Reference: this book's "google page"
Here in the Reference section one can find the values of the physical and chemical contants used for the calculations in this book, miscellaneous data used for comparisons, astronomical data, etc. Browse as you like or use the hyperlinks below to go to the area of interest.
Also included in the book, for those so inclined, are some reviews and mathematical instructions for two important processes: how to calculate using scientific notation (Scientific Notation Math, scientific notation is introduced in Chapter 2) and how to convert from one type of unit to another (Unit Conversion).
Link Index for Reference Lists on this page:
Physical Constants Used In This Book
Abbreviations Used In Formulae
Sizes/Volumes, Etc., Of Interest
METRIC PREFIXES
Here is a list of the internationally accepted Metric prefixes. Each prefix is basically used as a multiplier, indicating that the number it is used with needs to be multiplied by the associated power of 10. In this book we use, generally, only the range from “tera” to “pico”, and so only those are explained fully here.
Normally associated with Metric Units (for example, Kilograms, Megawatts, etc.) they can be used with anything in many surprising and interesting ways (e.g., Megasale, centipede, millipede, decathlon etc.).
Y, yotta, 1024
Z, zetta, 1021
E, exa, 1018
P, peta, 1015
T, tera, 1012
Indicates the number is to be multiplied by 1 trillion; e.g., 12 Tbytes (or terabytes), equals 12 trillion bytes.
G, giga, 109
Indicates the number is to be multiplied by 1 billion; e.g., 100 Gwatts (or gigawatts), equals 100 billion watts.
M, mega, 106
Indicates the number is to be multiplied by 1 million; e.g., 1.2 Mjoules (or megajoules), equals 1.2 million (1,200,000) joules.
k, kilo, 103
Indicates the number is to be multiplied by 1 thousand; e.g., 14 kg (or kgram, or kilogram), equals 14 thousand (14,000) grams.
h, hecto, 102
Not a commonly used prefix, indicates the number is to be multiplied by 100.
da, deca, 10
Not a commonly used prefix, indicates the number is to be multiplied by 10.
d, deci, 10-1
Indicates the number is to be multiplied by 1 tenth; e.g., 2 dl (or dliter, or deciliter), equals 2 tenths of a liter.
c, centi, 10-2
Indicates the number is to be multiplied by 1 hundredth; e.g., 6 cm (or cmeter, or centimeter), equals 2 hundredths of a meter.
m, milli, 10-3
Indicates the number is to be multiplied by 1 thousandth; e.g., 1 ml (or mliter, or milliliter), equals 1 thousandth of a liter.
µ, micro, 10-6
Indicates the number is to be multiplied by 1 millionth; e.g., 2 µm (or µmeter, or micrometer), equals 2 millionths of a meter. This is the general size range of living cells.
n, nano, 10-9
Indicates the number is to be multiplied by 1 billionth; e.g., 5 nm (or nmeter, or nanometer), equals 5 billionths of a meter. This is the general size range of atoms and visible light wavelengths.
p, pico, 10-12
Indicates the number is to be multiplied by 1 trillionth; e.g., 16 pm (or pmeter, or picometer), equals 16 trillionths of a meter. <does this say anything about "Pico Pica Hot Sauce"?>
f, femto, 10-15
a, atto, 10-18
z, zepto, 10-21
y, yocto, 10-24
LENGTH
km = kilometer • m = meter • cm = centimeter • mm = millimeter
µm = micrometer • nm = nanometer • Å = Ångström • LP = Planck Length
AU = Astronomical Unit (Earth to Sun distance) • pc = Parsec
ly, ld, lh, lm, ls = light year, day, hour, minute, second
English Units: mi = mile • yd = yard • ft = foot • in = inch
1 km = 1000 m = 0.621371192 mi
1 m = 100 cm = 1000 mm = 3.28084 ft = 1.093613298 yd
1 cm = 10 mm = 0.393700787 in
1 mm = 0.1 cm = 1000 µm = 1,000,000 nm
1 Å = 10-10 m = 0.1 nm = 1 × 10-4 µm = 10-8 cm = 3.94 × 10-9 in
LP= 1.616199(97)26 × 10-35 m (shortest possible length considerable with our science)
1 AU =149,597,870,700 m = 92,955,807.2735 mi = 4.9081 × 10-11 ft
1 ly (in Julian year) = 9.460731 × 1015 m = 0.30660137 pc = 5.878625 × 1012 mi
1 pc = 3.261564029 ly
1 light day = 2.59021 × 1013 m = 1.60948 × 1010 miles
1 light hour = 1.07925 × 1012 m = 6.70617 × 108 miles
1 light minute = 1.79875 × 1010 m = 1.11769 × 107 miles
1 light sec = 299,792,458 m = 186,282.4 miles
English Units:
1 mi = 1760 yd = 5280 ft = 63,360 in = 1609.344 m = 1.609344 km
1 ft = 12 in = 0.33… yd = 30.48 cm = 0.3048 m
1 in = 2.54 cm
1 m = 1.093613298 yd = 3.280839895 ft = 39.3700787 in
AREA
km2 = square kilometer • m2 = square meter • cm2 = square centimeter
ha = hectare
English Units: mi2 = square mile • yd2 = square yard • ft2 = square foot
in2 = square inch • ac = acre
1 m2 = 10-6 km2 = 10,000 cm2 = 1.195990046 yd2 = 10.763910417 ft2 = 1,550.00310006 in2
1 km2 = 1,000,000 m2 = 1010 cm2 = 100 ha = 0.386102159 mi2
1 ha = 10,000 m2 = 0.01 km2 = 2.471053815 ac
Area of square, rectangle, or parallelogram = base · height
Area of circle = π · radius2
Area of triangle = 1/2 · base · height
Area of trapezoid = 1/2 ( bottom base · top base) · height
