Distances
John Baez
December 29, 2015
You can learn a surprisingly large amount of physics just thinking
about how big various things are. So, here is a tour of distance
scales, from the very smallest known to the very largest. For a
better explanation of the Planck length, classical electron radius,
Compton wavelength of the electron and Bohr radius of the hydrogen
atom, try my related webpage on length scales
in physics.
Most (though not all) of the numbers here are approximate. This is
especially true of the very large distances.
Here we go:

1.6 × 10^{35} meters:
the Planck length
(measuring distances more accurately than this might create a black hole,
defeating the experiment)

2 × 10^{20} meters:
20 zeptometers; approximately the shortest
distance currently probed by particle physics experiments at the
Large Hadron Collider (with energies of approximately 10 TeV).

10^{15} meters:
a femtometer or fermi; approximate diameter of a
proton or
neutron

2.817939 × 10^{15} meters:
classical electron radius (radius a ball of charge would need to
have for its electrostatic energy to give it the mass of an
electron)

10^{12} meters:
a picometer

2.4263096 × 10^{12} meters:
Compton
wavelength of an electron (wavelength of a photon
whose energy equals mc^{2} where m is the electron mass)

5.291771 × 10^{11} meters:
Bohr radius
of a hydrogen atom

10^{10} meters:
an angstrom

10^{9} meters (10 angstroms):
a nanometer

2 × 10^{9} meters (20 angstroms):
diameter of a DNA helix

10^{7} meters (1000 angstroms):
approximate diameter of a
virus
or
chromosome

4 × 10^{7} meters (4000 angstroms):
typical wavelength of
violet light

5 × 10^{7} meters (5000 angstroms)
typical wavelength of
blue light

6 × 10^{7} meters (6000 angstroms)
typical wavelength of
yellow light

7 × 10^{7} meters (7000 angstroms):
typical wavelength of
red light

10^{6} meters:
a micron; typical diameter of a
bacterium

10^{5} meters:
typical diameter of a human
red blood cell

8 × 10^{5} meters:
typical diameter of a human hair

5 × 10^{4} meters:
typical diameter of a human
egg cell

10^{3} meters:
a millimeter

5 × 10^{3} meters:
typical length of a
red ant

10^{2} meters:
a centimeter

2.54 × 10^{2} meters:
an inch
(archaic American unit of distance)

.3048 meters:
a foot
(archaic American unit of distance)

.91 meters:
a yard
(archaic American unit of distance)

1 meter:
a meter is
now defined to be the distance light travels in a vacuum in
1/299,792,458 of a second.

1.7 meters:
typical height of a human

91.44 meters:
length of an American football field, excluding end zones

541 meters:
height of tower planned for World Trade Center site

10^{3} meters:
a kilometer

1.609 × 10^{3} meters:
a mile (archaic American unit of distance)

8.85 × 10^{3} meters:
height of highest mountain on Earth,
Mount Everest

1.11 × 10^{5} meters:
one degree of latitude
on Earth

3.48 × 10^{6} meters:
diameter of Moon

1.2756 × 10^{7} meters:
diameter of Earth at equator

1.5 × 10^{7} meters:
diameter of Sirius
B, a white dwarf

1.43 × 10^{8} meters:
diameter of Jupiter

3.84 × 10^{8} meters:
average radius of Moon's
orbit

6.959 × 10^{8} meters:
radius of the Sun

4 × 10^{10} meters (0.25 AU):
diameter of
Rigel,
a bluewhite giant

1.495987 × 10^{11} meters:
an astronomical
unit or "AU", average radius of Earth's orbit

4.8 × 10^{11} meters (3.2 AU):
maximum diameter of
Betelgeuse, a red supergiant

7.3 × 10^{12} meters (49 AU):
maximum distance of Pluto
from Sun

10^{14} meters (700 AU)
possible distance from the Sun to the
heliopause
(the point at
which the solar wind stops)

9.4605 × 10^{15} meters (63 thousand AU):
a light year,
the distance light travels in one year

1.5 × 10^{16} meters (1.5 light years):
typical size of a
Bok globule
(a nebula from which a star is formed)

