## Distances

#### 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 mc2 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

• 103 meters:
a kilometer

• 1.609 × 103 meters:
a mile (archaic American unit of distance)

• 8.85 × 103 meters:
height of highest mountain on Earth, Mount Everest

• 1.11 × 105 meters:
one degree of latitude on Earth

• 3.48 × 106 meters:
diameter of Moon

• 1.2756 × 107 meters:
diameter of Earth at equator

• 1.5 × 107 meters:
diameter of Sirius B, a white dwarf

• 1.43 × 108 meters:
diameter of Jupiter

• 3.84 × 108 meters:

• 6.959 × 108 meters:

• 4 × 1010 meters (0.25 AU):
diameter of Rigel, a blue-white giant

• 1.495987 × 1011 meters:
an astronomical unit or "AU", average radius of Earth's orbit

• 4.8 × 1011 meters (3.2 AU):
maximum diameter of Betelgeuse, a red supergiant

• 7.3 × 1012 meters (49 AU):
maximum distance of Pluto from Sun

• 1014 meters (700 AU)
possible distance from the Sun to the heliopause (the point at which the solar wind stops)

• 9.4605 × 1015 meters (63 thousand AU):
a light year, the distance light travels in one year

• 1.5 × 1016 meters (1.5 light years):
typical size of a Bok globule (a nebula from which a star is formed)

• 4 × 1016 meters (4.22 light years):
distance from Sun to Proxima Centauri (the nearest star to us)

• 3.0856 × 1016 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 arc-second

• 1017 meters (10 light years):
diameter of the Crab nebula (formed by a supernova)

• 1.6 × 1018 meters (165 light years):
diameter of M13 (a typical globular cluster, containing several hundred thousand stars)

• 6 × 1018 meters (600 light years):
diameter of Omega Centauri (one of the largest known globular clusters, containing several million stars)

• 6 × 1019 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 × 1020 meters (16 thousand light years):
diameter of the Small Magellanic Cloud (a dwarf galaxy orbiting the Milky Way)

• 3 × 1020 meters (28 thousand light years):
distance to the center of the Milky Way

• 9 × 1020 meters (100 thousand light years):
diameter of disc of the Milky Way (containing about 1011 stars)

• 1.6 × 1021 meters (170 thousand light years):
distance to the Large Magellanic Cloud (a dwarf galaxy orbiting the Milky Way).

• 6 × 1021 meters (600 thousand light years)
diameter of the corona of the Milky Way

• 3 × 1022 meters (3 million light years):
radius of the Local Group, a small cluster of about 10 galaxies containing the Milky Way

• 1023 meters (10 million light years):
radius of a typical cluster (containing 100-1000 galaxies)

• 6 × 1023 meters (60 million light years):
distance to the Virgo cluster, the nearest substantial galaxy cluster

• 1024 meters (100 million light years):
radius of a typical supercluster (containing 3-10 clusters, and with a mass about 1015 times that of the Sun)

• 5 × 1025 meters (5 billion light years):
distance to farthest observable galaxies

• 1026 meters (14 billion light years):
radius of observable universe (containing about 2 × 1012 galaxies or 1021 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 × 1026 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 × 1061 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 × 1041 of them. Try imagining a line of

870000000000000000000000000000000000000000

protons! The universe is a big place.