A posting

From: Mitchell N Charity 
Subject: Re: Distances/Time
Newsgroups: k12.chat.teacher
Date: 27 Feb 1997 18:40:41 -0500
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In-reply-to: Ken Keenan's message of 26 Feb 1997 11:26:05 GMT
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   From           Ken Keenan 
   Date           27 Feb 1997 00:54:36 GMT
   Newsgroups     k12.chat.teacher
   Message-ID     <5f2m0c$4ii@news0-alterdial.uu.net>

   I'm looking for information that would tell me the length of time it 
   would take to get to each of the planets in our solar system.  This is 
   for a third grade class, distaces in miles, Km or light years do not 
   give them the best idea of distance.



I gather your objective is to convey distances, with travel times
being one possible approach.

This post briefly discusses another possible approach - scale models.
Such as

  If earth is a grain of sand, then...
  The moon is a smaller grain next to it, an inch away.
  The sun softball is 30 feet away.
  The jupiter marble is 200 feet away.

  If earth is your fist held out sideways, then...
  The moon is your big toe.

  If earth is your head, then...
  The moon is a big mouthful across the room.

 The idea being to work outward from something you have a feel for.
Say the common `blue cloud-wrapped earth hanging in space' image.
Or a globe.
 One can then say `if I picture my head (this building, ball, salt
grain, globe, pencil eraser dust, whatever) as the earth, then the
moon (the sun, planets, geosynchronous communication satellites, L5, the
earth's teardrop of a magnetic envelope, whatever) is about over
here, shaped like this, and moving so'.

 Thats building up from the earth.  As an aside, it is also possible
to tie the earth ball image back down to ground level experience.
 My own mental link is a chain of images
 1) air photos to give a feel for how familiar things (buildings, etc)
look from the air.
 2) sideways air photos with both clouds and ground, to get a feel for
clouds, their heights and relation to a ground with familiar things.
 3) a low earth orbit (ie shuttle) photo which shows clouds from the
side, and their shadows on the ground, and a well curved horizon of
earth in the background.
 Its not something I would try to do from scratch - I've just seen the
photos over the years.  Perhaps someone will eventually (or has
already:) collected such images as a web page.

 A difficulty with the `travel time' as distance approach is its
tendency to degrade into `I cant really picture it - it just seems
really big'.  One has a feel for walking, and adults for driving.
But beyond the earth's surface, one ends up with travel times as
ungraspable as the distances.  `Well, it would take you 100,000 years
to walk there.'  When, my guess is, many third graders are still
having trouble with 100's and 1000's of years.
 One exception comes to mind.  Once one can picture the earth-moon
pair, which is about a light-second wide (light takes a bit more than
a second to travel the distance between) (an aside - it can be fun to
shuffle at light speed through the scale models), one can then use
light-minutes and -hours to measure out the inner and outer solar
system.  Also fun to picture the effect of blinking and waiving a

The earth-centered scale model approach unfortunately doesnt handle
the outer solar system very well.  The scales are just too big.  Earth
as pencil eraser dust (say 0.1mm) puts the outer planets hundreds of
feet away.  A distance from which you can't easily see the pencil dust.
One has to resort to `earth dust is here and uranus/neptune sand is at
the other side of the (big) yard'.  However, it does work nicely for
the inner system and out to jupiter.

A last preface - size in the solar system is nicely exponential - ie
details dont matter.  One asks whether something is about 10, 100,
10000, etc, rather than whether its 20 or 30.  So one gets quite a
good idea of the shape of things with just addition/subtraction and
exponential/scientific notation.  Unfortunately, this did not end up
being illustrated below.

Running low on time, this section is rather ratty.
I would be unsurprised by errors.  Caveat.

 Moon    diameter      3e6 m   (   3480 km)
 Earth   diameter      1e7 m   (  12700 km. I remember it as
                                       `twelve e six meters'.)
 Jupiter diameter      1e8 m   ( 142000 km)
 Sun     diameter      1e9 m   (1390000 km)
 Earth-Moon  distance  4e8 m   (3.84e8 m)
 Earth-Sun   distance  1e11 m  (1.48e11 m)
 Jupiter-Sun distance  8e11 m  (7.78e11 m)

 earth diameter x   1/4 is moon    diameter  (hence head vs big bite, etc)
                x    10 is jupiter diameter,
                x   100 is sun     diameter,
                x 10000 is earth-sun distance.
 earth-moon distance is about 3x jupiter diameter.
 jupiter-sun distance is 5x earth-sun distance.

A nice 1/10/100 earth/jupiter/sun diameter pattern.  The volume/mass
relation follows nicely, at 1 / 1000 (10^3) / 1000000 (100^3).
 Earth is the biggest bare rock, and jupiter the biggest planet,
framing things as `you have bare rocks up to earth size, and big outer
planets between earth and 10x earth size'.

So... a 1 inch earth (thus a scale of about 1e9),
has a 1/4 in moon 30 in (3 feet) away,
a 100 inch (8 foot) sun 10000in (800ft, 1/6 mile) away, and
a 10 inch jupiter a mile away.

Its easier in SI.
A 0.1mm pencil eraser dust earth (thus a scale of about 1e11),
phas a mote of a moon, 3 mm away,
a 10 mm sun, 1 m away, and
a  1 mm jupiter, 5 m away.


Having run out of time for this posting, I will leave a copy as
and if there proves to be interest, perhaps flesh it out.

A key caveat - I haven't really tried to teach kids using this approach.
I would be very interested in the experiences of anyone who has tried.


Comments encouraged. - mcharity@lcs.mit.edu.
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