10 m). Then, going to the large scales of astronomy, we have the
radius of the Earth, some 10
7
m (that is, 1 followed by 7 zeroes); that
of the Sun is 10
9
m; our orbit around the Sun is 10
11
m (or in more
readable units, 100 million km). For later reference, note that the
relative sizes of the Earth, Sun, and our orbit are factors of
about 100.
Distances greater than this become increasingly hard to visualize,
with large numbers of zeroes when expressed in metres, so a new
unit is used: the light year. Light travels at 300,000 metres per
second. This is fast but not infinite: it takes light a nanosecond, that
is 10
−9
s, to travel 30 cm, which is about the size of your foot. Modern
computers operate on such timescales, and such microtimes will
become central when we enter the world within the atom. For the
moment, we are heading to the other extreme – the very large
distances of the cosmos, and the long times that it takes for light to
travel from remote galaxies to our eyes here.
It takes light 8 minutes to travel the 150 million km from the Sun;
so we say the Sun is 8 light minutes away. It takes a year for light to
travel 10
16
m, and so this distance is referred to as a light year. Our
Milky Way galaxy extends for 10
21
m, or some 100,000 light years.
Galaxies cluster together in groups, extending over 10 million light
years. These clusters are themselves grouped into superclusters,
about 100 million light years in extent (or 10
24
m). The extent of the
visible universe is some 10 billion light years, or 10
26
m. These
actual numbers are not too important, but notice how the universe
is not homogeneous, and instead is clustered into distinct
structures: superclusters, clusters of galaxies, and individual
galaxies such as our own, with each being roughly 1/100 smaller
than its predecessor. When we enter the microworld, we will once
again experience such layers of structure, but on a much emptier
scale; not 1/100 but more like 1/10,000.
Having made a voyage out into the large scales of space, let’s now
take the opposite direction into the microworld of atoms, and their
13
How big and small are big and small?