1. Astronomers use very large and very small numbers that are difficult to work with. They use scientific notation to write these numbers in a simpler way by moving the decimal place and adding an exponent. 2. Distances in astronomy are immense, so different units are used including astronomical units (au), light years, and parsecs. Kepler's laws describe the motion of planets in elliptical orbits around the sun. 3. Early models of the solar system placed Earth at the center, but problems arose. The heliocentric model with the sun at the center solved these issues. Galileo and Kepler made discoveries that supported the heliocentric view through observations with early telescopes.

1. Notes -
1. – Astronomical Thinking
A) Astronomical Numbers: In astronomy
scientists deal with VERY large numbers
Planets have very large masses:
M sun=1,989,000,000,000,000,000,000,000,000,000 kg
Objects in space are very far apart:
149,597,900 km
S E
(on average)

2. 1. Scientific Notation: The standard way of
representing very large or very small numbers.
M sun=1,989,000,000,000,000,000,000,000,000,000 kg
Not
fun
to
calculate Much better M sun=1.989x10 30 kg
with
a. How:
- Move the decimal to the right or left
- Stop when you have one digit (not zero) on the left
- add “x10” with the number of moves as the exponent

3. Examples
a. How:
- Move the decimal to the right or left
- Stop when you have one digit (not zero) on the left
- add “x10” with the number of moves as the exponent
M earth =5,970,000,000,000,000,000,000,000 kg
24
M earth =5.97x10 kg
M proton=.00000000000000000000000000167 kg
M proton=1.67x10 -27 kg

4. Notes & Activity
b. In your calculator...
1.67x10 - 27 kg 1.67x10 ^ −27
or (even easier) 1.67e-27
c. Mini-Activity: Write each in scientific notation
1) 6,450,000 2) 0.0000034
3) .00029 4) 78,000
5) 3.14e-8 X 6.98e-9 6) 2.00e15 X 7.89e10
7) 9.87e-9 X 1.67e10

5. Notes
B) Astronomical Distances: Because the
distances between objects in space are so
great, astronomers have different units to
measure their distances.
1) au : Astronomical Unit = 150 million km
- The average distance from the earth to the
sun.
- Used for measuring distances within the solar
system 1 au
S E

6. Notes
2) ly : Light Year – The distance that light
travels in one year. 8
- Speed of light c = 3.00x10 m/ s
- Light Year = 63,240 AU
- Used for measuring distances between stars
3) pc : Parsec – Uses angles of stars to
calculate distance to a star.
- Parsec = 3.26 light years

7. A parsec is the
distance from the
sun to an
astronomical object
which has a parallax
angle of one
arcssecond.
1 arc sec = 1/60 arc min
1 arc min = 1/60 degree
1 degree = 1/360 circle

8. Activity
Calculate the following distances from the sun in
km and light years:
1) Mars = 1.52au 2) Jupiter = 5.2au 3) Neptune = 30.02au
Convert the distances to each star into parsecs
or light years:
4) Wolf 359 = 7.78ly 5) Sirius = 8.58ly 6) Ross 614= 4.095pc
7) What is the distance from the earth to the sun in light
years? Light minutes?

9. Practice
1) Convert each and write in scientific notation:
a. 3.75au to m b. 149,321km to au
c. 3.00e8 m/s to au/y d. 2.6m to ly
2) What units would you use to measure in each
situation?
a. nearby star b. Washington DC
c. Nearby Planet d. Radius of a Pencil

10. Notes
C) The Road to Modern Astronomy
1. The earliest models of the solar system were a
geocentric model based on the teachings of
Aristotle.
a. Geocentric: from the Greek “geo” and “centric”
centred
b. The Earth was placed at the V
S
center and all planets, stars
and other bodies went around
E
it in perfect circles

11. Notes
c. Problems with the geocentric model:
- Planets change brightness
- Planets have Retrograde Motion.
When they appear to slow down, go backwards
and then continue forwards again.
Watch
it
Happen

12. Notes
d. Ptolemaic Model: To explain retrograde motion,
had the planets moving on smaller circles called
epicycles as they moved around the Earth.
S
Ptolemy's E
idea

