ASTRONOMICAL NUMBERS

Four strategies that astronomers use to deal with vast array of numbers:1. Metric system2. Scientific notation3. Special Units4. Approximation

METRIC SYSTEM• Introduced in 1791• Allows easier conversion between larger and smaller

units of measure• E.g. meters, seconds, kilograms• Advantage: different units are related by factors of 10,

making it simpler to convert between different units• Exponent – it indicates how many times we multiple a

quantity by itself

METRIC PREFIXESPower of Ten Exponential Notation Metric Prefix Abbreviation

septillion 1024 yotta Ysextillion 1021 zetta Zquintillion 1018 exa Equadrillion 1015 peta Ptrillion 1012 tera Tbillion 109 giga Gmillion 106 mega Mthousand 103 kilo khundred 102 hecto hten 101 deca datenth 10-1 deci dhundredth 10-2 centi cthousandth 10-3 milli mmillionth 10-6 micro billionth 10-9 nano ntrillionth 10-12 pico pquadrillionth 10-15 femto fquintillionth 10-18 atto asextillionth 10-21 zepto zseptillionth 10-24 yocto y

3 Fundamental Units required in physical measurement length mass timeMKS system – stands for meter, kilogram and second• liter – unit of volume• density (mass per volume)

-- e.g. a planet with a density of 1 kg versus one with 5 kg

MKS UnitQuantity Metric Unit MKS Equivalent English Equivalent

length meter m 3.28 feetmass kilogram kg 2.2 pounds (of mass)time second sec (same)area square meter m2 10.76 square feetvolume liter (L) 10-3 m3 1.06 U.S. quartsspeed meters per second m/sec 2.24 miles per houracceleration meters per square

secondm/sec2 3.28 feet per square

seconddensity kilograms per liter 103 kg/m3 0.036 pounds per cubic

inchforce newton (N) kg m/sec2 0.225 pounds (of force)energy joule (J) kg m2/sec2 0.000948 BTUspower watt (W) kg m2/sec3 0.00134horsepower

***BTU – British Thermal Unit

SCIENTIFIC NOTATION• combines the powers-of-10 notation with the particular

value of the number• exponent – indicates how the decimal point has been

moved• general rules:

10A x 10B = 10A+B

10A/10B = 10A-B

SPECIAL UNITS• Represent enormous range of sizes, masses and times light year – the distance light travels in a year parsec – calculated by special geometric technique day – rotation period of Earth year – orbital period of Earth sun’s lifetime – estimated total time sun will generate energy speed of light – through an empty space Earth’s surface gravity – rate at which falling objects accelerate Kiloton of TNT – energy released by a standard 100 ton bomb Sun’s luminosity – energy the sun generates per second

SPECIAL UNITSQuantity Special Unit Abbreviation Metric Equivalent

Length Earth’s radiusSun’s radiusAstronomical unitLight-yearParsec

R+

R.AU ly

pc

6.37 x 106 m6.97 x 108 m1.50 x 1011 m9.46 x 1015 m3.09 x 1016 m

Mass Earth’s massSun’s mass

M+

M.5.97 x 1024 kg1.99 x 1030 kg

Time DayYearSun’s lifetime

dayyr t.

8.64 x 104 sec3.16 x 107 sec

3.16 x 1017 sec

Speed speed of light c 3.00 x 108 m/sec

Acceleration Earth’s surface gravity g 9.81 m/sec2

Energy Kiloton of TNT kt 4.18 x 1012 joules

Power Sun’s luminosity L. 3.86 x 1026 watts

APPROXIMATION • significant digits

e.g. 3 significant digits means that the first two digits are well determined, and the last one is fairly accurate• round off

e.g. 1 parsec = 3.261633 light years