Area of Ellipse = π · ab (ab are the semi-axes of the Ellipse)
Area of section of circle = 1/2 · radius2 · (angle in radians)
English Units (US):
1 mi2 = 2.589988 km2 = 640 ac = 3,097,600 yd2 = 27,878400 ft2 = 4,014,489,600 in2
1 yd2 = 0.83612736 m2 = 9 ft2 = 1,296 in2
1 ft2 = 0.09290304 m2 = 144 in2
1 in2 = 6.4516 cm2
VOLUME
L = Liter • cc (or cm3) = cubic centimeter • ml = milliliter (equivalent to cc)
m3 = cubic meter • km3 = cubic kilometer • bl = petroleum barrel
tsp = teaspoon • tbsp = tablespoon • c = cup • drop = drop
English Units: mi3 = cubic mile • yd3 = cubic yard • ft3 = cubic feet
in3 = cubic inch • fl oz = fluid ounce • qt = quart • gal = gallon
1 L = 1000 cc = 1000 ml = 4 c (metric) = 200 tsp (metric) = 66.66… tbsp (metric) = 20,000 drop (metric)
1 m3 = 1000 L = 1,000,000 ml = 10-9 km3 = 35.314666721 ft3 = 6.102374409 × 104 in3
1 km3 = 109 m3 = 1015 ml = 0.2399 mi3
1 bl = 158.987294928 L = 42 gal (English)
1 tsp (metric) = 5 ml = 100 drop (metric) = 60.86254 drop (US) = 1.0144207 tsp (English)
1 tbsp (metric) = 15 ml = 300 drop (metric) = 182.59572259 drop (US) = 1.014420681 tbsp (English)
1 cup (metric) = 0.25 L = 250 ml = 1.056688209 cup (English) = 8.45350567 fl oz (English)
Volume of cube or box = length · height · width
Volume of sphere = 4/3 ·π· radius3
Volume of cylinder = π · radius2 · height
Volume of Ellipsoid = 4/3 ·π· abc (abc = semi-axes of ellipsoid)
Volume of Pyramid = 1/3 · base · height
Volume of Cone = 1/3 ·π· radius2 · height
English Units (US):
1 mi3 = 4.1684 km3 = 5.451776 × 109 yd3 = 1.471980 × 1011 ft3 = 2.543581 × 1014 in3
1 yd3 = 0.764554858 m3 = 27 ft3
1 ft3 = 0.028316847 m3 = 28.316846592 L = 1728 in3
1 in3 = 16.387064 ml
1 gal = 3.785411784 L = 4 qt = 16 cup = 128 fl oz = 0.133680556 ft3
1 qt = 0.946352946 L = 2 pt = 4 cup = 32 fl oz
1 fl oz = 29.573529562 ml
TIME
a = Julian Year (std. abbrev. is yr)
d = day • h = hour • min = minute • s = second
tp = Planck Time
1 hour = 60 minutes = 3600 seconds
1 day = 24 hours = 1440 minutes = 86,400 seconds
1 week = 14 days
1 a (yr) = 365.25 d = 8,766 hr = 525,960 min = 31,557,600 sec
1 century = 10 decades = 100 a (yr) = 3.15576 × 109 s
1 millenium = 10 centuries = 100 decades = 1000 years = 365,250 days = 3.15576 × 1010 s
tp = 5.39106(32) × 10-44 s (Planck Time: shortest possible time considerable with our current science/technology)
1 tropical year = 365.24219 d
1 gregorian year = 365.2425 d
1 sidereal year = 365.256363004 d
age = 1,000,000 yr
epoch = 10,000,000 yr
era = 100,000,000 yr
eon = 109 yr
English Units:
Fortnight = 2 weeks
ANGLES
° = degree • rad = Radian • grad = Gradian
360 degrees in a circle
360° = 2π rad = 400 grad
1 rad = 57.295779513°
1° = 0.017453293 rad = 1.11… grad = 60 minutes = 3600 seconds
Right Angle = 90°
MASS
kg = kilogram • g = gram • mg = milligram • µg = microgram
t = Tonne • MP = Planck Mass • u = Atomic Mass Unit
English Units: lb = pound • oz = ounce • lb t = troy pound
oz t = troy oounce • sh tn = short ton • ton = long ton
Note: using “pounds” (and ounces) for Mass is not accurate, the unit of Mass in the English system is the “slug”. Pounds are included here because it is a commonly needed conversion for “weight”. In the Metric System, the kilogram is both the unit of “weight” and of “Mass”.
1 kilogram = 1000 grams = 2.20462 lb = 35.27396 oz
1 g = 1000 mg = 1,000,000 µg
1 t = 1000 kg =2,204.62262189 lb
MP = 2.176 51(13) × 10-8 kg
1 u = 1.66057 × 10-27 kilograms
English Units:
1 slug (English mass unit) = 14.5939029 kg = 32.174048556 lb
1 lb = 0.45359237 kg = 16 oz = 1.215277778 lb t = 14.5833… oz t
1 lb t = 0.373241722 kg = 12 oz t = 0.822857143 lb
1 sh tn = 2000 lb
1 ton = 2,240 lb
FORCE
N = Newton • dyn = Dyne • kgf = kilogram-force
English Units: lbf = pound-force • pdl = Poundal
1 N = 100,000 dyn = 0.101971621 kgf = 0.224808943 lbf = 7.233013851 pdl
English Units:
1 lbf = 444,822.161525 dyn = 32.174048556 pdl
DENSITY
Density is the measure of how much mass is contained in a given volume.
It is calculated by mass divided by volume and is given in either g/cm3 or kg/m3. It is a measure of how compact a material or object is. Greek small letter ρ is the symbol for density
ρ = mass / volume
Relative density is the ratio of one material's density to another's.
ρrel = ρ1 / ρ2
Relative density determines whether an object floats or sinks if material 2 is a liquid, semi-liquid, or a gas. When material 2 is water relative density has a special name: specific gravity.
If density 1 is less than density 2 ( ρrel < 1 ) the material floats or rises, if density 1 is more than density 2 ( ρrel > 1 ) the material sinks or descends.
Example: water -- wood floats while Iron sinks
Example: Mercury -- Iron floats while Gold sinks.
Since all materials swell with heating and contract with cooling (which changes its volume) it must be defined for specific temperatures, usually this is room temperature (20 °C) unless otherwise noted.
