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^-19 meters:
  0.1 attometers; the gravitational wave detector LIGO can detect roughly this change in distance between mirrors that are 4 kilometers apart.

• 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:
  average radius of Moon's orbit

• 6.959 × 10⁸ meters:
  radius of the Sun

• 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

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

protons! The universe is a big place.

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