cable, which is buried in the mud at the ocean’s floor and lies roughly along a great circle between Seattle
and Hawaii. Fiber optic is made of glass, and the speed of light in the glass cable is about 2/3 of that in
vacuum. This fact can be gleaned either from numerous web sites of optic cable manufacturers (which are
easy to find!)
8
, or through a discussion of refraction and measurement of the index of refraction in a glass
sample
9
(a nice touch, but probably not what you want to do the first day of classes, for which this
exersize is designed!). The speed of light moving through a fiber optic cable is basically the same as speed
of propagation of an electrical signal through a computer network (’category−5 ethernet’) cable. Of
course, this is not an accident, but space here precludes that discussion. For the earnest student(s), we note
only that the speed of propagation of a signal in a network cable can be rather directly and simply
measured in a laboratory experiment using two laptops and a few network cables of different (but modest)
lengths
10
.
Returning to our Seattle−Hawaii transmission, assuming that most of the 24.4 ms delay is
propagation in the cable, and using the relation d=vt = (2/3 x 3.0 x 10
8
m/s ) x (24.4 x 10
−3
s) = 4800 Km
is an estimate of the cable distance
11
.
Assuming that your classroom globe of the earth accurately reproduces the scaled distance
between points, and that the cable is laid approximately along a great circle (since that would be the
shortest and thus cheapest way to lay cable) students can use ratio and proportion to convert the above
measurement of the distance between Seattle and Hawaii to an estimate of the radius of the earth . We used
a 15.3 cm radius globe and found a string length between Seattle, Washington and Hawaii along the
surface of the globe to be about 10.4 cm long, yielding an estimate of the earth radius of 15.3*4800/10.4 =
7100 Km. Alternatively, students may use web site calculators
12
to compare the cable distance with the
actual distance along the globe to again use ratio and proportion to convert their cable distance
measurement to an estimate of the radius of the earth.
This is quite simple for the students to do individually or in small groups. Each group can find its
own targets, and analyze a unique set of traceroute data to come up an estimate they contribute to a class
average. Along the way they learn some basic facts about the Internet, some geography and how to read
the traceroute output. By far, the most difficult part of this laboratory is determining the geographic
location of the nodes on either side of the transoceanic cable that you are using. Sometimes the machine
names are non−descript or not given. In either case a web resource called netgeo is often useful
13
in
translating the IP numbers to locations.
Table I below contains typical data found by some of our students between various shore points,
along with the associated estimate of the earth’s radius for each. As a warning, the final entry is an
example between land points, where the many repeaters and non−great circle path chosen generally
complicate the interpretation of the times and lead to very poor estimates of the earth’s radius.
It is noteworthy (***) that the data displayed for New York to Iceland naively yields an estimate
of 8600 Km for the earth radius. However, there is actually no great circle sea−route between the two sites.
An obvious obstacle, Newfoundland , Canada sticks out far east into the Atlantic and precludes lying a
cable along a great circle from New York to Iceland! The Table I earth radius estimate for that datum
results from draping a string on the globe along a sea route that is entirely offshore between New York
and Iceland and using its length (which for our globe was 13 cm). The apparent errors in the short hops
from the mainland US to nearby island (in Table I, Bermuda, though Puerto Rico and other ’short hops’
traceroutes are similar) may indicate that systematic delays have a proportionally larger impact on the data
quality for small time differences (short routes). Additionally, there were some sites we found that, for one
reason or another (cable route unknown, network topology, inability to determine location of node, etc)
did not work well. These include traceroutes from the USA to Fiji, Japan, India and Italy. However, in our
experience most clear, long , ocean routes gave estimates like those of Table I. The ** for the string
distance from Lisbon Portugal indicates that for this data the student actually used one of the web
calculators alluded to earlier to compare with the cable length determined by traceroute ; string and globe
would give essentially the same earth size estimate.
These data for transoceanic cable routes yield estimates of the earth’s radius typically some 10%−