Water is usually taken as having a density of 1 g/cm3 but this is not exact (see table). But for most uses it is fine.
| Material | g / cm3 | kg / m3 |
| Aerogel | 0.00016 | 0.16 |
| Air (sea level | 0.001217 | 1.217 |
| Wood (approx) | 0.75 | 750 |
| Water (boiling at 100 °C) | 0.9584 | 958.4 |
| Water (ice at -20 °C) | 0.9935 | 993.547 |
| Water (ice at -10 °C) | 0.9981 | 998.117 |
| Water (ice water at 0 °C) | 0.9998 | 998.8395 |
| Water (ice water at 4 °C) | 0.99997 | 999.972 |
| *Water (working value) | 1 | 1000 |
| Sun (average) | 1.408 | 1408 |
| Earth (crustal average) | 2.5 | 2500 |
| Aluminum | 2.7 | 2700 |
| Earth (Mantel average) | 4.4 | 4400 |
| Earth (average) | 5.515 | 5515 |
| Iron | 7.87 | 7870 |
| Lead | 11.35 | 11,350 |
| Earth (core average) | 12.5 | 12,500 |
| Earth (core) | 13.1 | 13,100 |
| Mercury | 13.56 | 13,560 |
| Gold | 19.3 | 19,300 |
| Osmium | 22.59 | 22,590 |
| Sun (core) | 162.2 | 162,200 |
| White Dwarf star | 105 - 107 | 108 - 1010 |
| Neutron Star | 1014 - 1015 | 1717 - 1018 |
| Black hole - estimated :-0 | ∞ | ∞ |
PRESSURE
atm = Atmosphere • bar = Bar • torr = Torr • N = Newton
Pa = Pascal (N/ m2) • kg = kilogram • cm2 = sq. centimeter • m2 = sq. meter
English Units: ft2 = sq. foot • in2 = sq. inch • lb = pound
psi = pounds per square inch = lb/in2
psf =pounds per square foot = lb/ft2
1 atm = 1.01325 bar = 760 torr = 101,325 Pa = 1.033227453 kg/cm2 = 10,332.2745279 kg/m2 = 14.695948761 lb/in2 = 2,116.21657867 lb/ ft2
1 Pa = 9.869 × 10-6 atm = 7.500617 × 10-3 torr = 10-5 bar = 0.101971621 kg/m2
English Units:
1 psi = 143.99999706 psf = 0.068045964 atm = 0.070306958 kg/cm2
1 psf = 6.944445 × 10-3 psi = 4.72541 × 10-4 atm = 4.88242774 kg/m2
ENERGY
J = Joule • erg = Erg • kW-h = kilowatt-Hour • eV = Electronvolt
cal = calorie • kcal (or Cal) = kilocalorie (kcal is assoc. with food)
English Units: btu = British Thermal Unit
1 J = 107 erg = 0.238845897 cal = 6.2415 × 1018 eV = 2.78 × 10-7 kW-h = 9.47817 × 10-4 btu
1 erg = 6.2415 × 1011 eV
1 cal = 0.001 kcal = 4.1868 J = 41,868,000 erg = 2.6132 × 1019 eV
1 kcal = 1000 cal = 4,186.8 J = 4.1868 × 10-10 erg = 1.163 × 10-3 kW-h
1 kW-h = 3,600,00 J = 859.845227859 kcal
English Units:
1 btu = 1,055.05585262 J = 0.251995761 kcal = 2.93071 × 10-4 kW-h
1 Joule is:
the energy released when a small, 100 g, apple falls one meter to the ground
the heat required to raise the temperature of 1 g of water by 0.24 oC.[6]
the average energy released as heat by a person every 90th of a second
The Watt (the unit of electrical power) is defined as the use of 1 Joule of energy per second (a Watt-second). A Kilowatt-hour is then 1000 Joules used in 3600 seconds which equals 3,600,000 Joules. A 100 Watt lightbulb burning for 10 hours uses 1 Kilowatt-hour of energy.
ENERGY COMPARISON
Energy Contents in Joule, kcal, and kW-h (some figures are averaged or rough).
Note: any “ton” below uses the USA 2000 lb ton (907.2 kg):
| Source | J | kcal | kW-h |
|---|---|---|---|
| Avg. molecule of air | 10-21 | 2.39 × 10-25 | 2.78 × 10-28 |
| Photon of light | 10-19 | 2.39 × 10-23 | 2.78 × 10-26 |
| Chemical reaction per atom | 10-18 | 2.39 × 10-22 | 2.78 × 10-25 |
| Electron mass-energy | 10-13 | 2.39 × 10-17 | 2.78 × 10-20 |
| Fission of 1 Uranium nucleus | 10-11 | 2.39 × 10-15 | 2.78 × 10-18 |
| Flea hopping | 10-7 | 2.39 × 10-11 | 2.78 × 10-14 |
| Cricket chirp | 10-3 | 2.39 × 10-7 | 2.78 × 10-10 |
| Human heartbeat | 0.5 | 0.0001194 | 1.39 × 10-7 |
| Apple dropped 1 m | `1 | 0.000239 | 2.78 × 10-7 |
| AA Alkaline battery | 1,000 | 0.239 | 0.0003 |
| Burning match | 1,000 | 0.239 | 0.0003 |
| Candy bar | 1,000,000 | 239 | 0.3 |
| 1 pound of TNT | 2,092,000 | 499.7 | 0.581 |
| 1 Kilowatt-hour | 3,600,000 | 859.86 | 1 |
| 1 kg of TNT | 4,612,023.2 | 1,101.6 | 1.28 |
| Human daily diet | 8 × 106 | 2000 | 2.33 |
| 100w Light bulb a day | 8.64 × 106 | 2063.7 | 2.4 |
| 1 kg of coal | 3 × 107 | 7,165.5 | 8.33 |
| 1 L of gasoline | 3.42424 × 107 | 8,202.6 | 9.5395 |
| 1 kg of fat | 3.8 × 107 | 9,076.3 | 10.55 |
| 1 kg of jet fuel | 4.7 × 107 | 11,225.9 | 13.05 |
| 1 kg of rocket fuel | 1.43 × 108 | 34,155.45 | 39.72 |
| Burning 1 m3 wood | 3 × 109 | 7.165 × 105 | 833.3 |
| 1 ton of TNT | 4.184 × 109 | 999,331.23 | 1162.2 |
| Lightening bolt | 1 × 1010 | 2.3885 × 106 | 2,777.8 |
| Saturn V Rocket | 1 × 1011 | 2.3885 × 107 | 27,777.8 |
| Space Shuttle | 1 × 1013 | 2.3885 × 109 | 2.7778 × 106 |
| Fission of 1 kg of Uranium-235 | 8.16 × 1013 | 1.9483 × 1010 | 2.26584 × 107 |
| 20,000 ton of TNT (Hiroshima A-Bomb) | 8.368 × 1013 | 1.998691 × 1010 | 2.32444 × 107 |
| Thunder Storm | 1 × 1014 | 2.3885 × 1010 | 2.7778 × 107 |
