## The Universe in Perspective

Appendix A: Reference

"To acquire knowledge, one must study; but to acquire wisdom, one must observe." - Marilyn vos Savant 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).

Metric Prefixes

Length

Area

Volume

Time

Angles

Mass

Force

Density

Pressure

Energy

Energy Comparison

Power

Light

Temperature

Earth

Moon

Sun

The Planets

Astronomical Miscellaneous

Physical Constants Used In This Book

Formulae

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

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.

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):

Energy Comparisons
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) × 59 = (°R − 491.67) × 59

°K = °C + 273.15 = (°F + 459.67) × 59 = °R × 59

English Units:

°F = (°C × 95) + 32 = (°K × 95) − 459.67 = °R − 459.67

°R = (°C + 273.15) × 95 = °K × 95 = °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

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

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)

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