13. Notes
e)The Heliocentric Model: From the Greek -
“Helio” for sun and “centric” for centred
1) Places the Sun at the centre of
the solar system and has the S
planets revolving around it. E
2) Credited to Nicholas Copernicus

14. Notes
3) The heliocentric model solved the problems of
the geocentric model
- Planets change brightness because they change
distance
- Retrograde motion happens when the earth passes
other planets in its orbit. (more to come)

15. Notes
4) Galileo Galilei: Was the first to observe the sky
with a telescope
- Discovered the phases of venus
- First to see the rings of Saturn
- First to see Jupiter’s 4 largest moons
5) Johannes Kepler: Used the data collected by
Tycho Brahe to come up with the three laws of
planatary motion. (More to come)

16. Notes
4) Sir Isaac Newton: Discovered…
a. Law of Universal Gravitation: Every
particle in the universe attracts every
other particle in the universe with a force
proportional to the product of the masses
and inversely proportional to the square
of the distance between them.
Gm1 m2
F= 2
r

17. Notes
D) Kepler's Laws of Planetary Motion
1. Kepler's First Law: The orbital paths of planets are
elliptical (not circular), with the sun at one focus.
a. Parts of an ellipse: (sketch this)
Focus 1 Focus 2
Major Semi-Major
Axis Axis

18. Notes
b. Keep in mind that the planets orbits are not
very elliptical. The two focuses are almost on
top of each other.
Slightly Elliptical
Perfect circle

19. Notes
2. Kepler's Second Law: An imaginary line
connecting a planet to the sun sweeps out equal
areas in equal amounts of time.

20. Ellipse Activity
Work in Pairs...
1) obtain two thumbtacks and a piece of string
2) Tie the ends of the string together
3) Place the loop around one thumbtack and use a
pencil/pen to pull it tight.
4) Drag the pen around the tack and label this figure A
5) Move the first tack so your figures will not overlap
6) Place the tacks 2 boxes apart. Place the string loop
over both tacks and make another figure
7) Repeat with the tacks 4 and 6 boxes apart
8) What happens to the shape as the tacks move
further apart?
9) Are any of the figures a perfect cricle?

21. Notes
3. Kepler's Third Law: The square of a planets
orbital period (year) is proportional to the cube
of it's semi-major axis.
2 3
P =a
(P) in Earth Years (a) in Astronomical Units
Example 1: Calculating how long a year on
Mars is if it's semi-major axis is 1.524 au
2 3
P =a
PP2 = 1.5243 = 3.540 P=1.88 years
P = √ 3.540

22. Example 2: What is the length of the semi-major
axis for Neptune if its period is 164.8 years?
a=30.1 au
Activity
Fill in the chart below using Kepler's Laws.
Semi-Major Orbitlal
Planet Major Axis
Axis Period
Venus .723 au
Jupiter 10.406 au
Uranus 84.01 y
Saturn 9.539 au

23. What is the force of gravity between the sun and
the earth?
−11
Gm1 m2 G=6.67x10
F= 2
m sun=1.989e30kg
r mearth=5.974kg
2 Gm
v orbit= 2 3
d P =a
Planet X is about 23.7 au from the sun. How long
is its year? What is its speed in its orbit?

24. Notes
5. Measuring Distant Objects
a. Scientists cannot directly measure distances
and sizes beyond the earth.
b. Indirect Measurement of size: Uses angles
and known distances to calculate the size of
an object. (more to come)
Known Distance

25. c. Indirect Measurement of Distance: Uses
the property known as parallax to calculate
the distance to objects.
- Parallax: The apparent movement of an object
in the foreground compared to an object in the
background.
- Try it: Hold your thumb out at arms length.
Close one eye and cover an object on the wall.
Switch eyes. Your thumb will appear to move.
Try it again with your thumb closer to your face.
It will appear to move more.

26. With stars….

Scientists observe the position of a star twice a
year. Each 6 months apart.

This gives us a right triangle.

27. With stars….

The angle formed is called the Parallax Angle
θ

28. With stars….
θ