| Million tons coal | 1 × 1016 | 2.3885 × 1012 | 2.7778 × 109 |
| 1 kg completely converted to Energy ( e = mc2) | 8.9875 × 1016 | 2.147 × 1013 | 2.4965 × 1010 |
| 100-megaton H-bomb | 1 × 1017 | 2.3885 × 1013 | 2.7778 × 1010 |
| Hurricane | 1 × 1018 | 2.3885 × 1014 | 2.7778 × 1011 |
| Earthquake Richter 8 | 1 × 1018 | 2.3885 × 1014 | 2.7778 × 1011 |
| Krakatoa Exploding | 1 × 1019 | 2.3885 × 1015 | 2.7778 × 1012 |
| Tidal Friction daily | 1 × 1020 | 2.3885 × 1016 | 2.7778 × 1013 |
| Earth's daily Geothermal | 1 × 1021 | 2.3885 × 1017 | 2.7778 × 1014 |
| Fossil Fuels used so far | 1 × 1023 | 2.3885 × 1019 | 2.7778 × 1016 |
| 1 yr. Earth’s Sunshine | 1 × 1025 | 2.3885 × 1021 | 2.7778 × 1018 |
| Energy Earth’s Spin | 1 × 1029 | 2.3885 × 1025 | 2.7778 × 1022 |
| Energy Earth’s Orbit | 1 × 1033 | 2.3885 × 1029 | 2.7778 × 1026 |
| Sun’s yearly emission | 1 × 1034 | 2.3885 × 1030 | 2.7778 × 1027 |
| Supernova explosion | 1 × 1044 | 2.3885 × 1040 | 2.7778 × 1037 |
| Radio Galaxy | 1 × 1055 | 2.3885 × 1051 | 2.7778 × 1048 |
| Big Bang (theorized) | 1 × 1068 | 2.3885 × 1064 | 2.7778 × 1061 |
POWER
W = Watt • J = Joule • Hp = Horsepower • sec = second
1 W = 1 J/sec = 1.341 × 10-3 Hp = 0.7376 foot-pounds/sec
English Units:
1 Hp = 550 foot-pounds/sec = 745.7 W
Power is how much energy is used how quickly; i.e., energy over time.
Approximate or rough figures of power in Watts (Joules/second):
10 W : Electric razor
90 W : Average Human
100 W : "Old School" Light bulb
1,000 W : Electric Stove
109 W : Large Power Plant
1014 W : Photosynthesis on Earth per day
1017 W : Sunshine on Earth
1027 W : Sun’s output
LIGHT
lm = lumen • Lux = lm/m2 • Phot = lm/ cm2 • cd = candela
eV = electronvolt • J = Joule • Hz = Hertz ( 1 Hz = 1 cycle/second)
m = meter • cm = centimeter • mi = mile • s = second
English Units:
footcandle = lm/ft2 • L = Lambert
1 cd = 12.57 lm
1 Lux = 0.0001 Phot = 0.09290304 Footcandle
English Units:
1 Lambert (L) = 3,183.09886188 cd/m2 = 295.719560885 cd/ft2
A common candle emits approximately 1 candela of luminance.
Speed of Light in a vacuum: 299,792,458 m/s (186,282.4 mi/s). Approximations = 3 × 108 m/s = 3 × 1010 cm/s
| Electromagnetic Radiation | Wavelength | Frequency (Hz) | Energy (J) | Energy (eV) |
| Radio Waves | > 10 cm | < 3 × 109 | < 2 × 10-24 | < 1.25 × 10-5 |
| Microwave | 1 mm - 10 cm | 3 × 109 - 3 × 1011 | 2 × 10-24 - 2 × 10-22 | 1.25 × 10-5 - 1.2 × 10-3 |
| Infrared | 700 nm - 1 mm | 3 × 1011 - 4 × 1014 | 2 × 10-22 - 3 × 10-19 | 1.2 × 10-3 - 1.8725 |
| Visible Light | 400 nm - 700 nm | 4 × 1014 - 7.5 × 1014 | 3 × 10-19 - 5 × 10-19 | 1.8725 - 3.1208 |
| Ultra-Violet | 10 nm - 400 nm | 7.5 × 1014 - 3 × 1016 | 5 × 10-19 - 2 × 10-17 | 3.1208 - 124.83 |
| X-ray | 0.01 nm - 10 nm | 3 × 1016 - 3 × 1019 | 2 × 10-17 - 2 × 10-14 | 124.83 - 1.25 × 105 |
| Gamma-ray | < 0.01 nm | > 3 × 1019 | > 2 × 10-14 | > 1.25 × 105 |
Sunlight gives 1,361 J/second/m2 at the top of Earth’s atmosphere. Composed (by total energy) of about 50% infrared light, 40% visible light, and 10% ultraviolet light.
The total amount of energy received at ground level from the sun at the zenith is 1,004 watts per square meter, which is composed of 532 watts of infrared radiation, 442 watts of visible light, and 30 watts of ultraviolet radiation.
Starlight gives about 30 ergs/second/m2 at top of Earth’s atmosphere (30 ergs = 3 × 10-6 J), we get 454 million times more energy from the Sun than from starlight).
The total pressure of solar radiation on the earth is 6 × 1013 dynes (6 × 108 N), or 1013 times less than the sun’s gravitational attraction.
Visible starlight energy density = 4.8 × 10-13 erg/cm3 = 0.3 eV/cm3 = 0.3 MeV/m3
The following table shows the varying amounts of power received at the planets in our Solar System. It varies between perihelion (closest distance) and aphelion (farthest distance) which are given as multiples of AU (Astronomical Unit, the average distance of Earth from the Sun).
| Planet | Distance in AU | Power in W/m2 | ||
| Perihelion | Aphelion | Maximum | Minimum | |
| Mercury | 0.3075 | 0.4667 | 14,446 | 6,272 |
| Venus | 0.7184 | 0.7282 | 2,647 | 2,576 |
| Earth | 0.9833 | 1.017 | 1,413 | 1,321 |
| Mars | 1.382 | 1.666 | 715 | 492 |
| Jupiter | 4.950 | 5.458 | 55.8 | 45.9 |
| Saturn | 9.048 | 10.12 | 16.7 | 13.4 |
| Uranus | 18.38 | 20.08 | 4.04 | 3.39 |
| Neptune | 29.77 | 30.44 | 1.54 | 1.47 |
Photon Ships (spacecraft equipped with a sail that use light's pressure to accelerate):
Sail loading (areal density) is an important parameter, which is the total mass divided by the sail area, expressed in g/m2. It is represented by the Greek letter σ.
