23
C H A P T E R 2
Looking Outward
2.1 EARTH, MOON, AND SUN
2.1.1 THE SHAPE OF THE EARTH
Anyone can look out the window and see that Earth is flat. I say this with my tongue only
partly in cheek, because there is a sense in which it is true. e Earth is very nearly locally flat;
it is very difficult to come up with an experiment to prove Earth is a sphere, if one uses only
evidence from within the small confines of a laboratory. Peer out the window of the laboratory
for a prolonged period of time, on the other hand, and other evidence comes into play. e stars
appear to take a daily (diurnal) trip around us, and the illusion is that they are all attached to a
vast celestial sphere. e Sun and Moon seem to do the same, but not quite; they have their own
much-slower apparent motions superimposed upon the diurnal motion of the celestial sphere.
What is the best explanation for these observations? e devil is in the details of the word
“best,” and to pick that apart is to explore much of the history of the birth of modern science.
But one obvious idea has been articulated since at least ancient Greece: Earth rotates on an axis
once per day, and carries us along with it. Of course, that fact alone does not preclude the idea
that it is a flat earth that rotates. But it is easy to bring in other kinds of non-local data that does
not square with a flat-Earth hypothesis.
Consider what happens when one looks at the sky from other locations on Earth. e left
side of Figure 2.1 shows the position of the stars in the sky as seen at midnight, when facing
South from Appleton, Wisconsin on New Year’s Day at 10:30 pm. e familiar constellation
Orion is high in the sky. e right side of Figure 2.1 shows a photograph I took of those same
stars, also on a night in early January, but from central Chile, in the southern hemisphere. From
the point of view of a Cheesehead in Chile, Orion is upside down.
We can add even more evidence by traveling to other laboratories, in other parts of Earth,
and making similar observations and comparing them. ese observations, taken together, show
that the following is true.
e zenith—the point directly overhead—points toward different directions in space
as seen from different parts of Earth.
is basic observation is easy to make in the modern world. Simply find a friend thousands
of miles away and use Internet instant messaging to ask them to precisely describe the position
of the Sun, Moon or stars right now. ese observations are perfectly consistent with a (roughly)
spherical Earth, surrounded by a very distant Sun, Moon, and stars. And the zenith—“up”—
24 2. LOOKING OUTWARD
Figure 2.1: e familiar constellation of Orion. Left: e view from Appleton, Wisconsin
(USA), at roughly 45
˝
North latitude (as mapped by the software package Stellarium, avail-
able from stellarium.org). Right: As photographed from near Casablanca, Chile, at about 33
˝
South latitude (photograph by the author).
means away from the center of Earth. ere is no way to reconcile these observations with a flat
Earth without playing hard and fast with easily verifiable facts.
But why do we all experience our local zenith to be away from the center of Earth? e
answer is, of course, gravity—a topic we take up in detail in Part IV. But let us ask a related
question. Is it possible to determine that Earth is a sphere without looking at the sky? Could
one move around to different parts of Earth, making only local measurements as one moves, and
so prove Earth is a sphere? Let us imagine making the following three-legged trip.
1. Start at the North Pole, and travel due south along the 78
˝
30
1
W longitude line to the
equatorial city of Calacali, Ecuador.
2. From Calacali, turn 90
˝
to the left (due east) and travel in a straight line along the equator
until reaching longitude 11
˝
30
1
E, in central Gabon.
3. From central Gabon, again turn 90
˝
to the left (now heading due north) and travel back
along that longitude line to the North Pole.
is imaginary journey forms a triangle—three points connected by straight lines; see
Figure 2.2. Our triangle seems to have curved lines, and in three dimensions they are curved.
But if we constrain ourselves to the two-dimensional surface of Earth, there is an important
sense in which the lines of our triangle are straight; they are the shortest possible paths between
their end points. is is, in fact, the mathematical definition of a straight line. We could—in
our imagination anyway—tediously use trial-and-error to find these shortest paths between the
2.1. EARTH, MOON, AND SUN 25
Figure 2.2: A triangle on the surface of Earth, plotted with Google Earth. e three lines are
straight on the two-dimensional surface; they are the shortest possible paths between their end-
points. (Images copyright 2018 by Google, U.S. Department of State Geographer, image Landsat/Copernicus,
Data SIO, NOAA, U.S. Navy, NGA, GEBCO.)
three points of our triangle, even with no knowledge of longitude and latitude or that Earth is
a sphere.
