28 2. LOOKING OUTWARD
concern can be properly addressed, and these theories were not developed in full until the late
17th century (primarily by Isaac Newton).
After Newton’s synthesis of motion and gravity (discussed in detail in Part IV), there was
no longer any reason to prefer a rotating celestial sphere over a rotating Earth. And so nearly
all scientists since that time assumed it is Earth that rotates, even though more than 150 years
would pass before there was any direct experimental evidence for a rotating Earth.
1
e results of
the Foucault Pendulum experiment, publicly demonstrated in 1851 by Léon Foucault, are exactly
as predicted for a rotating Earth.
I call attention to this history as an example of an important fact about science. We be-
lieve a scientific theory to be true not necessarily because it has been “proven” in some logical
manner—such a mathematical proof is usually possible only for rather trivial details. Rather, we
believe a theory when, given all else that we know, it seems unreasonable to disbelieve it (see,
for example, Beaver [2018], Ch. 1 and references therein).
2.1.3 THE SPHERICAL EARTH: AN EXAMPLE
Figure 2.5 illustrates a personal example that combines both the rotation of Earth and the non-
Euclidean geometry of its two-dimensional surface. On a flight from Chicago, Illinois to Ed-
inburgh, Scotland, the rising full Moon was directly out the window next to my seat. e full
Moon is directly opposite the Sun in the sky, and so it rises just at sunset (left-hand image).
Notice the dark band just above the horizon; it is, essentially, the shadow of Earth. e full
Moon in the picture is very near the edge of that shadow, demonstrating that it is very nearly
opposite the Sun.
e second image was taken hours later, after waking briefly during the overnight flight.
But the Moon was still located directly out my window, and this is an odd thing. For not only
was Earth turning, carrying its surface, atmosphere and the Boeing 757 with it, but the aircraft
was flying at nearly 900 km s
´1
in roughly the same direction relative to Earth’s surface. And
so over the course of a few hours, one would think the roughly Southeast-facing wing of the
aircraft would be pointing far to the left of the Moon, leaving it well behind in my view out the
window.
If the aircraft had been flying merely due East, along a latitude line, that would indeed
have been the case. Edinburgh is at a considerably higher latitude than Chicago, so of course
the flight initially traveled generally northeast. But the heading of the plane changed drastically
over the course of the flight. You can see something close to the actual path of the plane in
Figure 2.5, where I used the ruler tool in Google Earth. e flight began with a heading of
about 47
˝
North of East, but by the time the aircraft was over the Labrador sea, it was headed
only 15
˝
North of East. And it crossed 30.5
˝
longitude heading due East. Flying over Scotland
toward Edinburgh, the plane was headed 22
˝
South of East.
1
ere were important earlier hints as well, in the late 16th and early 17th centuries, from Galileo’s groundbreaking
studies of physics, the observations of planetary motion by Tycho Brahe, and the investigations of Johannes Kepler.
2.1. EARTH, MOON, AND SUN 29
Figure 2.5: While flying across the Atlantic Ocean, the Moon was visible out my window for
hours, even though both the surface of the rotating Earth and the high-speed motion of the
aircraft progressed Eastward. (Photographs by the author.)
Figure 2.6: e shortest path along the surface of Earth—a geodesic—connecting Chicago and
Edinburgh extends to latitudes more northerly than either city. e path looks curved com-
pared to the grid of longitude and latitude. (Image copyright 2018 by Google, U.S. Department of State
Geographer, image Landsat/Copernicus, Data SIO, NOAA, U.S. Navy, NGA, GEBCO.)
And so, relative to our grid of longitude and latitude, the airplane followed a curved path,
and its heading slowly rotated as it flew, partly counteracting the effect of Earth’s rotation re-
garding the view of the Moon out my window. But this seemingly curved path is in an important
sense not curved at all; it is a geodesic—the shortest path along the curved surface of Earth, as
discussed in Section 2.1.1. Stretch a string on a globe between the two cities and it will naturally
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