__An Introduction__

(This course is a subset of www.physicsphenomena.com the web site devoted to physics and related sciences and engineering)

In this course you, the student, will have the opportunity to learn about the science of astronomy which is a subset of the science of physics. You will explore:

1. The scientific skills, tools, and processes that astronomers
use to study our universe.

2. The motion of the earth and how it affects the environment
and what we see.

3. The motion of the moon and how it produces eclipses
and phase changes over time.

4. The laws Kepler defined explaining planetary motion
and the law of gravity defined by Newton.

5. The solar system with its "9" planets, moons, asteroids,
and comets.

6. The nature and properties of light, optics, and the
use of telescopes to explore the heavens.

7. The electromagnetic spectrum (of Light) and how it
is used to study the universe.

8. The study of our sun, other stars, galaxies, black
holes, and other things in the universe.

9. The study of cosmology and the "big bang" theory.

10. The study of space travel and the science of propulsion,
including chemical rockets.

**----------> #1**

"The fundamentals: 'scientific skills, tools, and processes used by astronomers' ".

1. Measurement in the science of Astronomy: As in all
of the sciences, today, Astronomy uses the **metric system** as the
basis for all measurements.

a) **The metric system**: A system of measurement that
uses "standardized" definitions of the base unit for each category of measurement

The metric system is measuring system defined in terms of the decimal system. Each category of measurement, such as length, has a base unit of measurement. (i.e. The base unit for length is the meter, the base unit for mass is the gram, the base unit for volume is the liter, and the base unit for time is the second.)

For measurement values larger or smaller than each category's
base unit of measure the metric system uses prefixes. The more common prefixes
are:

Prefix | Symbol | Value (x base unit) | Value (x base unit) |

Tera | T | 1 x 10^12 | 1,000,000,000,000 |

Giga | G | 1 x 10^9 | 1,000,000,000 |

Mega | M | 1 x 10^6 | 1,000,000 |

Kilo | K | 1 x 10^3 | 1,000 |

hecto | h | 1 x 10^2 | 100 |

deka | da | 1 x 10^1 | 10 |

base unit |
(symbol for unit used) | 1 x 10^0 | 1 |

deci | d | 1 x 10^-1 | 0.1 |

centi | c | 1 x 10^-2 | 0.01 |

milli | m | 1 x 10^-3 | 0.001 |

micro | m | 1 x 10^-6 | 0.000001 |

nano | n | 1 x 10^-9 | 0.000000001 |

pico | p | 1 x 10^-12 | 0.000000000001 |

femto | f | 1 x 10^-15 | 0.000000000000001 |

b) **Fundamental units of measure**: The fundamental
units of measure are the measurements from which all other measurements
are derived. Or to put it another way, all other units of measure are defined
in terms of one or more of these measurements. Here is a list of the fundamental
units of measure.

MEASUREMENT | UNIT | ABBREVIATION |

Length | meter | m |

Time | second | s |

Mass | kilogram | kg |

Electric Current | ampere | A |

Temperature | Kelvin | K |

Amount of Substance | mole | mol |

Luminous Intensity | candela | cd |

c) **Derived units of measure**: The
derived units of measure are all of the units of measure other than the
fundamental units of measure. Derived units of measure are themselves derived
from one or more fundamental units of measure. Some examples of derived
are described here in the following table.

Measurement |
Unit of Measure |
symbol |
Unit(s) it is derived from |
Example |

Area | meter^2 | m^2 | meter | 16 m^2 |

Volume | meter^3 | m^3 | meter | 8 m^3 |

Speed (velocity) | meter / second | m / s | meter & second | 5 m / s |

Acceleration | meter / second^2 | m / s / s | meter & second | 2 m / s / s |

Force | newton | N | Kg, meter, & second | 25 N |

Density | kg / meter^3 | kg / m^3 | Kg & meter | 1.5 Kg / m^3 |

**d) Working with metric measurements:** In any
measurement system it is often necessary to be able to work with more than
one kind of measurement unit while doing math calculations. Units of measurements
are handled and manipulated in calculations by essentially the same rules
used for handling variable symbols. They can be added together, multiplied
by one another, subtracted from each other, and divided by one another,
just as any variable symbols such as x and y. Similarly, other operations,
such as raising measurement values to powers or finding their roots, require
that you treat the measurement units in the same manner as you would any
variable symbol as you do the calculation

--> Rule for addition and subtraction: When adding or subtracting measurements, the units of measure must be the same.

i.e. Two masses, a 5 kg mass and a 10.5 kg mass, are being
added together. These two measurements are have the same unit so the numerical
values can be added resulting in a sum having the same unit as the individual
measurements.