Our imaginary journey would thus form what seems to be an ordinary, albeit huge, tri-
angle. It is three points on the surface of Earth, all connected by straight lines—the shortest
possible paths between the points. But this would be an odd sort of triangle indeed. One of the
first rules of plane geometry is that the inside angles of any triangle must add to 180
˝
. But see
Figure 2.3; the interior angles of our giant Earth triangle add instead to 270
˝
. Also, notice from
Figure 2.3 that when we zoom in to a small region of our triangle, the lines do indeed appear
straight, not curved. And so from the local point of view of making our triangle, nothing would
seem to be amiss. It is only when we compare the results from different locations—measuring
the angles at each vertex and adding the results—that we find something unusual.
Faced with such experimental evidence, we would be left with two possible explanations
for our observations. Either the surface of Earth is not flat—it has curvature into the third
26 2. LOOKING OUTWARD
Figure 2.3: All three vertexes of the triangle shown in Figure 2.2 are right angles, meaning the
interior angles add to 270
˝
, rather than the 180
˝
the angles would add to if the triangle were on
a flat surface. Over a small enough region, the curved surface of Earth is indistinguishable from
flat. (Images copyright 2018 by Google, U.S. Department of State Geographer, image Landsat/Copernicus,
Data SIO, NOAA, U.S. Navy, NGA, GEBCO.)
dimension, consistent with the surface of a sphere. Or else the rules of plane geometry we learned
in high school are somehow incorrect, and it is only small triangles that obey the 180
˝
rule.
We know of course that the first explanation is the correct one for our giant Earth triangle;
Earth is a sphere. But it turns out that there are other geometries besides the plane geometry
familiar from high school, and some of these non-Euclidean geometries do indeed allow the inte-
rior angles of a triangle to add to more than 180
˝
, even in three dimensions. is is an important
part of Einstein’s explanation for gravitation, and we take it up in more detail in Part IV of e
Big Picture.
2.1.2 THE ROTATION OF EARTH
Figure 2.4 shows two time-exposure photographs of the stars; the shutter of the camera was left
open for roughly 10 min in each case. e stars show up as streaks, demonstrating the apparent
diurnal motion of the celestial sphere. e picture on the left was taken with the camera pointing
north, from Glacier National Park in Montana, while the right-hand picture was taken from
central Chile, in the Southern hemisphere, with the camera facing southward.
Both images show the stars seeming to swirl around a particular point on the celestial
sphere. For the northern example, a star (called Polaris) happens to be at the pivot point; the
southern hemisphere example on the other hand is a relatively blank region of the sky.
One could explain these observations by assuming the stars are attached to a very large
sphere that is vastly larger than the diameter of Earth. And we could imagine that this celestial
2.1. EARTH, MOON, AND SUN 27
Figure 2.4: Time exposures of stars, showing Earth’s rotation; the camera shutter was left open
for approximately 10 min. Left: from Glacier National Park in Montana, in the Northern Hemi-
sphere. Right: from central Chile in the Southern Hemisphere. e seeming pivot points are
directly above Earth’s north pole (left) and south pole (right). Photographs by the author.
sphere rotates around Earth once per day. e seeming pivot points in our picture would then
represent the actual southern and northern points of the rotation axis of this celestial sphere.
We know of course that there is a much simpler explanation; the stars are relatively fixed
in space, and it is the spherical Earth that rotates on its axis. It is gravity that determines what is
up and what is down; up is simply away from the center of Earth. And so as Earth turns on its
axis from west toward the east carrying us along with it, the stars appear to move in the opposite
direction, like a slower car seeming to go backward as one passes it on the highway. And the
northern axis of Earth happens by chance to point very nearly in the direction of the naked-eye
star Polaris (while the southern axis points toward nothing in particular).
But how do we know it is this second explanation, rather than the first, that is correct?
To the modern mind, the first explanation seems absurd on the face of it. We humans seem to
have a natural tendency to prefer the simpler explanation, whenever we are confronted with two
explanations that agree equally well with known facts. is is sometimes called Occam’s razor,
and it is an important part of the scientific process.
But a rotating Earth—instead of a rotating celestial sphere—is the simpler explanation
only from the point of view of much else that we now know. To the ancient mind, the notion of
a rotating Earth raised troubling questions. e ancient Greeks, for example, had measured the
size of Earth (see Section 2.1.4), and so it was easy to see that a point on the equator would be
carried along by the rotating Earth at nearly 1700 km/hr (over 1000 mi/hr). Why don’t we fly off?
It is only in the light of workable theories of gravitation and motion that this quite-reasonable
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