Astronomy 161:
An Introduction to Solar System Astronomy
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Lecture 2: Astronomical Numbers
Key Ideas:
Scientific Notation
- Express numbers using powers of 10
- Standard Prefixes (kilo-, mega-, etc.)
Metric System of Units
- Units of Length
- Units of Time
- Units of Mass
- Weight versus Mass
Big Numbers
Astronomical Numbers are, well, Astronomical!
Examples:
- Average distance of the Earth from the Sun: 149,597,900 kilometers
- Mass of the Sun: 1,989,000,000,000,000,000,000,000,000,000 kilograms
- Age of the Earth: 4,550,000,000 years (4.55 Billion years)
Other big numbers, while not "astronomical" for comparison:
- Number of OREO cookies sold to date: 490,000,000,000
[source: Nabisco]
- US National Debt: $13,464,896,653,374.11 (as of 2010 Sept 20).
[source: U.S.
Treasury Department, Bureau of the Public Debt].
Because the numbers we will encounter in this course range from the very
larger to the very small, we need a way of dealing with such numbers
sensibly so we don't go crazy counting zero's, risking factor of 10 or
greater mistakes at every turn.
Scientific Notation
Scientific Notation is a compact and convenient way of expressing very
large and very small numbers using powers of 10. You've all probably
encountered scientific notation before. I hope the examples below are
reminders for those who haven't used it in a while. If you need a
detailed review, please see Section 1-6 of Kaufmann &
Freedman.
Examples of Scientific Notation:
- The Mass of the Sun:
- 1,989,000,000,000,000,000,000,000,000,000 kilograms = 1.989x1030 kilograms
- The Size of a Hydrogen Atom:
- 0.0000000000106 meters = 1.06x10-11 meters
In each case, use of scientific notation eliminates most of the zeros
which are just place-holders for factors of ten, letting us concentrate
on the significant figures. In a field such as astronomy that deals
with scales ranging from subatomic particles to the entire universe,
this notation is a great simplification!
The Metric System
Astronomers use the Metric System exclusively. The basic units of the
metric system are:
- Length in Meters
- Mass in Kilograms
- Time in Seconds
The metric system is also known as the International System of Units (or
"SI" for "Systeme Internationale"). At present, only the United States,
Liberia & Myanmar (aka Burma) have not adopted SI units as their
primary system of units. For more information on the SI units, see the SI Units page at the US National Institute of Standards &
Technology (NIST).
Standard Prefixes
In everyday use, we often add a prefix to the base unit to indicate
common powers of ten. A brief listing of some of the more common is
given below:
Factor |
Prefix |
Examples |
103 |
kilo- |
kilogram, kilometer, kilobyte |
106 |
mega- |
megawatt, megayear, megabyte, megaton |
109 |
giga- |
gigayear, gigaton, gigabyte |
1012 |
tera- |
terawatt, terabyte |
10-2 |
centi- |
centimeter |
10-3 |
milli- |
millimeter, millisecond, milliliter |
10-6 |
micro- |
microsecond, micron |
10-9 |
nano- |
nanosecond, nanometer |
Common Examples
- Length:
- 1 kilometer = 103 meters (1000 meters)
- 1 centimeter = 10-2 meters (1/100th of a meter)
- 1 millimeter = 10-3 meters (1/1000th of a meter)
- 1 micron = 10-6 meters (short for "micrometer")
- Time:
- 1 nanosecond = 10-9 s (1 billionth of a second)
- 1 Gigayear = 109 years (1 Billion years)
- 1 Megayear = 106 years (1 Million years)
Units of Length
The basic unit of length is the meter (m)
- Traditional Definition:
- 1 ten-millionth the distance from the North Pole to the Equator of the
Earth.
- Modern Definition:
- The distance traveled by light in a vacuum
in 1/299792458th of a second.
We will most commonly encounter meters and kilometers.
Astronomical Units of Length
Meters and kilograms are fine for most terrestrial applications, but
when we start talking about the enormous distances between the planets,
or between stars and galaxies, we need to define special units to keep
the numbers from getting too big. The most important of these for our
purposes in this course are:
The Astronomical Unit (AU):
1 AU is the Mean Distance from the Earth to the Sun:
- 1 AU = 1.496x108 kilometers
The AU is used for expressing the distances between planets.
In round numbers, you can use "1 AU = 150 Million km" for the purposes
of this class.
The Light Year (ly):
1 Light Year (ly) is the Distance Traveled by Light in 1 Year:
- 1 ly = 9.46x1012 kilometers
The light year is used for expressing the distances between stars.
Space is BIG
For example, what is the distance between the Earth and:
- The Moon: 384,000 kilometers
- The Sun: 1 AU (149,600,000 km)
- Alpha Centauri (nearest star): 4.2 light years (266,000 AU)
- Center of the Milky Way Galaxy: 26,000 light years (1.65x109 AU)
As you can see, if you only use kilometers or meters, the numbers would get
out of hand very fast.
Units of Time
The basic unit of time is the second (s):
- Traditional Definition:
- 1/86400th of the mean solar day.
- Modern Definition:
- 9,192,631,770 oscillations of a 133Cesium atomic clock.
We will usually measure time in units of seconds, minutes, hours, and
years.
Units of Mass
The basic unit of mass is the kilogram (kg):
- Traditional Definition:
- 1 kilogram is the mass of 1 liter of pure water.
- Modern Definition:
- 1 kilogram = mass of the international prototype of the kilogram.
- This is a piece of platinum-iridium alloy kept at the
International
Bureau of Weights & Measures in Sèvres, France.
We will be most often use masses in kilograms.
Mass versus Weight
Mass and Weight are NOT the same!
Strictly speaking:
- Mass is the amount of matter in an object.
- Weight is the force of gravity on an object.
Of the two, Mass is the more fundamental quantity.
- Mass is the same everywhere regardless of the strength of the local
gravitational field
- Weight depends on the strength of the local gravity field (i.e.,
it is different on the Earth and Moon for the same mass.)
Mass and Weight in Everyday Units
- Metric:
- Mass in kilograms
- Weight in Newtons
- English Units:
- Mass in slugs
- Weight in pounds
In commercial and everyday usage, "weight" is synonymous with "mass",
and the metric unit of the kilogram is used. In engineering and
physics, however, we need to be careful to make the distinction, and so
weight takes units of Netwons, and mass units of kilograms.
This double meaning often causes confusion: a subtlety not often
appreciated is that the conversion between pounds (weight) and kilograms
(mass) that you can find in tables of weights and measures is only
strictly true at the surface of the earth (and then only for an assumed
mean gravitational force at the sea-level)!
On the Moon or Mars, where the gravity is different at the surface, the
conversion is also different!
Updated: 2010 September 20, Todd A. Thompson
Copyright © Richard
W. Pogge, All Rights Reserved.