A sail craft has a characteristic acceleration, ac, which it would experience at 1 AU when facing the sun. It is related to areal density by: ac = 8.25 / σ, in mm/s2 (assuming 90% efficiency).
The lightness number, λ, is the dimensionless ratio of maximum vehicle acceleration divided by the sun's local gravity; using the values at 1 AU: λ = ac / 5.93
| Sail Type | σ | ac (mm/s2) | λ | Size |
| Square sail | 5.27 | 1.56 | 0.26 | 820 m |
| Heliogyro | 6.39 | 1.29 | 0.22 | 15 km |
| Lattice sailer | 0.07 | 117 | 20 | 1 km |
TEMPERATURE
C = Centigrade (or Celsius) • K = Kelvin
English Units:
F = Fahrenheit • R = Rankine
°C = °K - 273.15 = (°F − 32) × 5⁄9 = (°R − 491.67) × 5⁄9
°K = °C + 273.15 = (°F + 459.67) × 5⁄9 = °R × 5⁄9
English Units:
°F = (°C × 9⁄5) + 32 = (°K × 9⁄5) − 459.67 = °R − 459.67
°R = (°C + 273.15) × 9⁄5 = °K × 9⁄5 = °F + 459.67
Freezing point of water (° is not used by Kelvin):
0° C = 273.15 K = 32° F = 491.67° R
Boiling point of water (usually, as below, taken as 100° C, it is actually 99.9839° C):
100° C = 373.15 K = 212° F = 671.67° R
Absolute Zero:
0 K = 0° R = -273.15° C = -459.67° F
Planck Temperature = 1.416 833(85) × 1032 K
| Kelvin | Celsius | Fahrenheit | Rankine | |
| Absolute zero | 0 | −273.15 | −459.67 | 0 |
| Lowest recorded surface temperature on Earth | 184 | −89.2 | −128.6 | 331 |
| Ice melts (at standard pressure) | 273.15 | 0 | 32.00 | 491.67 |
| Triple point of water | 273.16 | 0.01 | 32.018 | 491.688 |
| Average Earth surface temperature | 288 | 15 | 59 | 519 |
| Average human body temperature | 310 | 37 | 98 | 558 |
| Highest recorded surface temperature on Earth | 331 | 58 | 136.4 | 596 |
| Water boils (at standard pressure) | 373.1339 | 99.9839 | 211.97102 | 671.64102 |
| Titanium melts | 1941 | 1668 | 3034 | 3494 |
| The surface of the Sun | 5800 | 5500 | 9900 | 10400 |
| Hot Blue (Type O) Star | 40,273 | 40,000 | 72,032 | 72,492 |
| Center of the Sun | 1.5 × 107 | 2.7 × 107 | ||
| Supernova | 1011 | 1.8 × 1011 | ||
| Created in Laboratory | 4 × 1012 | 7.2 × 1012 | ||
| Big Bang after 10-43 seconds | 1032 | 1032 |
RADIOACTIVITY
Gy = Gray • rad = rad
Ci = Curie • Bq = Becquerel • J = Joule
g = gram • kg = kilogram • s = second
1 Gy = 1 J/kg = 100 rad
1 rad = 100 ergs/g = 0.01 Gray
1 Bq = 1 decay/s = 2.702703 × 10-11 Ci
1 Ci = 3.7 × 1010 decay/s = 3.7 × 1010 Bq
Half-Life: Time taken for one half of a quantity of Radioactive substance to decay.
| # of half-lives elapsed | Fraction remaining | Percentage remaining |
| 0 | 1/1 | 100 |
| 1 | 1/2 | 50 |
| 2 | 1/4 | 25 |
| 3 | 1/8 | 12.5 |
| 4 | 1/16 | 6.25 |
| 5 | 1/32 | 3.125 |
| 6 | 1/64 | 1.563 |
| 7 | 1/128 | 0.781 |
| … | … | … |
| n | 1/2n | 100/(2n) |
| Isotope | Half-life | Approximate Time required for 1 kg of isotope to completely decay |
| Hydrogen-7 | 2.3 × 10-23 sec | 1.84 × 10-21 |
| Boron-17 | 0.00508 sec | 0.4064 sec |
| Carbon-15 | 2.449 sec | 3.2653 min |
| Carbon-11 | 20.334 min | 27.112 hr |
| Vanadium-48 | 15.9735 days | 3.51 years |
| Caesium-134 | 2.0652 years | 165.216 years |
| Plutonium-238 | 87.7 years | 7,016 years |
| Carbon-14 | 5,715 years | 457,200 years |
| Plutonium-239 | 24,110 years | 1,928,800 years |
| Uranium-236 | 23,420,000 years | 1,873,600,000 years |
| Uranium-238 | 4,468,000,000 years | 3.5744 × 1011 years |
| Tellurium-128 | 2.2 × 1024 years | 1.76 × 1026 years |
| Proton (conjectured) | 1032 years | 8 × 1033 years |
EARTH
Radius = 6,371,000 m = 6,371 km = 3,958.756 mi = 20,902,230.9 ft
Circumference (Equatorial) = 40,075,017 m = 40,075.017 km = 24,901.461 mi = 131,479,714.57 ft
Surface Area = 5.10072 × 1014 m2 = 510,072,000 km2 = 196,939,900.2 mi2 = 5.4904 × 1015 ft2 (70.8% of this area is Ocean)
Volume = 1.08321 × 1021 m3 = 3.82532 × 1022 ft3
Mass = 5.97219 × 1024 kg = 1.316643 × 1025 lb
Average density = 5.515 g/cc
Average Land Elevation = 840 m = 2,756 ft
Lowest Point (Dead Sea) = -418 m = 1,371.4 ft
Highest Point (Mount Everest) = 8,848 m = 29,028.9 ft
Ocean mass = 1.35 × 1021 kg = 2.976241 × 1021 lb
Average Ocean Depth = 3,682 meters = 12,080 ft = 2.289 mi
Est. Ocean Volume = 1.332 × 1018 m3 = 4.704 × 1019 mi3
Ocean salinity is 3.598%
Deepest location is Challenger Deep = −10,911.4 m = 35,798.56 ft
Of all water on the Planet:
97.5% is salt water Ocean
2.5% is fresh water, of this fresh water:
68.7% is in the form of ice
29.9% exists as fresh ground waters.
