Measuring Continental Drift: The Laser Ranging Experiment
Background Information:
Scientists are interested in knowing how far they can see on the Earth’s curved surface. The
reason scientists want to see a long way is because they want to measure the distance between fixed points
on two or more continents. If they can measure this distance accurately, they will be able to answer
questions like:
 Are the crustal plates moving? How fast are they moving? In what direction are they moving?
 Are the motions of these plates constant?
 Do the plates stretch?
 Does a whole plate move as one piece?
Scientists have not answered these questions yet, but they are trying. It is not easy to measure
slow movements accurately—just centimeters per year—between continents. Scientists are devising
instruments that can be placed almost anywhere on Earth and then establish the precise location of that spot
on the Earth. The instrument shoots a laser beam at the moon. The beam is reflected from a reflector
placed on the moon by the astronauts.
Since the astronomers know precisely where the moon is located at all times, they can use the
equations necessary to locate the laser instrument on the Earth. These equations include the variables that
astronomers use to determine the precise position of the instrument. Some of these instruments are mobile
and can be placed at many different locations on the Earth.
Astronomers will make many observations from these same points during the next ten or more
years. Changes of distance between any two points will be measured, and the rate and direction of
movements can be established.
This complex problem involves a rotating Earth and a moving moon. However, the moon’s
position is known mathematically and is considered as being fixed at the moment the moon is on the
Earth’s meridian passing through the observing site. Similarly, in the activity the moon is thought of as
being fixed and the Earth’s turning is the only variable being observed.
The Greek mathematician Pythagoras (6th Century B.C.), worked out a formula for finding the
length of the sides of all right triangles. (A right triangle is one that has one angle of 90°.) Every right
triangle has two sides shorter than the third. This long side is known as the hypotenuse. Pythagoras said to
take each short side, and square it (multiply it by itself), and add these two products together. The answer
will equal the longest side multiplied by itself. For those of you already familiar with the geometry, I am,
of course speaking of the equation A2 + B2 = C2 . In part A of this lab, you will apply Pythagoras’ idea to
our problem with the mountain.
Objectives:
At the completion of this whole lab activity, you should be able to:

Calculate how far on the Earth you can see from a mountaintop.

Explain what is meant by the phrase “line-of-sight”.

Explain how the curvature of the Earth affects how far we can see along the Earth’s surface.

Discuss what happens to the distance between a point of the Earth and a point on the moon, in terms of the
Earth’s rotation

Graph data on a grid and draw a curve to fit the data.

Explain how scientists might accurately measure the distance between two points located on different crustal
plates.
Part A
Question:
How far on the Earth can we see from a mountaintop?
X
When you stand on the surface of the Earth at sea-level,
you are approximately 6,400 km from the center of the Earth.
How far are you from the center of the Earth if you stand on a
mountaintop that is 2 km above the surface? ANS: 6,402 km. If
you look at the figure to the right, this would represent side AT of
triangle AUT, or side AX of triangle AUX.
Let’s focus for a minute on triangle AUT. Side AU is
6,400 km long, because the person standing at point U is at sealevel. Side AT is 6,402 km, because the person standing at point
T is 2 km above sea-level on top of the mountain. Now, use the
Pythagorean Theorem to solve for side UT.
U
A
A2 + B2 = C2
In this equation, C2 is always the hypotenuse, which is the
longest side of the right triangle (opposite the right angle). So the
hypotenuse in the example is represented by side AT. Another
way to look at this equation, when you are given C2 is:
2
2
2
C -A =B
B2 is what you are solving for. You are given A and C, and you simply have to square them. So, plug in
your numbers to the equation.
A= side AU, so 6,4002 = 40,960,000 km2
C= side AT, so 6,4022 = 40,985,604 km2
We still need to find UT. To find the length of side UT, you must subtract.
So: 40,985,604 – 40,960,000 = 25,604
Wait…you’re not done yet. This number is squared. You must take the square root of this answer to find
the actual distance of UT. So the square root of 25,604 is approximately 160 km. Side XT is twice the
length of side UT. Therefore, the length of XT is 320 km. This number is the distance between two
mountains that are 2 km high, if you could stand on top of one and just barely see the other over the
curvature of the Earth. The line XT along which you can see, is called your line-of-sight.
Finding a high place from which to observe makes your line-of sight longer. This is a problem for
people like us, who live in relatively flat places, or areas that are close to sea-level. Our line-of-sight is
shorter. No mountains on Earth are high enough to enable you to see a place which is several thousand
kilometers away. Therefore, you cannot measure distances across continental plates, or plate movements,
from a mountaintop. The curvature of the Earth will always get in your way. You must find another way
to make measurements over very long distances. This new way could use points on the Earth and the
moon, satellites, and even other planets.
T
Problems:
1. In your journals, make a sketch of what each the following might look like
(similar to example), and show all calculations:
a. What would the length of your line-of-sight be from the top of Mt.
Everest, which is 8,848 m?
b. What would the length of your line-of-sight be from Mt. McKinley in
Alaska, which is 6,194 m?
c. What would be the length of your line-of-sight from the Clark Airport, in
Justin, Tx, which is 705 ft above sea level?
2. What are some issues that may arise to keep you from realizing your line-of-sight
in the above named regions?
3. List three other places from which you might take measurements.
You may use the internet to do conversions.