4 × 10^{16} meters (4.22 light years):
distance from Sun to
Proxima
Centauri (the nearest star to us)

3.0856 × 10^{16} meters (3.26 light years):
a parsec,
the distance you'd have to be for the radius of the Earth's
orbit to subtend an angle of one arcsecond

10^{17} meters (10 light years):
diameter of the Crab
nebula (formed by a supernova)

1.6 × 10^{18} meters (165 light years):
diameter of M13
(a typical globular cluster, containing several hundred thousand
stars)

6 × 10^{18} meters (600 light years):
diameter of Omega
Centauri (one of the largest known
globular clusters, containing several million stars)

6 × 10^{19} meters (6.5 thousand light years):
distance to the
Crab Nebula
(in the Perseus arm of the Milky Way, right next to the
Orion arm where we live)

1.5 × 10^{20} meters (16 thousand light years):
diameter of the
Small Magellanic Cloud
(a dwarf galaxy orbiting the Milky Way)

3 × 10^{20} meters (28 thousand light years):
distance to the center of the
Milky Way

9 × 10^{20} meters (100 thousand light years):
diameter of disc of the
Milky Way
(containing about 10^{11} stars)

1.6 × 10^{21} meters (170 thousand light years):
distance to the
Large
Magellanic Cloud (a dwarf galaxy orbiting the Milky Way).

6 × 10^{21} meters (600 thousand light years)
diameter of the corona of the Milky Way

3 × 10^{22} meters (3 million light years):
radius of the
Local Group,
a small cluster of about 10 galaxies containing the Milky Way

10^{23} meters (10 million light years):
radius of a typical
cluster
(containing 1001000 galaxies)

6 × 10^{23} meters (60 million light years):
distance to the
Virgo
cluster, the nearest substantial galaxy cluster

10^{24} meters (100 million light years):
radius of a typical
supercluster
(containing 310 clusters, and with a mass about 10^{15} times that
of the Sun)

5 × 10^{25} meters (5 billion light years):
distance to farthest observable
galaxies

10^{26} meters (14 billion light years):
radius of observable
universe (containing about 10^{10} galaxies or
10^{21} stars)
Warning: Nobody knows what the shortest possible distance is,
if there is one. It could be much bigger than the Planck length, or
much smaller — or there could be no shortest distance. All we know is
that if it exists, it must be smaller than about 10^{18}
meters.
Warning: Nobody knows if the whole universe is finite
or infinite in size. The further we look, the older stuff we see,
so the radius of the "observable universe" is limited by the
age of the universe (about 13.7 billion years), and we'll never see much
farther — except by waiting.
Warning: The above figures for distances don't take the
expansion of the universe into account. This only matters much for
the really big distances. So, when I say the farthest observable
galaxies are 5 billion light years away, I really mean that the light
we see from them took 5 billion years to get here. They're farther
away now!
Similarly, when I say the radius of the observable universe is about
14 billion light years, I really just mean that the universe is about
14 billion years old. If we look at something that old and ask how
far it would be now, we'd get a figure of about 46 billion light
years, thanks to the expansion of the universe. If you find this
confusing, you're not alone. The ultimate cure is to learn
more physics.
Warning: The diameter is twice the radius. So, if the
observable universe has now expanded to a radius of 46 billion light
years, its diameter is about 92 billion light years.
Since the observable universe has expanded to a diameter of 92 billion
light years, or about 8.7 × 10^{26} meters, while the
Planck length is a measly 1.6 × 10^{35} meters, we can
say that the current radius of the observable universe is roughly 5.4
× 10^{61} Planck lengths. That's
54000000000000000000000000000000000000000000000000000000000000
Planck lengths! A large but finite number.
Of course, we haven't really explored distances down the Planck
length; there might not be anything that small. A more conservative
unit might be the proton diameter, about 10^{15} meters. So,
if you lined up protons across the current diameter of the observed
universe, you could line up about 8.7 × 10^{41} of them.
Try imagining a line of
870000000000000000000000000000000000000000
protons! The universe is a big place.
© 2015 John Baez
baez@math.removethis.ucr.andthis.edu