Problem - add masses | Measurements | Operation |

1st mass | 5 kg | addition |

2nd mass | 10.5 kg | sum = mass(1) + mass(2) |

Answer | 15.5 kg |

--> Rule for multiplication and division: When multiplying or dividing measurements, the units do not have to be the same. However, all units, except those that legitimately divide out (sometimes referred to as canceling), must be retained.

i.e. An object travels 3,000 km in a time interval of
15 seconds. Using the equation for speed of an object, v = d / t, calculate
the speed of the object.

Problem - calculate speed | Measurements | operation |

distance | 3,000 m | division |

time | 15 s | speed = distance / time |

Answer | 200 m / s |

--> Other operations: Always perform other math operations, when using measurement unit symbols, as you would any variable symbol values such as x and y. All units must remain in the answer along with the numerical value arrived at, unless they actually divide out, and are legitimately gone from the answer.

i.e. A rectangular shaped object is placed upon a scale and found to have a mass of 25 grams. The dimensions of the object, measured with a ruler, were found to be 5 cm long, 3 cm high, and 2 cm tall. Calculate (1) the volume of the object and (2) the density of the object.

(1) Volume is found by the equation V = L x W x H (length,
width, and height, respectively). so the calculation looks like:

Problem step labels | Problem statements | Comments |

Given statement (G:) | Length is 5 cm, Width is 3 cm, and Height is 2 cm | write what you are given |

Find statement (F:) | Find the volume of the object | write what you are to find |

Equation statement (E:) | V = L x W x H | write the equation |

Substitution Statement (S:) | V = 5 cm x 3 cm x 2 cm | write the substitution of values into the equation |

Answer statement (A:) | V = 30 cm^3 | write the answer |

(2) Density is found by dividing the mass of the object
by its volume. The equation is D = M / V.

Problem step labels | Problem statements | Comments |

Given statement (G:) | Mass is 25 g, Volume is 30 cm^3 | write what you are given |

Find statement (F:) | Find the density of the object | write what you are to find |

Equation statement (E:) | D = M / V | write the equation |

Substitution statement (S:) | D = 25 g / 30 cm^3 | write the substitution of values into the equation |

Answer statement (A:) | D = 0.83 g / cm^3 | write the answer |

*The problem solving format places emphasis on displaying
the solution to a problem in a logical series of steps. This approach emphasizes
critical thinking skills and over time will improve your ability to solve
problems quickly. Always remember that, if you cannot get the units of
measurement in your solution (not the correct one) to work out correctly,
there is no point picking up your calculator, because when the units of
measurement do not work out correctly, there is something wrong in your
choice of math operations you have chosen to solve the problem. This applies
to all kinds of problems involving the use of math, not just problems using
the metric system.

**2. Working with LARGE and small
measurements:** Measurements can have reasonably
manageable numbers and be relatively easy to manipulate. On the other hand,
especially in the sciences, numbers associated with measurements can be
quite large, as in the case of Astronomical data, or numbers associated
with measurements can be quite small, as in the case of Quantum Theory.
To deal with the very large and the very small, mathematics has given us
exponential notation. Exponential notation as used in the sciences is often
called scientific notation. Scientific notation is defined as "A method
of writing or displaying numbers in terms of a decimal number between 1
and 10 multiplied by a power of 10. The scientific notation of 10,492,
for example, is 1.0492 × 10^4. The basics of scientific notation
is modeled in the following table.

Numerical Value | Scientific Notation format | Comment |

1,000,000,000 | 1 x 10^9 | one billion |

1,000,000 | 1 x 10^6 | one million |

1,000 | 1 x 10^3 | one thousand |

100 | 1 x 10^2 | one hundred |

10 | 1 x 10^1 | ten |

1 | 1 x 10^0 | one |

0 | ---* | --- |

0.1 or 1/10 | 1 x 10^-1 | one tenth |

0.01 or 1/100 | 1 x 10^-2 | one hundredth |

0.001 or 1/1000 | 1 x 10^-3 | one thousandth |

0.000001 or 1/1,000,000 | 1 x 10^-6 | one millionth |

0.000000001 or 1/1,000,000,000 | 1 x 10^-9 | one billionth |

*The number 0, itself, is not a power of ten. It can't be written as 10 to the something power.

