Scientific Notation
The star Proxima Centauri is 23,400,000,000,000 miles
away from Earth. If we could travel in a spaceship at 5,000
miles/hour, it would take over 534,000 years to get there.
Scientific Notation eliminates all unnecessary place holders
by making use of powers of 10
E.g.
2000 = 2 x 103
The star Proxima Centauri is 2.34 x 1013 miles away from
Earth. If we could travel in a spaceship at 5 x 103
miles/hour, it would take over 5.34 x 105 years to get there.
How to Write a Number in Scientific Notation
Distance to Proxima Centauri = 2.34 x 1013 miles
Scientific notation is a mantissa multiplied by the appropriate power of ten (10)
Step 1: Find the mantissa by moving the decimal so that there is only
one digit to the left and two to the right (eliminate unnecessary digits).
7,180,000 = 7.18 x 106
0.00942 = 9.42 x 10-3
Step 2: Multiply by the appropriate power of 10:
• when moved to the left, power = + number of places moved
• when moved to the right, power = - number of places moved
Measurement Systems
Every measurement consists of a value and a unit
It is 215 miles from Boston to New York City
Having one system of units allows everyone to be on the same page
A measurement system needs a standardized basis and should
be easy to convert measurements to different scales
The metric system is both the scientific standard and the world
standard (including U.S. though the British Imperial System is
use in everyday experience)
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The Metric System
Seven basic properties of nature are identified within the SI System and
each has an assigned base unit.
Base Unit
Basic Physical Property
Distance
meter (m)
Mass
kilogram (kg)
Time
second (s)
Temperature
Kelvin (K)
Electric Current
Ampere (A)
Amount of a Substance
Mole (mol)
Intensity of Light
Candela (cd)
Other Units of Measure
Velocity (v) – how fast something is moving
Base Unit: meters-per-second (m/s)
Acceleration (a) – rate something changes velocity
Base Unit: meters-per-square-second (m/s2)
Force (F) – push or a pull on an object
Base Unit: Newton (N)
Luminosity (L) – light energy emitted over time
Base Unit: Watts (W)
Extension of Base Units Within Metric System
Conversion Factor
Gigameter (Gm)
109 m
Megameter (Mm)
106 m
Kilometer (km)
Base Unit
1000 m
Hectometer (Hm)
100 m
Decameter (Dm)
10 m
Meter (m)
Decimeter (dm)
1m
0.1 m
Centimeter (cm)
0.01 m
Millimeter (mm)
0.001 m
Micrometer (µm)
10-6 m
Nanometer (nm)
10-9 m
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Conversion Between Different Systems
Problem: Convert 26.1 miles to kilometers
• Set up a proportion using the proper conversion factors:
1 mile = 1.6 km
x km
=
26.1 miles
1.6 km
1 miles
• Cross multiply:
x · (1) km = 1.6 · 26.1 miles
• Solve for unknown:
x = 41.76 km
Using a Ruler
Measure the length of the double ended arrow.
cm
1
2
3
4
5
6
11
7
8
12
9
10
11
12
13
14
13
cm
Length of the arrow = 11.73576498 cm
Read the ruler to the nearest millimeter (1 mm = 0.1 cm)
Correct answers will have leeway of 1 mm (0.1 cm)
Basic Algebra Review
Substitution Method
Insert known values into an equation and calculate the value for the desired unknown
Determine the value of y if x = 4.
Determine the value of y if x = 3.2 and z = 1.4
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Basic Algebra Review
Inverse Operations
To get an unknown value by itself, apply inverse operations to both sides of an equation.
The primary inverse operations are as follows:
Addition
Subtraction
Multiplication
Division
Raising to a Power
Taking a Root
Determine the value of y
Add 7 to both sides
Multiply both sides by 4
Take the square root of both sides
Data Analysis Using a Graph
Pressure (psi)
70
Depth (ft)
Pressure (psi)
20
24
40
31
60
43
80
49
100
62
50
30
20
40
60
80
100
Depth (ft)
To get the rate at which the pressure increases with depth:
(1) Draw in a line that fits the data points the best
(2) Get the coordinates of two arbitrary points on the line
P1 = (13, 20)
P2 = (90, 54)
(3) Use the coordinates to find the slope of the line
Comparing Measurements
Two measurements can be compared by using subtraction
or ratios
Compare the size of the Earth (Diameter = 12,756 km)
to the size of Venus (Diameter = 12,118 km)
Diameter of Earth - Diameter of Venus = 12,756 - 12,118 = 638 km
(The Earth is 638 km larger than Venus)
For many cases in astronomy, subtraction is not very useful
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Comparing Measurements
Compare the distance between Earth and the Sun
(150,000,000 km) to the distance from Earth to the star,
Sirius (81,700,000,000,000 km)
(Earth-Sirius distance) - (Earth-Sun Distance)
(81,700,000,000,000 km) - (150,000,000 km) = 81,699,850,000,000 km
Sirius is 81,699,850,000,000 km further from Earth
than the Sun.
Ratios
We use a ratio to see “how many times larger” one
measurement is compared to another
(Distance from Earth to Sirius)
(Distance from Earth to the Sun)
81,700,000,000,000 km
150,000,000 km
=
8.17 x 1013 km
1.50 x 108 km
= 5.45 x 105
Sirius is 545,000 times further from Earth than the Sun
Astronomical Measurements
Astronomers use more accessible dimensions to visualize larger scales
Astronomical Unit: the average Earth-Sun distance (150 million km)
- distances within star-planet & star-star systems
Light-year (LY): the distance light travels in a year (9.5 trillion km)
- nearest star is Proxima Centauri @ 4.3 LY
- “solar neighborhood” ~ few thousand LY
- diameter of our Galaxy ~ 100,000 LY
- nearest major galaxy (M31) ~ 2.5 Million LY
- “diameter” of observable universe ~ 93 Billion LY
On small scales, the distance to an object in light-years provides the
“look-back” time
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