A B C
D E
B. How high are those balloons?
To begin our analogy, let's say you and your family have stopped at a
restaurant. While you're there, you notice a couple of hot air
balloons, one hovering nearby, the other a a few kilometers away. From
where you are, both balloons are at the same altitude.
From other locations, though, the two balloons are at different
altitudes. Because the earth is curved, how high something is depends
on the location of the observer. That's because which way is up
depends on where one is, as can be seen from the diagram.
The
diagram makes a few points clear:
-
For each location on earth, the vertical and horizontal
directions are different.
-
The angle by which the vertical axes differ at different
locations
directly corresponds to the angle by which the horizontal planes differ
at those locations. (In fact, the angles between the vertical axes
and the horizontal planes are equal, but for now we just note that the
angles are related.)
Another noteworthy point is that it's easy to understand how
the height difference between balloons depends on your location if our
diagram takes in a large portion of the earth's circumference. If we
compare balloon heights as seen from two places much closer together, we see
that the results are more similar. Two people standing next to each
other have so little difference in perspective that the balloons' vertical
separation would be practically the same to both.
These conclusions all depend on the fact that the earth is a
roughly spherical object, which makes vertical distances between objects
different which respect to different points on the earth's surface.
Einstein found that, in a similar way, time durations between events are
different with respect to different velocities through space. A few
years after Einstein discovered this, one of his former professors, Hermann
Minkowski, found a way to illustrate the relationship with a diagram.
(.....continued)
A
B C D
E