0.26% in lakes, reservoirs and river systems
Atmosphere mass = 5.1480 × 1018 kg = 1.13494 × 1019 lb
Atmospheric Pressure = 101.325 kPa = 1 atm (atmosphere) = 14.69595 psi (lb/in2) = 760 Torr
Average Density of Air at Sea Level = 1.2 kg/m3 = 0.0012 g/cc = 1.2 g/L = 4.3353 × 10-5 lb/in3
Average mass of Water Vapour = 1.27 × 1016 kg = 2.8 × 1016 lb
Air: 78.09% Nitrogen, 20.95% Oxygen, 0.93% Argon, 0.039% Carbon Dioxide, others trace amounts.
Air mass concentrations:
50% is below 5,600 m = 18,373 ft
90% is below 16,000 m = 52,493 ft
99.99997% is below 100,000 m (62.137 mi; 328,084 ft), the Kármán line (here begins “outer space”)
Distance to Sun (i.e., radius of Earth Orbit): 149,597,870,700 m = 92,955,807.2735 mi = 4.9081 × 1011 ft (This is known as the “Astronomical Unit” [abbreviated au or AU]).
The AU in terms of light speed: 499 light-seconds
Average Orbital Velocity = 29.78 km/s = 107,200 km/h = 66,610.99 mi/h
Equatorial Rotation Velocity = 465.1 m/s = 1,674.36 km/h = 1,040.4 mi/h
Equatorial surface gravity = 9.780327 m/s2 = 0.99732 g
Escape velocity =11,186 m/s = 11.186 km/s = 6.9507 mi/s = 36,699.4751 ft/s
MOON
Radius = 1,737,100 m = 1,737 km = 1,079.384 mi = 5,699,146.982 ft
Circumference (Equatorial) = 10,921,000 m = 10,921 km = 6,785.995 mi = 35,830,052.49 ft
Surface area = 3.793 × 1013 m2 = 3.793 × 107 km2 = 1.46448548 × 107 mi2 = 4.083 × 1014 ft2
Volume = 2.1958 × 1019 m3 = 7.754395 × 1020 ft3
Mass = 7.3477 × 1022 kg = 1.619891 × 1023 lb
Average density = 3.3464 g/cc
Atmosphere mass = < 10,000 kg = < 22,000 lb
Atmospheric Pressure = 0.3 nPa = 3 × 10-15 atm = 2.04 × 10-10 psi (lb/in2) = 2.28 × 10-12 Torr
Distance to Earth: 384,400,000 m = 238,855.0863 mi = 1,261,154,855 ft. This distance in terms of light speed: 1.26 light-seconds.
Orbital period = 27.321582 d = 27 d, 7 h, 43 min, 6 s
Synodic period = 29.530589 d = 29 d, 12 h, 44 min, 2.9 s)
Average Orbital Velocity = 1,022 m/s = 3,353.018 ft/s
Equatorial Rotation Velocity = 4.627 m/s = 15.1804 ft/s
Equatorial surface gravity =1.622 m/s2 = 0.1654 g
Escape velocity = 2,380 m/s = 2.38 km/s = 1.4789 mi/s = 7,808.399 ft/s
SUN
Radius = 696,342 km = 432,686.86 mi
Circumference (Equatorial) = 4,379,000 km = 2,720,984.4 mi
Surface area = 6.0877 × 1018 m2 = 6.0877 × 1012 km2 = 2.3505 × 1012 mi2 =6.55275 × 1019 ft2
Volume = 1.412 × 1027 m3 = 4.986431 × 1028 ft3
Mass = 1.9891 × 1030 kg = 4.385215 × 1030 lb
Average density = 1.408 g/cc
Center density = 162.2 g/cc
Surface Temperature = 5,500 °C = 9,900 °F
Core Temperature = 1.5 × 107 °C = 2.7 × 107 °F
Solar Power output = 3.846 × 1033 ergs/second = 3.846 × 1026 Joules/second
Spectral Type = G2V
Absolute Magnitude = +4.83
Apparent Magnitude = −26.74
Pressure at Centre = 2.477 × 1016 Pa = 2.445 × 1011 atm = 3.593 × 1012 psi (lb/in2) = 1.858 × 1014 Torr
Equatorial Rotation Velocity = 1,996.94 m/s = 6,551.655 ft/s
Equatorial surface gravity = 274.0 m/s2 = 27.94 g
Escape velocity = 617,700 m/s = 617.7 km/s = 383.821 mi/s = 2,026,574.8 ft/s
Average distance from Milky Way core = 2.6 × 1020 m = 2.6 × 1017 km = 1.6 × 1017 mi = 27,200 light-years
Galactic period (Galactic “year”) = ~230,000,000 Earth years
Velocity:
around centre of Galaxy: ~220,000 m/s = 220 km/s = 136.7 mi/s = 721,785 ft/s
relative to microwave background: ~370,000 m/s = 370 km/s = 230 mi/s = 1,213,911 ft/s
Angular Diameter from Earth at 1 AU: 1,919 seconds of arc.