**3. Displaying and processing data:** Gathering, recording,
and processing data are skills associated with serious research into any
human endeavor. An important data chart compiled by using accurate measurements
produced by astronomers is the Planetary Data Chart. A version of this
chart appears below.

Name of Object | Pronunciation | Average distance from the sun (m) | Mass of the object (kg) | Size of object Average radius (m) |

Sun | Sun | 0 | 1.991 x 10^30 | 6.96 x 10^8 |

Mercury | Mer qu ree | 5.8 x 10^10 | 3.2 x 10^23 | 2.43 x 10^6 |

Venus | Vee nus | 1.081 x 10^11 | 4.88 x 10^24 | 6.073 x 10^6 |

Earth | Earth | 1.4957 x 10^11 | 5.979 x 10^24 | 6.3713 x 10^6 |

Mars | Mars | 2.278 x 10^11 | 6.42 x 10^23 | 3.38 x 10^6 |

Jupiter | Joo pi ter (short i) | 7.781 x 10^11 | 1.901 x 10^27 | 6.98 x 10^7 |

Saturn | Sat ern | 1.427 x 10^12 | 5.68 x 10^26 | 5.82 x 10^7 |

Uranus | Yoo ray nes | 2.870 x 10^12 | 8.68 x 10^25 | 2.35 x 10^7 |

Neptune | Nep toon | 4.5 x 10^12 | 1.03 x 10^26 | 2.27 x 10^7 |

Pluto | Ploo toh | 5.9 x 10^12 | 1.2 x 10^22 | 1.15 x 10^6 |

**Data Charts** such as the one above are referred
to as data tables. A table provides a means of organizing and displaying
data that has been collected through observations.

Observations fall into two categories: One of the types
of observation is the __qualitative__ observation, while the other is
the __quantitative__ observation.

--> The **qualitative** observation is a descriptive
observation. It involves a clear and concise description of an object or
circumstance. It does not involve the making of measurements (quantities).
Some examples of qualitative measurements are:

Example 1 | The sky is blue |

Example 2 | The leaves on the tree are green |

Example 3 | The metal is soft enough to bend |

Example 4 | The surface of the wood is rough |

Example 5 | The liquid is very thick |

--> The **quantitative** observation is a measurement.
It involves an accurate measurement expressed with as much precision as
the measuring tool being used will allow. Some examples of quantitative
measurements are:

Example 1 | The length of the table is 2.0000 m |

Example 2 | The person's height is 150 cm |

Example 3 | The mass of the truck is 900 kg |

Example 4 | The volume of orange juice is 1.89 L |

Example 5 | The speed of the object is 1.5 m/s |

__Accuracy__ and __Precision__ always come into
play when anyone is making quantitative observations (measurements).

**Accuracy** is defined as "The ability of a measurement
to match the actual (correct) value of the quantity being measured." It
is a concept that deals with whether a measurement is correct when compared
to the known value or standard for the particular measurement being made.
When this comparison is being made using a percent, it is referred to a
__percent
error__.

--> Example of accuracy. Suppose that a carpenter is making a cabinet to fit in an exact space having a width of 1.15 m. Now what happens if in his effort to cut the materials he makes his cuts 1.14 m. What effect does this have on the making of the cabinet? Well on the first look, it may seem that this 0.01 difference is quite small. However, upon closer inspection, 0.01 m is a whole centimeter, which is close to one half of an inch. The cabinet will now show a gap of almost a half an inch, because the carpenter was not accurate in measuring. This why in terms of measurement, carpenters, etc., have always said "measure twice and cut once".

In the above situation, more careful measurement would reveal the true (correct) width, either by measuring more carefully or by using a more precise ruler, perhaps one that measured to the 3rd or even the 4th decimal place should be used. However, when measurements are being made of the very large (astronomical distances) or of the very small (subatomic scale) for the very first time, accuracy is difficult to determine, because no one has access to correct answer. In this kind of a situation, we turn to precision and statistics to help us ascertain the usefulness of our measurements.

