Useful Measures of Distance

A kilometer is a thousand meters (see the table "International System Prefixes"), and a light-year is the distance light travels in a vacuum during one year (exactly 299,792,458 m/sec, but commonly rounded to 300,000,000 m/sec). A light-year, therefore, is the distance that light can travel in one year, or:

299,792,458 m/sec x 60 sec/min x 60 min/hr x 24 hr/day x 365 days/yr = 9.4543 3 1015 m/yr.

For shorter distances, some astronomers use light minutes and even light seconds. A light minute is 17,998,775 km, and a light second is 299,812.59 km.The nearest star to Earth, Proxima Centauri, is 4.2 light-years away from the Sun.The next, Rigil Centaurs, is 4.3 light-years away.

An angstrom (10-10m) is a unit of length most commonly used in nuclear or particle physics. Its symbol is A.The diameter of an atom is about one angstrom (though each element and isotope is slightly different).

An astronomical unit (AU) is a unit of distance used by astronomers to measure distances in the solar system. One astronomical unit equals the average distance from the center of the Earth to the center of the Sun.The currently accepted value, made standard in 1996, is 149,597,870,691 meters, plus or minus 30 meters.

One kilometer equals 0.62 miles, and one mile equals 1.61 kilometers.

The following table gives the most commonly used of the units derived from the fundamental units above (there are many more derived units not listed here because they have been developed for specific situations and are little-used elsewhere; for example, in the metric world, the curvature of a railroad track is measured with a unit called "degree of curvature," defined as the angle between two points in a curving track that are separated by a chord of 20 meters).

Though the units are given in alphabetical order for ease of reference, many can fit into one of several broad categories: dimensional units (angle, area, volume), material properties (density, viscosity,

DERIVED UNITS

Unit symbol

Measurement

(derivation)

Comments

acceleration

unnamed

(m/sec2)

angle

radian

One radian is the angle centered in a circle that

rad

includes an arc of length equal to the radius. Since

(m/m)

the circumference equals two pi times the radius, one

radian equals 1/(2 pi) of the circle, or approximately

57.296°.

steradian

The steradian is a unit of solid angle. There are four pi

sr

steradians in a sphere. Thus one steradian equals about

(m2/ m2)

0.079577 sphere, or about 3282.806 square degrees.

angular velocity

unnamed

(rad/sec)

area

unnamed

(m2)

density

unnamed

Density is mass per volume. Lead is dense, styrofoam

(kg/m3)

is not. Water has a density of one gram per cubic

centimeter or 1,000 kilograms per cubic meter.

electric charge or

coulomb

One coulomb is the amount of charge accumulated

electric flux

C

in one second by a current of one ampere. One

(A-sec)

coulomb is also the amount of charge on 6.241506 X 1018

electrons.

electric field

unnamed

Electric field strength is a measure of the intensity of an

strength

[(kg-m)/(sec3-A)

electric field at a particular location. A field strength of

= V/m]

one V/m represents a potential difference of one volt

between points separated by one meter.

electric potential,

volt

Voltage is an expression of the potential difference in

or electromotive

V

charge between two points in an electrical field. Electric

force (often called

[(kg-m2)/(sec3-A)

potential is defined as the amount of potential energy

voltage)

= J/C = W/A]

present per unit of charge. One volt is a potential of

one joule per coulomb of charge. The greater the

voltage, the greater the flow of electrical current.

Unit symbol

Measurement

(derivation)

Comments

energy, work, or

joule

(= kg-mVsec2)]

electron volt

The electron volt, being so much smaller than the

eV

joule (one eV= 1.6 x I0-17 J), is useful for describing small systems.

force

newton

This unit is the equivalent to the pound in the English

N

system, since the pound is a measure of force and not

(kg-m/sec2)

mass.

frequency

hertz

Frequency is related to wavelength as follows: kilohertz x

Hz

wavelength in meters = 300,000.

