Astronomy Notes - 1

Two Important Questions:

What is physics? - Physics is the study of the physiccal world, from objects as small as atoms to objects as big as galaxies. It is a study of matter and energy and the relationship between them.
(see textbook p. 4)

What kinds of Questions does physics help us answer? - Particularly two questions: What? and How?
(see textbook p. 8 & 9, also)

I. Astronomy and the Universe:

A. Beginning Concepts:

1. Astronomy is the study of the universe.

2. Modern city dwellers pay little attention to the night sky.

3. Very little of what is in the night sky can be seen because of light pollution.

4. Many, many generations lived without this light pollution and grew up knowing the heavens.

5. The sky was the central feature of peoples environment.

6. cycles of light and darkness and cycles of planting and harvesting were based upon observations of the heavens.

7. Our definition of time came from the observation of the natural rhythms of objects appearing to move in the sky.

8. One rotation period is the day.

9. One revolution period is a year.

10. Navigation (deliberate change in a person's position) was based upon the sky.

B. Measuring position and distance.

1. Angular measurement:

a. Angles are used as means of measurement.

b. Compass measurements have been around since the discovery of magnetism.

c. The combination of the use of magnets along with the geometry of circles allows for measurements of directions.

d. The horizon which completely wraps around your field of vision is a 360 degree circle.

e. Compass directions divide the circle into four equal quadrants of 90 degrees each.

f. Dividing the compass circle as drawn on a piece of paper:

- North (N) is upwards
- South (S) is downwards
- East (E) is to the right
- West (W) is to the left

g. Directions between the four compass points are described in terms such as 40 degrees east of north.

h. Angle measured at 45 degrees from one of the compass points are described as:

- Northeast, NE (exactly half way between N and E)
- Southeast, SE (exactly half way between E and S)
- Southwest, SW (exactly half way between S and W)
- Northwest, NW (exactly half way between W and N)

i. Angles are expressed in the following units:

- Degree, use the degree symbol (1 degree is 1/360 of the arc of a circle)
- arc minute, use the apostrophe symbol (1 arc minute is 1/60 of a degree)
- arc seconds, use the quotation mark symbol (1 arc second is 1/60 of a minute)

j. The height of an object measured from the horizon line is expressed as an angle.

k. Distances across the sky are measured as angles, such as the moon's angular diameter or size is 1/2 degrees. Astronomers would say that the moon subtends an angle of 1/2 degree. Ten full moons could fit between the two pointer stars in the Big Dipper.

What is the angular distance between the two pointer stars?

l. Another example: On January 5, 1987, Venus has an angular diameter as viewed from earth of 28.27 seconds.

2. Powers of Ten Notation:

a. Distances in space are huge, so exponential or what is often referred to as scientific notation is used to keep the numerical values under control.

b. Powers of ten are also referred to as the decimal system or the base ten numerical system.

c. For your information all powers of ten will be written in the form of a number between 1 and 9.9999... multiplied by ten raised to a power. The raising of ten to a power will be written as 10^n, where n is some number. Correct exponential notation does not use a carrot (^) symbol but rather writes the power as a superscript numerical value also called an exponent.

d. Some examples of powers of ten greater or equal to one:

--> 10^0 = 1
--> 10^1 = 10
--> 10^2 = 10 x 10 = 100
--> 10^3 = 10 x 10 x 10 = 1,000
--> 10^4 = 10 x 10 x 10 x 10 = 10,000

e. Some examples of powers of ten less than or equal to one:

--> 10^0 = 1
--> 10^-1 = 1/10 = 0.1
--> 10^-2 = (1/10) x (1/10) = 1/100
--> 10^-3 = (1/10) x (1/10) x (1/10) = 1/1,000
--> 10^-4 = (1/10) x (1/10) x (1/10) x (1/10) = 1/10,000

f. As an example 1.1 x 10^-8 cm is the diameter of a hydrogen atom.

g. Larger power of ten exponents are needed for measuring large distance measurements.  Here are a few that are used regularly.

--> 10^3 = 1,000                                  (one thousand)
--> 10^6 = 1,000,000                          (one million)
--> 10^9 = 1,000,000,000                  (one billion)
--> 10^12 = 1,000,000,000,000        (one trillion)

h. Small power of ten exponents are needed for measuring small distance measurements. Here are a few that are used regularly.

--> 10^-3 = 1/1,000                              (0.001)
--> 10^-6 = 1/1,000,000                      (0.000001)
--> 10^-9 = 1/1,000,000,000              (0.000000001)
--> 10^-12 = 1/1,000,000,000            (0.000000000001)

3. Arithmetic with exponents:

a. Addition: exponent must be the same number:

--> 2 x 10^3 + 3 x 10^4 = 2 x 10^3 + 30 x 10^3 =

b. Subtraction:

c. Multiplication:

d. Division:

e. Raising to a power:

f. Finding a root:

4. Small angular formula:

a. Astronomers usually have to deal with objects that subtend tiny angles.

b. When the distance to an object is known it is possible to convert its angular size into a linear size. This conversion is accomplished through the use of the small angle formula.

c. The small angle formula is written as d = ?D / 206,265

--> d is the linear size of the object
--> D is the distance from the observer
--> ? is the angle that the object subtends

d. As an example, On July 3, 1981, Jupiter was at a distance of 824.7 million km from earth.  Jupiter's angular diameter on that date was 35.72 seconds of arc.  What is the planet's diameter?

