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Jun 01, 2007

How High the Moon?

Moonearth_580
For some reason, I keep forgetting how little I know about the relative size of things that might seem more knowable.

Today, a quizlet in three multi-part parts (answers in the Comment section):

1.a  Let's say you have a globe the size of a basketball (or maybe you just buy one) and you want a matching-scale model of the moon.  Which of these objects is close to the right size?

(a) a pea
(b) a grape
(c) a baseball

1.b  And if you wanted to show the moon in its proper orbit, more or less how far away would you put the pea, grape, or baseball from your globe?

(a) arm's length
(b) opposite corners of the your living room
(c) opposite corners of a basketball court

2.a  According to a recent article in The Economist, approximately how many Jewish people are there in the world?

(a) less than 1 million
(b) ~13 million
(c) ~54 million

2.b  How do the Jewish populations in Israel and the US compare?

(a) far more Jews in Israel than the US
(b) far more Jews in the US in Israel
(c) about the same number in both countries.

3.a   Imagine taking everyone in the world and stacking them into a cube.  How big would that cube be? For the "stacking", assume that the people are racked up shoulder to shoulder, heel to toe, and standing on each other's heads.  What does your intuition tell you?  How about your calculator and some estimating?

(a) ~ 3/4 mile on each side
(b) ~4 miles on a side
(c) ~8 miles on a side

3.b  Pretend you have a model of the Earth that's the size of a pool ball, with the cube of people (at the appropriate scale) glued somewhere on the surface of the pool ball.  Would you be able to feel the bump?

(a) yes
(b) no
(c) yes if you were blind and could read Braille.

01:01 AM in Misc.Blog 2007 | Permalink

Comments

1.a -- (c) a baseball
1.b -- (b) across the living room

See here for a nice pic:
http://tinyurl.com/2cp3tr

2.a -- (b)~13 million (12.9 per The Economist)
2.b -- (c) about the same (5.4 million in Israel and 5.2 million in the US (per the Economisst)

3.a -- (a) about a quarter mile on a side
3.b -- (a) most likely. The cube of people would be about 1/16th the thickness of a piece of paper. I doubt I could feel that. I doubt that a Braille reader could, either.

Notes:
Question 1 is a common topic for high school science students.

The answers to Question 2 appeared in a recent article in the Economist. I lost a $5 bet today because I incorrectly remembered the total as ~6 million (not 12.9). Sadly, I lost that bet to someone who thought the total was around 60 or 70 million. I should have asked for a bigger spread.

Question 3 just occurred to me one afternoon a few years ago. For my calculation, I assumed shoulder-to-shoulder spacing at 2 ft, heel-to-toe spacing at 1 ft, and an average human height of 5'6" (a little short for adults, but figure that there are a bunch of kids in there, too). With those figures, the "box" for each person would take up 11 cubic feet. Multiplied by a current world population of 6.6 billion people, you'd get a 72.6 billion cubic feet block, which would be ~4,172 feet on each side (a mile is 5280 feet).

For some mental comparisons, consider that the Sears Tower in Chicago and the Petronas Towers in Kuala Lumpur are all ~1,400 feet high. Wallace Wade football stadium at Duke University is ~600 feet on a side. So imagine a footprint that's seven stadiums wide by seven stadiums long, and imagine the Sears Tower on top of Petronas Tower One on top of Petronas Tower Two. Got it? That's us. All of us.

Posted by: Phil | Jun 3, 2007 1:24:05 AM

For question number 3--so the cube may be less than a mile on a side, but the line for the bathroom would surely extend to the moon. And what about the parking structure?

Posted by: Dave | Jun 22, 2007 4:20:38 AM

In case you were wondering about the sun in this picture:

With your basketball earth and your grape moon (across the corners of your living room), the sun would be a little smaller than a basketball court, sitting not quite 2 miles away (more or less the distance from downtown Durham to Ninth St.)

Posted by: Phil | May 6, 2008 4:36:52 PM