| Hydrogen | 73.46% |
| Helium | 24.85% |
| Oxygen | 0.77% |
| Carbon | 0.29% |
| Iron | 0.16% |
| Neon | 0.12% |
| Nitrogen | 0.09% |
| Silicon | 0.07% |
| Magnesium | 0.05% |
| Sulfur | 0.04% |
THE PLANETS
| Name | Eq. Radius FoE | Area FoE | Volume FoE | Mass FoE | Orbital Radius (AU) | Orbital Period yr | Rotation (Earth days) |
| Terrestrial Planets | |||||||
| Mercury | 0.3829 | 0.147 | 0.056 | 0.055 | 0.31–0.47 | 0.24 | 58.64 |
| Venus | 0.949 | 0.902 | 0.866 | 0.815 | 0.72 | 0.62 | −243.02 |
| Earth | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| Mars | 0.532 | 0.284 | 0.151 | 0.107 | 1.52 | 1.8808 | 1.03 |
| Gas Giants | |||||||
| Jupiter | 11.209 | 129.9 | 1321.3 | 317.8 | 5.26 | 11.862 | 0.41 |
| Saturn | 9.4492 | 83.703 | 763.59 | 95.15 | 9.54 | 29.4571 | 0.43 |
| Uranus | 4.007 | 15.91 | 63.086 | 14.536 | 19.229 | 84.323 | −0.72 |
| Neptune | 3.883 | 14.98 | 57.74 | 17.147 | 30.104 | 164.79 | 0.67 |
| Selected Dwarf Planets | |||||||
| Ceres | 0.075 | 0.0056 | 0.0004 | 0.0002 | 2.56–2.98 | 4.60 | 0.375 |
| Pluto | 0.181 | 0.035 | 0.0065 | 0.0022 | 29.8–49.3 | 247.74 | 6.39 |
| Eris | 0.183 | 0.033 | 0.0061 | 0.0028 | 37.9–97.6 | 558.04 | 1.08 |
Mercury:
Equatorial surface gravity = 3.7 m/s2 = 0.38 g
Escape velocity = 4,250 m/s = 4.25 km/s = 2.641 mi/s = 13,943.6 ft/s
Apparent Magnitude = −2.6 to 5.7
Angular Diameter = 4.5” – 13”
Venus:
Equatorial surface gravity = 8.87 m/s2 = 0.904 g
Escape velocity = 10,360 m/s = 10.36 km/s = 6.437 mi/s = 33,989.5 ft/s
Apparent Magnitude = −4.9 to -3.8
Angular Diameter = 9.7” – 66”
Atmospheric Pressure = 9.2 MPa = 90.8 atm = 1,334.35 psi (lb/in2) = 69,005.7 Torr
Mars:
Equatorial surface gravity = 3.711 m/s2 = 0.376 g
Escape velocity = 5,027 m/s = 5.027 km/s = 3.124 mi/s = 16,492.8 ft/s
Apparent Magnitude = +1.6 to -3.0
Angular Diameter = 3.5” – 25.1”
Atmospheric Pressure = 0.636 kPa = 6.28 × 10-3 atm = 0.092 psi (lb/in2) = 4.77 Torr
Phobos (moon) mass = 9.629 × 1015 kilograms
Deimos (moon) mass = 1.926 × 1015 kilograms
Jupiter:
Equatorial surface gravity = 24.79 m/s2 = 2.528 g
Escape velocity = 59,500 m/s = 59.5 km/s = 36.97 mi/s = 195,209.97 ft/s
Apparent Magnitude = -1.6 to -2.94
Angular Diameter = 29.8” – 50.1”
The four main Moons are: Io, Europa, and Ganymede, and Callisto.
Saturn:
Equatorial surface gravity = 10.44 m/s2 = 1.065 g
Escape velocity = 35,500 m/s = 35.5 km/s = 22.059 mi/s = 116,469.82 ft/s
Apparent Magnitude = +1.47 to -0.24
Angular Diameter = 14.5” – 20.1” (excluding rings)
The two main Moons are: Titan and Rhea.
Uranus:
Equatorial surface gravity = 8.69 m/s2 = 0.886 g
Escape velocity = 21,300 m/s = 21.3 km/s = 13.235 mi/s = 69,881.89 ft/s
Apparent Magnitude = +5.9 to +5.32
Angular Diameter = 3.3” – 4.1”
The five main Moons: Miranda, Ariel, Umbriel, Titania and Oberon.
Neptune:
Equatorial surface gravity = 11.15 m/s2 = 1.14 g
Escape velocity = 23,500 m/s = 23.5 km/s = 14.602 mi/s = 77,099.74 ft/s
Apparent Magnitude = +8.02 to +7.78
Angular Diameter = 2.2” – 2.4”
The two main Moons: Triton and Nereid.
ASTRONOMICAL MISCELLANEOUS
Universe:
Radius = 4.6 × 1010 light-years
13.798 ± 0.037 billion years old (as of 2013)
contains 4.9% ordinary matter, 26.8% dark matter and 68.3% dark energy.
Hubble constant (expansion of Universe) was measured to be 67.80 ± 0.77 (km/s) / Megaparsec.
Estimated 3 × 1023 stars.[2010 study]
Closure density of Universe needed to collapse: 2 × 10-29 g/cc
Density = 9.9 × 10-30 g/cc (on the order of a single hydrogen atom for every 4 m3)
Diameter of a typical galaxy = 30,000 light-years
Diameter of Milky Way = approx. 100,000 light-years
PHYSICAL CONSTANTS USED IN THIS BOOK
Speed of Light in a vacuum: 299,792,458 m/s (186,282.4 mi/s), good approximations: 3 × 108 m/s = 3 × 1010 cm/s
Elementary charge (e.g.. of an electron) = 1.60 × 10-19 Coulomb
Planck constant = 6.62606957(29) × 10-34 Joule-sec
Planck Charge = 1.875545956(41) × 10-8 Coulomb
Electron rest mass = 9.11 × 10-31 kilograms = 0.51 mega-eV
Proton rest mass = 1.67265 × 10-27 kilograms = 938.3 mega-eV
Neutron rest mass = 1.67495 × 10-27 kilograms = 939.6 mega-eV
Avogadro constant = 6.0221413 × 1023 particles per mole
Boltzman constant = 1.3806488 × 10-23 Joules/°K m2 kg/s2 °K
Stefan-Boltzman constant = 5.670373(21) × 10-8 W/m2 °K4
Universal gravitation constant = 6.67384 × 10-11 m3/kg s2
Velocity of sound = 0.349 kilometers/second = 1145 feet/second
Carbon-Carbon bond = 82.6 Kcal/mole = 3.6 eV/bond
Carbon-Carbon double bond = 145.8 Kcal./mole = 6.3 eV/bond
Carbon-Carbon triple bond = 199.6 Kcal./mole = 8.7 eV/bond
FORMULAE
<Also abbreviations for formulae below>
Circumference of a circle = π d = 2 π r
Area of a circle = π r2
Area of a sphere = 4 π r2
Volume of a sphere = 4/3π r3
Equations associated with smooth acceleration:
VF = V0 + at
s = V0t + 1/2at2
t = ( 2s / a )1/2
s = [ ( V0 V ) / 2 ] t
