Chapter 1
About Science
About Science
Scientific Measurement
Size of Earth
Size of the Moon
Distance to the Moon
Distance to the Sun
Size of the Sun
Mathematics – The Language of
Science
Scientific Methods
Scientific Observation and
Measurement
How do you know whether the earth is flat or round?
Is there any evidence that we can see from here?
Where would be the best place to find this evidence?
Evidence:
Best place – on a large body of water – large, flat, level surface
Activity – watch a boat sail out over the horizon
Observations – (Evidence for a curve surface)
Boat disappears sailing out – bottom first
Boat reappears sailing in – top first
Climbing to a higher vantage point brings the boat back
into view.
Other Observations
The Sun and moon are round so why not the earth?
The shadow of the earth on the surface of the moon during
an eclipse of the moon showed that the surface of the earth
was round.
When did people first figure out the earth was round?
~500 B.C. – Pythagoreans gave the similar shape
reasoning (Induction argument)
~300 B.C. – Aristotle used the disappearing boat
argument.
Educated people knew the earth was round in the 3rd century
B.C. but didn’t know how to measure it.
Size of Earth
Eratosthenes (Egyptian director of the Library at
Alexandria) – 1st known calculation of the size of the earth.
~235 B.C. Eratosthenes performed a measurement in
Alexandria, Egypt that allowed him to calculate the radius
of the earth.
Somehow, Eratosthenes came to know about the well in
Aswan (where the big dam is located), south of Alexandria,
where the sun shines straight down to the bottom of the
well at noon on the summer solstice
At the Summer Solstice the earth’s
axis is tilted 230 toward the sun.
This brings the sun directly
overhead in Aswan at noon on this
day.
While not directly south of
Alexandria is wasn’t far off. (This
would effect Eratosthenes’ ability
to synchronize “noon” in both
locations.)
Aswan, Aswan
Lat. 24:06:55N (24.1152)
Long. 33:00:47E (33.0131)
Alexandria, Egypt
Lat. 31o 7' North
Long. 29o 54' East
Aswan (anciently Syene) was
on the Tropic of Cancer
Earth’s Dimensions
Polar radius 6,356.6 km
Equatorial radius 6,378.2 km
Equatorial circumference 40,075 km
Surface area 510,900,000 sq. km
Caitlin,
The correct tilt angle is 23
degrees 27 minutes,
which is approximately 23.45
degrees.
David R. Cook
Atmospheric Research Section
Environmental Research Division
Argonne National Laboratory
Do the math here
On Jun 22 – summer soltice – “only day the sun shone down the
well at noon”
This synchronized the measurement in Alexandria
d/H = Shadow / Height = 1/8
Angle ~7.20 or 7.2/360 = 1/50 of circumference
The distance from Alexandira to Aswan
D= 5000 statia ( =800km)
Therefore Circumference = 5000 (50) = 250,000 stadia (
=40,000 km) or within 5% of the presently accepted value.
Size of the Moon
The info needed to complete the next series of
calculations
Earth radius  Moon radius  Moon distance
 Distance to Sun  Sun diameter
Size of moon
Use the size of shadows during eclipses of the sun and Moon
Solar Eclipse –
Moon between Sun and Earth (Moon shadow on Earth)
Lunar Eclipse –
Earth between Moon and Sun (Earth shadow on Moon)
Aristarchus in around 240 B.C. measured moon’s
diameter and distance from earth.
Presently accepted value of diam is 3640 km which is
within 5% of Aristarchus’ value.
Moon’s shadow on earth
tapers to a point.
It tapers by one moon
diam.
Hence the earth’s shadow
must taper by one moon
diam.
During a lunar eclipse the
earth’s shadow on the
moon is 2.5 moon diam.
Therefore the earth real
diam is 3.5 x moon diam.
Gives Earth diameter as 3.5 times Moon’s diameter
Distance to the Moon
Similar triangles give: Moon diam / Moon distance = 1/110
Early Greeks knew this.
However, they needed Aristarchus’ measurement of the moon’s
diameter to complete the calculation.
Distance to the Sun
The coin on the window
trick doesn’t work with the
sun. The method needs a
radius or diameter.
It’s also dangerous to look
at the sun
Moon and sun subtend the
same angle. This is
observed.
Half-lit moon determined geometry.
Earth-moon distance known
Measure angle x
Calculate Earth –Sun distance
Remember the moon’s
shadow tapered to a point
during the solar eclipse.
Same apparent size.
Moon exactly covers sun
Size of the Sun
This is another way to
determine the 1/110 ratio.
Pin hole camera – with
lenses and film (or CCD) you
have today’s modern
cameras.
Camera Obscura – Camera
(Room) Obscura (Dark)
Mathematics – The Language
of Science
Science and mathematics came together some four
centuries ago.
Physics is based on concepts and mathematics provides
an efficient, unambiguous means of expressing the
relationship between theses concepts.
We will be emphasizing the understanding of the
concepts of Physics.
But we will use equations for their ability to
summarize relationships.
Mathematics
In some cases we will use simple mathematics to
estimate relative sizes to further aid in understanding
the concepts.
There is no math prerequisite for this course – all the
math we will need will be developed right here.
 Similar triangles
 Ratios
 Estimation techniques
 A little trig
Scientific Method
Hypothesis  Experiment  Confirmation
A Theory must explain currently known phenomena.
A Theory must make predictions that can be tested.
Goals:
 Theory as simple as possible
 Few or no adjustable constants
Scientific Method
CONCEPT - an abstract or generic idea generalized from particular
instances.
FACT - something that has actual existence <space exploration is
now a fact>. Or an actual occurrence <prove the fact of damage>
HYPOTHESIS implies insufficient evidence to provide more than a
tentative explanation <a hypothesis explaining the extinction of the
dinosaurs>.
LAW implies a statement of order and relation in nature that has
been found to be invariable under the same conditions <the law of
gravitation>.
THEORY - a plausible or scientifically acceptable general principle
or body of principles offered to explain phenomena <wave theory of
light>
Scientific Method
As soon as a theory is established scientists start to
investigate how far it can be stretched:
 smaller dimensions,
 larger dimensions,
 larger and smaller masses.
Scientific Method
Disagreements with established theory
 Initially attempt to modify the theory to fit in the new results
 Try to add new concepts to theory
Discoveries are not always that orderly but can benefit from
luck, accidents and a prepared mind.
X-Rays were discovered when leaks in shielding exposed some
nearby photographic plates.
Cosmic Background Radiation was discovered when trying to
eliminate electrical noise in telephone transmission equipment.
The Rest of the Stuff
The Scientific Attitude
Rightness – Wrongness
Honesty in Science.
Pseudoscience
Science, Art and Religion
A little person opinion from the author
Science and Technology
Risk Assessment
Physics – The Basic Science
Some boasting by Hewitt
Science and Technology
Risk Assessment
Physics – The Basic Science
Some boasting by Hewitt