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Physics LibreTexts

1.8 Mass, Length, and Time

Astronomy covers a vast range of time and space. The tables below gives rough values of mass, length, and time, ranging from the interior of an atom to the universe of galaxies.

Examples of Mass in kilograms

  • 10-30 Mass of electron
  • 10-27 Mass of proton
  • 10-25 Mass of uranium atom
  • 10-15 Mass of a bacterium
  • 10-5 Mass of mosquito
  • 10-2 Mass of a hummingbird
  • 100=1 One liter of water (1qt)
  • 102 Mass of a person
  • 103 Mass of a car
  • 108 Mass of a large ship
  • 1013 Mass of a small mountain
  • 1015 Mass of a comet nucleus
  • 1023 Mass of the Moon
  • 1025 Mass of the Earth
  • 1030 Mass of the Sun
  • 1042 Mass of the Milky Way
  • 1053 Mass of known universe

Lengths span a factor of 1053/10-30 = 1080 ! Notice the fantastic range of physical quantities. The mass range from an electron to the entireuniverse is 1080 — one with eighty zeros after it!

 

Examples of Length in meters

  • 10-35 Planck length
  • 10-17 Smallest observable scale
  • 10-15 Diameter of proton
  • 10-14 Diameter of uranium nucleus
  • 10-10 Diameter of hydrogen nucleus
  • 10-8 Thickness of cell membrane
  • 10-6 Wavelength of visible light
  • 10-3 Size of a grain of sand
  • 100=1 Height of a young child
  • 102 Length of a football field
  • 104 Greatest ocean depth
  • 107 Diameter of the Earth
  • 1011 Earth-Sun distance (1 A.U.)
  • 1016 One light-year
  • 1021 Diameter of Milky Way Galaxy
  • 1022 Distance from Earth to M31
  • 1026 Size of observable universe

Lengths span a factor of 1026/10-35 = 1061 !

 

Examples of Time in seconds

  • 10-43 Planck time
  • 10-34 Inflationary era
  • 10-23 Light crosses a proton
  • 10-22 Mean life of unstable nucleus
  • 10-15 Oscillation of visible light
  • 10-13 Vibration of an atom in solid
  • 10-8 Oscillation of FM radio wave
  • 10-3 Duration of nerve impulse
  • 100=1 One heartbeat
  • 105 One day
  • 107 One year
  • 109 Human life expectancy
  • 1011 Recorded history
  • 1012 Light crosses the Milky Way
  • 1016 Age of youngest quasar
  • 1017 Age of the Earth
  • 1018 Age of universe

Lengths span a factor of 1018/10-43 = 1061 !

 

In addition to units based on mass, length, and time, there are two pure numbers that occur frequently in science and mathematics. Each of these numbers can be calculated with arbitrary accuracy — the sequence of digits after the decimal points is random (or unpredictable) and never repeats. The first dozen or so significant figures are given below; three significant figures are sufficient for most calculations.


The symbol for pi. Click here for original source URL.

  • π = 3.141592653589793238… ≈ 3.14
  • e = 2.718281828459045235… ≈ 2.72

The fundamental constants of nature that are encountered most frequently in astronomy are given in the table below. Many of these numbers are known to a very high precision, but we only quote five significant figures here.

Fundamental Constant Symbol Value Units

  • Speed of light c = 2.9979 x 108 m/s
  • Gravitational constant G = 6.6726 x 10-11 N m2/kg2
  • Planck’s constant h = 6.6261 x 10-33 N s
  • Boltzmann’s constant k = 1.3807 x 10-23 J/K
  • Stefan-Boltzmann constant ? = 5.6705 x 10-8 W/m2 K4
  • Mass of an electron me = 9.1094 x 10-31 kg
  • Mass of a proton mp = 1.6726 x 10-27 kg
  • Size of a hydrogen atom = 5.2900 x 10-11 m

Astronomers mostly use the metric (or SI) system, but certain other units have been retained for convenience or sometimes for historical reasons. The most important examples are given below.

Astronomical Constant Symbol Value Units

  • Astronomical Unit A.U. = 1.50 x 1011 m
  • Parsec pc = 3.09 x 1016 m
  • Light year ly = 9.48 x 1015 m
  • Solar mass Msun = 1.99 x 1030 kg
  • Solar luminosity Lsun = 3.90 x 1026 W
  • Solar constant = 1.39 x 103 W/m2
  • Earth mass Mearth = 5.98 x 1024 kg
  • Earth radius Rearth = 6.37 x 106 m

Since the scales of the universe are so large, we use these units so we do not always have to deal with extremely large numbers. It does not make sense to measure the distance between stars in meters or to measure the mass of a galaxy in kilograms. For example, you will see density expressed in several different units. In a normal situation on Earth, the most appropriate units for density are kilograms per cubic meter (kg/m3). In interstellar space, the most useful units are atoms per cubic meter. However, on the enormous scales defined by a galaxy, the best units to use are solar masses per cubic parsec (Msun/pc3).