**Precision** is defined as "The ability of a measurement
to be consistently reproduced." and "The number of significant digits to
which a value can be reliably measured." The first definition is the main
focus of scientists and engineers who are looking at the work of others.
After studying what the other people had done, they set out to test the
shared (often in the form of published reports) information to see whether
they can reproduce the results. Reproducible results are much more likely
to be accurate (correct) than results that cannot be reproduced. The second
definition is the main focus of anyone using a measuring device. How precise
or exact the measuring device is that you are using is based upon the degree
to
which the measurement units are broken down (subdivided). Precision
is the concept which deals with the degree of exactness when using a specific
measuring tool and expressing a measurement made with that tool. The precision
of any measuring tool and the exactness of the measurement made with that
tool is limited by how precise the instrument is capable of being. the
precision of a measuring tool is based upon the smallest defined unit of
measure on the devise. The number of digits used to express a measurement
when using a tool whose degree of precision (smallest unit available) are
called __significant digits__. See the example below:

**Handling Measurements in Calculations: The use of
significant digits in problem solving.**

In all problem solving situations where measurements are
involved, not only should you carry units along with each math operation
performed, but you need to take into consideration the number of significant
digits being expressed in each measurement being used, so each and every
calculation using measurements is never expressed with more precision than
the measurements themselves. That would be absurd (or, if you prefer, ridiculous).
In working with measurements expressed in significant digits, there are
three things you always need to consider. They are:

Recognizing the number of significant digits in another persons measurement | This requires that you can properly identify the use of zeros in measurements |

Using significant digits in both the addition and the subtraction operations | This requires that you can identify the number of significant digits in measurements |

Using significant digits in both the multiplication and and the division operations | This requires that you can identify the number of significant digits in measurements |

** The Rules of zeros (0's) used in identifying the
number of significant digits in a measurement.** The rules are as
follows:

Rule #1 | All none zero digits in a number are significant. | Example: 25.34 cm has four significant digits |

Rule #2 | All zeros between any two non zero digits are significant | Example: 100.052 g has six significant digits |

Rule #3 | When no decimal point is designated, all zeros to the right
of the last non zero digit are not significant
(Writing in a designated decimal point would indicate that all
of the zeros to the right of the last non zero digit are significant)
(A bar can be placed over a zero indicating that it and any other zeros between it and the last non zero digit are significant) |
Example 1: 23,000 km has three significant digits
Example 2: 23,000 Example 3: If a bar were written above the 2nd zero following the 3 in the value 23,000 km, there would be four significant digits |

Rule #4 | All zeros that come before the first non zero digit, which, itself, comes after a designated (written) decimal point, are only place holder zeros and place holder zeros are not considered to be significant. | Example 1: 0.000052 Gm has only two significant digits
Example 2: 0.00205 cm has only three significant digits. |

Rule #5 | All zeros after a designated decimal which are also to the right of a non zero digit are significant. | Example: 0.050400 km has five significant digits |

Rule #6 | When writing numbers in scientific notation, all non significant digits, including non significant zeros are dropped from the value being written. | Example 1:
0.0060720 kg = 6.0720 x 10^-3 kg Example 2: 705,200 km = 7.052 x 10^5 km |

**Significant Digits in Calculations:** The precision
in the answer to a calculation where new information is derived from existing
information cannot be greater than the precision of the least precise measurement.

Now the handling of this sort of situation where measurements are used in simple math operations is divided into two categories of math problems. They are the Addition-Subtraction problems and the Multiplication-Division problems.

--> 1. __Addition and Subtraction Problems:__ When
adding or subtracting measurements where precision and significant digits
are being used, the answer can be no more precise than the measurement
with the least amount of precision. In the following example you will be
rounding off to the second decimal place (the one-hundredths column), because
nothing is known about the 3rd decimal value in the measurement 3.11 kg.
This makes the 3rd decimal in the final answer too uncertain to be recorded.
So we round off correctly to the 2nd decimal place. In Addition and subtraction
it is the measurement with the least number of decimal places that affects
how much you are to round off to.

55.656 kg | Always | ||

14.3430 kg | Align | ||

+ |
03.11 kg | <---- least significant | Your |

ANSWER |
73.109 kg | --> 73.11 kg | Numbers |

10.9 cm - 8.364 cm = 2.536 cm = 2.5 cm |

Note: 10.9 cm has only one decimal place |

--> 2. __Multiplication and Division Problems:__ When
multiplying or dividing measurements where precision and significant digits
are being used, the answer can be no more precise than the measurement
with the least amount of precision. In the following example you will be
rounding off to only two digits, because in multiplication (and division)
you round off to the number of digits in your answer equal to the value
with the least amount of significant digits being used in the problem.
In multiplication and division it is the measurement with the least number
of significant digits that affect how you are to round off.

4.11 m | |||

x |
3.2 m | <----least significant | |

822 | <-- | Watch your | |

1233 | <-- | Alignment | |

ANSWER |
13.152 m | --> 13 m^2 | Here |

3.14165 g / 11.9 cm^3 = 0.2640042 = 0.264 g/cm^3 |

Note: 11.9 has only 3 significant digits |