(cycles/sec)

inductance

henry

Inductance is the amount of magnetic flux a material pro

H

duces for a given current of electricity. Metal wire with an

(Wb/A)

electric current passing through it creates a magnetic field; different types of metal make magnetic fields with different strengths and therefore have different inductances.

magnetic field

unnamed

Magnetic field strength is the force that a magnetic field

strength

(A/m)

exerts on a theoretical unit magnetic pole.

magnetic flux

weber

The magnetic flux across a perpendicular surface is the

Wb

product of the magnetic flux density, in teslas, and the

[(kg-m2)/(sec2-A)

surface area, in square meters.

= V-sec]

magnetic flux

tesla

A magnetic field of one tesla is strong: The strongest

density

T

artificial fields made in laboratories are about 20 teslas,

[kg/(sec2-A) =

and the Earth's magnetic flux density, at its surface, is

Wb/m2]

about 50 microteslas (^T). Planetary magnetic fields are sometimes measured in gammas, which are nanoteslas (I0-9 teslas).

momentum, or

unnamed

Momentum is a measure of moving mass: how much

impulse

[N-sec (= kg •

mass and how fast it is moving.

m/sec)]

(continues)

DERIVED UNITS (continued)

Unit symbol

Measurement

(derivation)

Comments

power

watt

Power is the rate at which energy is spent. Power can be

W

mechanical (as in horsepower) or electrical (a watt is

[J/s (= (kg-

produced by a current of one ampere flowing through an

m2)/sec3)]

electric potential of one volt).

pressure,

pascal

The high pressures inside planets are often measured in

or stress

Pa

gigapascals (I09 pascals), abbreviated GPa. ~I0,000 atm =

(N/m2)

one GPa.

atmosphere

The atmosphere is a handy unit because one atmosphere is

atm

approximately the pressure felt from the air at sea level on

Earth; one standard atm = 101,325 Pa; one metric atm = 98,066

Pa; one atm ~ one bar.

radiation per unit

gray

The amount of radiation energy absorbed per kilogram of

mass receiving it

(J/kg)

mass. One gray = 100 rads, an older unit.

radiation

sievert

This unit is meant to make comparable the biological effects

(effect of)

Sv

of different doses and types of radiation. It is the energy of

radiation received per kilogram, in grays, multiplied by a

factor that takes into consideration the damage done by the

particular type of radiation.

radioactivity

becquerel

One atomic decay per second

(amount)

Bq

curie

The curie is the older unit of measure but is still

Ci

frequently seen. One Ci = 3.7 X I010 Bq.

resistance

ohm

Resistance is a material's unwillingness to pass electric current.

O

Materials with high resistance become hot rather than allowing

(V/A)

the current to pass and can make excellent heaters.

thermal

unnamed

This unit is per degree, measuring the change in volume of a

expansivity

(/°)

substance with the rise in temperature.

vacuum

torr

Vacuum is atmospheric pressure below one atm (one torr =

1/760 atm). Given a pool of mercury with a glass tube

standing in it, one torr of pressure on the pool will press

the mercury one millimeter up into the tube, where one

standard atmosphere will push up 760 millimeters of mercury.

Unit symbol

Measurement

(derivation)

Comments

(m/sec)

viscosity

unnamed

Viscosity is a measure of resistance to flow. If a force of

[Pa-sec (= kg/

one newton is needed to move one square meter of the

(m-sec))]

liquid or gas relative to a second layer one meter away at a speed of one meter per second, then its viscosity is one Pa^s, often simply written Pa^s or Pas. The cgs unit for viscosity is the poise, equal to O.lPa s.

volume

cubic meter (m3)

thermal expansivity), properties of motion (velocity, acceleration, angular velocity), electrical properties (frequency, electric charge, electric potential, resistance, inductance, electric field strength), magnetic properties (magnetic field strength, magnetic flux, magnetic flux density), and properties of radioactivity (amount of radioactivity and effect of radioactivity).

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