The Solar System

604 APPENDIX A

Introduction

The metric system is used worldwide as the system of units,
not only in science but also in engineering, business, sports, and
daily life. Developed in 18th-century France, the metric system
has gained acceptance in almost every country in the world
because it simplifi es computations.
A system of units is based on the three fundamental units for
length, mass, and time. Other quantities, such as density and force,
are derived from these fundamental units. In the English (or British)
system of units (commonly used only in the United States, Tonga,
and Southern Yemen, but, ironically, not in Great Britain) the funda-
mental unit of length is the foot, composed of 12 inches. Th e metric
system is based on the decimal system of numbers, and the funda-
mental unit of length is the meter, composed of 100 centimeters.
Because the metric system is a decimal system, it is easy to
express quantities in larger or smaller units as is convenient. You
can give distances in centimeters, meters, kilometers, and so on.
Th e prefi xes specify the relation of the unit to the meter. Just as
a cent is 1/100 of a dollar, so a centimeter is 1/100 of a meter. A
kilometer is 1000 m, and a kilogram is 1000 g. Th e meanings of
the commonly used prefi xes are given in ■ Table A-1.

The SI Units

Any system of units based on the decimal system would be easy
to use; but, by international agreement, the preferred set of units,
known as the Système International d’Unités (SI units) is based on
the meter, kilogram, and second. Th ese three fundamental units
defi ne the rest of the units, as given in ■ Table A-2.
Th e SI unit of force is the newton (N), named after Isaac
Newton. It is the force needed to accelerate a 1 kg mass by 1 m/s^2 ,
or the force roughly equivalent to the weight of an apple at Earth’s
surface. Th e SI unit of energy is the joule (J), the energy produced
by a force of 1 N acting through a distance of 1 m. A joule is
roughly the energy in the impact of an apple falling off a table.

Exceptions

Units can help you in two ways. Th ey make it possible to make
calculations, and they can help you to conceive of certain quanti-
ties. For calculations, the metric system is far superior, and it is
used for calculations throughout this book.
Americans commonly use the English system of units, so for
conceptual purposes this book also expresses quantities in English

units. Instead of saying the average person would weigh 133 N on

the moon, it might be more helpful to some readers for that weight

to be expressed as 30 lb. Consequently, this text commonly gives

quantities in metric form followed by the English form in parenthe-

ses: Th e radius of the moon is 1738 km (1080 mi).

In SI units, density should be expressed as kilograms per

cubic meter, but no human hand can enclose a cubic meter, so

that unit does not help you grasp the signifi cance of a given den-

sity. Th is book refers to density in grams per cubic centimeter. A

gram is roughly the mass of a paperclip, and a cubic centimeter

is the size of a small sugar cube, so you can easily conceive of a

density of 1 g/cm^3 , roughly the density of water. Th is is not a

bothersome departure from SI units because you will not have to

make complex calculations using density.

Conversions

To convert from one metric unit to another (from meters to

kilometers, for example), you have only to look at the prefi x.

However, converting from metric to English or English to metric is

more complicated. Th e conversion factors are given in ■ Table A-3.

Appendix A

Units and Astronomical Data

■ Table A-1 ❙ Metric Prefi xes

Prefi x Symbol Factor

Mega M 106

Kilo k 103

Centi c 10 ^2

Milli m 10 ^3

Micro μ 10 ^6

Nano n 10 ^9

units. Instead of saying the average person would weigh 1 33 N on

■ Table A-2 SI (Système International) Metric Units

Quantity SI Unit

Length

Mass

Time

Force

Energy

Meter (m)

Kilogram (kg)

Second (s)

Newton (N)

Joule (J)