VF2 = V02 + 2as
g = G M / r2
F = G M1 M2 / D2
VESC = ( 2 G M / r )1/2
Kinetic Energy = 1/2mv2
Potential Energy = mgH
Energy to move something through Earth’s gravity
= G ME m ( 1 / RE - 1 / RE+ )
Relativity formulae:
VF = at / ( 1 + ( at / c )2 )1/2
m = mo / ( 1 - v2 / c2 )1/2
Gravitational relativity factor = [ 1 - ( 2GM / c2 r ) ]1/2
E = mc2 (at rest)
E = mc2 / ( 1 + [ v2 / c2 ] )1/2 (moving)
addition of velocities = V1 + V2 / ( 1 + [ V1V2 / c2 ] )
E = hv or hc / L
λ = Vm / υ (when the wave is light Vm = c, the speed of light)
To calculate the energy in a photon use the equation below. "h" is Plancks constant in J-sec and c is in meters per second. Below correcting factors are used to convert Joules to electronvolts and meters to micrometers. Then when the wavelength of the light is specified in micrometers the answer is the Energy in eV:
Eph = hc / λ = hc × (correcting factors) / λ (in µm) = 1.23998 / λ (in µm)
Area of Hexagon: ( 3 s2 √3 ) / 2 (s = side length)
Horizon Calculation: d ≈ 3.57 √h (h is in meters, d comes back in km)
Spherical Cap:
(h = height of cap, a = radius of cap, r = radius of sphere)
Area = 2 π r h or π ( a2 + h2 )
Volume = ( π h / 6 ) ( 3a2 + h2 ) or ( π h2 / 3 )( 3r - h )
ABBREVIATIONS USED IN FORMULAE
π = 3.141592654 (good approximation is 3.1416)
λ = Wavelength
υ = Frequency in Hz (cycles per second)
µm = Micrometers (millionths of a meter)
a = Acceleration (m/s2)
c = Speed of light (299,792,458 m/s , approximations = 3 × 108 m/s = 3 × 1010 cm/s)
d = Diameter of body
D = Distance between bodies
E = Energy in Joules
Eph= Energy of a photon in eV
F = Force in Newtons
g = Local accel. of gravity (m/s2)
G = Universal gravitational constant = 6.67 × 10-11 (using meters & kilograms)
h = Planck’s constant (6.62606957(29) × 10-34 Joule-sec)
H = Height above Earth surface (meters)
L = Wavelength of light (meters)
m0 = Rest mass
M, M1, M2, m = Mass in kg.
ME= Mass of Earth = 5.97219 × 1024 kg
r = Radius
RE = Radius of Earth = 6,371,000 m
RE+ = Distance of object from Earth’s center
s = Distance in meters
t = Time in seconds
VF= Final velocity (m/s)
V0 = Initial velocity (m/s)
VESC= Velocity of escape (m/s)
Vm = Velocity in medium (for light waves this is the speed of light)
SIZES/VOLUMES, ETC., OF INTEREST
| Object | Mass |
| Hydrogen atom | 1.67 × 10-24 g |
| Ping Pong Ball | 2.7 g |
| Tennis Ball | 58 g |
| Cue Ball | 170 g |
| Liter of Water | 1.000028 kg |
| Pyramid of Khufu | 5.23 × 109 kg |
| Object | Size |
| Atomic nucleus radius | around 10-15 m |
| Atom radius | around 10-10 m |
| Cell (typical, cuboidal) | around 2 × 10-5 m |
| Human hair thickness | 0.1 mm |
| Fine Sand grain | 0.25 mm |
| Eye of Needle | 0.44 mm |
| Sugar grain per side (Table Sugar) | 0.5 mm |
| Beer Bottle Cap Diameter | 2.6 cm |
| White Piano Key | 2.3 cm wide (approx.) |
| Ping Pong Ball | 4 cm diam. (radius 2 cm) |
| Cue Ball | 5.27 cm diam. (radius 2.86) |
| Tennis Ball | 6.75 cm diam. (radius 3.375) |
| Football ("Soccer") | 22 cm diam. |
| A4 paper width | 0.21 m |
| A4 paper length | 0.297 m |
| Tennis Court Width | 10.97 m |
| Tennis Court Length | 23.78 m |
| Olympic Pool Width | 25 m |
| Olympic Pool Length | 50 m |
| Football (Soccer) Field Width | 68 m |
| Football (Soccer) Field Length | 105 m |
| Pyramid of Khufu | 147 m |
| Mt. Everest | 8848 m |
| Object | Area |
| Cell (typical, cuboidal, one side) | 4 × 10-10 m2 |
| Sugar grain, 1 side of the grain (Table Sugar) | 0.25 mm2 |
| Beer Bottle Cap | 5.3 cm2 |
| Ping Pong Ball | 50.265 cm2 |
| Cue Ball | 102.79 cm2 |
| Tennis Ball | 143.14 cm2 |
| Top of your head | 258 cm2 |
| A4 paper (one side) | 0.0624 m2 |
| Tennis Court | 260.87 m2 |
| Olympic Pool | 1250 m2 |
| Football (Soccer) Field | 7140 m2 |
| Pyramid of Khufu footprint | 5.3 × 104 m2 |
| Object | Volume (cc and cm3 and ml are equivalent) |
| Atomic nucleus (using radius of 1.2 × 10-13 cm) | 7.24 × 10-39 cc |
| Atom (roughly) | 4.19 × 10-24 cc |
| Cell (typical, cuboidal) | 8 × 10-15 m3 |
| Sugar grain (Table Sugar) | 0.125 mm3 = 1.25 × 10-4 cc |
| Beer Bottle Cap | 3.2 cc |
| Ping Pong Ball | 33.51 cc |
| Cue Ball | 102.75 cc |
| Tennis Ball | 161 cc |
| Bag of Sugar 1 kg | 1200 cc |
| Olympic Pool Volume | 2,500,000 L = 2,500 m3 |
| Pyramid of Khufu | 2,580,000 m3 |
Ratio of volume of atom to volume of nucleus = 5.8 × 1014
Pyramid of Khufu at Giza Egypt: Consisting of 2,300,000 blocks each weighing, at a minimum, of 2,270 kg = 2.5 short ton
Estimated that the average cell contains 1014 atoms.
Moderate Snow Storm (personal measurement): about 1,550 snowflake/second/m2 (equivalent to 1 snowflake/second/in2)
Sand
--------------------------------
> 4mm (gravel)
2 to 4mm (fine gravel)
0.5 to 2mm (coarse sand)
0.25 to 0.5mm (medium)
0.15 to 0.25 mm (fine sand)
0.1 to 0.15 mm (very fine)
< 0.1 mm (silt-clay)
