CHAPTERS 2, 3 & 4: SPACE, TIME AND MATTER
Recall that the physical world consists of space, time,
matter and energy. Since formulas for energy are
derived from the other three, we focus for now on space
(Chapter 2), time (Chapter 3) and matter (Chapter 4).
CHAPTER 2: SPACE
“Space” can be 1-dimensional (i.e. “length”), 2dimensional (i.e. “area”, with dimensions length2) or 3dimensional (i.e. “volume”, with dimensions length3). It
follows that as relative size increases by a factor k, area
grows at a rate of k2 and volume grows at a rate of k3.
Expansion
Factor k
1
2
3
Length
Area
Volume
L
2L
3L
A
4A
9A
V
8V
27V
SCIENTIFIC NOTATION AND ORDER OF
MAGNITUDE
A number is in scientific notation if it expressed with one
digit to the left of the decimal, and followed by an
appropriate power of 10.
The order of magnitude of a number is its associated
power of 10.
e.g. The radius of the Earth is about 6,380,000 m.
In scientific notation, this is 6.38  106 m,
so the order of magnitude is 106 m.
e.g. The mass of the Earth is about
5,980,000,000,000,000,000,000,000 kg.
In scientific notation this is 5.98  10__ kg,
so the order of magnitude is 10__ kg.
e.g. Our “Earth day” consists of exactly
24 hr  60 min/hr  60 s/min = 86,400 s.
In scientific notation this is ______  10_ s,
so the order of magnitude is 10_ s.
e.g. One liter (l) contains exactly 1,000 ml or 1,000 cm3.
But 1 cm = 0.01 m (the meter is the standard unit
of length), i.e. (1 cm)3 = (0.01 m)3 = 0.000001 m3.
Hence, 1 l = 1,000 cm3 = 1,000(0.000001) m3 = 0.001
m3. In scientific notation this is 1  10–3 m3,
so the order of magnitude of 1 liter is 10–3 m3.
e.g. The wavelength of “sodium yellow” light is about
590 nanometers (nm). But 1 nm = 10__ m, i.e. the
wavelength of “sodium yellow” is 590  10__ m.
In scientific notation this is ____  10__ m,
so the order of magnitude is 10__ m.
SCIENTIFIC NOTATION ON A CALCULATOR
On a scientific calculator, numbers in scientific notation
(e.g. 5.98  1024) may typically be entered as follows:
1. enter the decimal portion of the number (e.g.
“5.98”);
2. locate and press the “exponent button” (usually
labelled “Exp” or “EE”); and
3. enter the appropriate power of 10 (e.g. “24”),
including the negative sign if required.
Calculations involving several different numbers in
scientific notation can easily be carried out.
e.g. Use your calculator to determine the average density
of the Earth.
a) find the volume V of the Earth using
4 3
V  r
3
i) enter the radius r = 6.38  106;
ii) press “x3” and “=” to determine r3;
iii) press “”, “” and “=” to find r3;
iv) press “”, “4” and “=” to find 4r3;
v) press “”, “3” and “=” to find V; and
record to 2 decimals.
Volume V =
b) find the density  = m/V (“ρ” is the Greek letter
“rho”, often used for volume densities)
i) enter the Earth’s mass m = 5.98  1024 (in
kg);
ii) press “”, enter the recorded volume V (in
m3), press “=” and record the density  to
the nearest kg/m3.
Density ρ =
Compare this density with those found in the textbook in
Table 2.1 (p. 27)!
EXPONENTIAL SCALES
An exponential scale may be used to compare similar
quantities (e.g. lengths, areas, volumes, masses, times,
etc) which range widely in size from extremely small to
very large. This variation is usually displayed by
employing orders of magnitude. (See the example on p.
23 of the text.)
CO-ORDINATES AND GRIDS
Points in space can be located using a system of coordinates and grids.
Locally, the Earth seems reasonably flat, so a “flat grid”
(of so-called Cartesian co-ordinates) may be used. Any
roadmap provides a familiar example of this.
Because the Earth is in fact (nearly) spherical, global
locations have to be recorded differently. Hence, we use
a “polar grid” with angular co-ordinates which we call
“latitude” and “longitude”.
“Latitude” is an angle measured north or south of the
equator. Hence any point on the equator has latitude 0,
while the north and south poles are found at 90 N and
90 S. (Surprisingly, North Bay isn’t as far “north” as
you might think, with a latitude of 46 N, barely over
half-way between the equator and the north pole!)
“Longitude” is an angle measured east or west of
Greenwich, England (whose longitude was chosen to be
0). Unlike lines of latitude which are equally-spaced,
longitudinal lines are farthest apart at the equator, and
approach one another at both poles. Since the Earth
spins once (completing a 360 rotation) every 24 hours,
there are 24 “time zones” located 15 apart at the
equator (24 timezones  15 degrees/timezone = 360).
North Bay’s longitude is roughly ____.
Another polar grid, called the “celestial sphere” can be
imagined to exist directly above the Earth in all
directions, and can be used to locate astronomical bodies
(planets, stars, the center of our own Milky Way galaxy,
other galaxies, etc.). We won’t need to concern ourselves
with this co-ordinate system in this course, however.
THE EXPONENTIAL SCALE OF DISTANCE
If you skim through pages 36 – 73 of the text, you will
experience the range of distances associated with the
universe as we presently theorize it to be. These
distances are all expressed in terms of their order of
magnitude (or power of 10) in meters.
Some highlights:
10-15 m size of “quarks” (more on these later)
10-14 m diameter of the largest atomic nuclei (more
later)
10-10 m diameter of an atom (more later)
10-9 m size of large “simple molecule” (more later)
10-8 m size of “complex molecule” (e.g. DNA)
10-4 m size of a single plant or animal cell
100 m height of a person, length of a car
101 m width of a house, height of an apartment
building
102 m length of a soccer field, circumference of a track
103 m size of a university campus or typical
neighbourhood
104 m size of a small city, cruising height of
commercial jet
105 m height of space station, distance from NB to TO
106 m radius of the Earth
107 m diameter or circumference of the Earth
1011 m Earth – Sun distance (1 AU = 1.50  1011 m)
1012 m diameter of the solar system
1016 m distance to “nearest” stars (1 LY = 9.46  1015
m)
1021 m diameter of our “Milky Way” galaxy
1026 m size of the (known) universe (10 – 15 billion LY!)
The “frontier” of the size of the universe is continually
being pushed, and has frequently changed as better
telescopes and measuring techniques are developed.