Answer: 142,800 km

5. Laws of Motion:

a. Tycho Brahe with the support of a Danish king had an astronomical observatory built on an island. He also had a number of people assisting him in his quest to map the night sky.  He then proceeded to make observations about each and every object visible in the night sky. Using only sophisticated angle measuring devices (telescopes had not been invented yet) he plotted the motion of all the visible objects over the course of 20 plus years.  The data gathered was tremendous in size and represented the position vs time location of every object over the course of all of those years.

b. Johannes Keppler took Brahe's data and over the course of approximately another 20 years he developed three laws of planetary motion, known as Kepler's Laws.

--> 1st Law:  Planetary orbits are elliptical in shape.
--> 2nd Law:  An imaginary line connecting a planet with the sun would sweep out equal areas in equal amounts of time.
--> 3rd Law:  The radius of a planets orbit and its period* are related by the equation  K = r^3 / T^2, where K is a value unique to an individual solar system.

c. Isaac Newton came along and studied Kepler's work and added it to his much larger works collectively referred to as Newtonian Mechanics.

d. Newton developed a proportionality which described two important aspects of gravitational force between any two objects including celestial ones. His Law of Universal Gravitation said:

--> the force of gravity is proportional to the masses of the objects exerting gravitational force on each other.

 F ? m

--> the force of gravity is inversely proportional to the distance between the two objects squared.

 F ? 1 / d^2

e. Newton developed an equation called the Universal Gravity equation, but did not have the means to determine the value of the proportionality constant G, in order to be able to use the equation to solve problems

 F = G m1 m2 / d^2

e. Henry Cavendish came along about a hundred years after Newton and found the value for the proportionality constant in Newton's Law.  He found that G is 6.67 x 10^-11 N m^2 / kg^2.

6. Distances in space:

a. Astronomical distances are often extremely large. This is true even within our own solar system.

b. The AU , astronomical unit, is based upon the average distance between the earth and the sun.  Another way to phrase it, is that 1 AU is equal to the average radius of the earth's orbit.

--> 1 AU = 1.496 x 10^8 km = 93 million miles

c. An example of the use of this measurement unit is that we can express the distance between the Sun and Jupiter as 5.2 AU.

d. A light year ( abbreviated ly) is a distance measurement.  It is the distance that light travels in one year.

--> 1 ly = 9.46 x 10^12 km = 63,240 AU

e. A parsec (abbreviated pc) is even a larger distance than a light year.  One parsec is defined as the distance at which 1 AU subtends an angle of 1 second of arc.

--> 1 pc = 3.09 x 10^13 km = 3.26 ly

f. Often distance in space are so large that kiloparsecs and megaparsecs are used.

--> 1 kpc = 1 x 10^3 pc
--> 1 Mpc = 1 x 10^6 pc

7. Units of length, time, speed, and mass:

a. Length measurements in metric:

--> 1 mm = 0.1 cm
--> 1 m = 100 cm
--> 1 km = 1000 m or 1 x 10^5 cm

b. Common English conversions:

--> 1 inch = 2.54 cm
--> 1 foot = 30.48 cm
--> 1 mile = 1.609 km

c. When working with very small distances we will use:

--> ?  (the micron) = 1 x 10^-4 cm = 1 x 10^-6 m
--> A (the angstrom*) = 1 x 10^-8 cm = 1 x 10^-10 m

* a small circle should be written in above the upper case A.

d. The basic unit of time is the second (s)

--> 1 minute = 60 sec.
--> 1 hour = 3600 sec
--> 1 day = 86,400 sec
--> 1 year = 3.16 x 10^7 sec

e. The unit of speed can be expressed in cm / sec,  km / sec, miles / hr:

--> 1 km/sec = 1 x10^5 cm/sec
--> 1 km/sec = 2237 miles/hr
--> 1 mile/hr = 44.7 cm/sec
--> 1 mile/hr = 1.47 ft/sec

f. The unit of mass can be expressed in grams, kilograms, and solar masses (the symbol is an upper case M followed by a small circle with a dot in the center in the subscript position):

--> 1 kg = 1000g
--> 1 kg = 2.20 lb
--> 1 lb = 453.6 g
--> 1 Solar Mass = 1.99 x 10^33 g

8. Common vocabulary you need to know:

angular measure
arc minute
arc second
angular diameter
angular size
small angle formula
Newtonian Mechanics
astronomical unit
light year