page created in 0.541 seconds with 25 sceptic queries.
Google visited last this page February 26, 2019, 15:43:56 PM
Privacy Policy