Foundations-Copernican Revolution
Lecture 3: Final Thoughts
At this time, actual distances of planets from Sun were
unknown, but were later measured. One technique is "parallax"
"Earth-baseline parallax" uses
telescopes on either side of Earth to
measure planet distances.
Finding the distance to and the size of
objects we see in the sky
• Radians vs. degrees => arc length
• Finding distance – using parallax
• Finding angular size
Clicker Question:
Two cars are pushed with equal force on a street
covered in ice (no friction). One car has twice the
mass of the other. The one with twice the mass
will have
A: motion with no acceleration – constant speed.
B: twice the acceleration as the lighter car.
C: half the acceleration of the lighter car.
D: the same acceleration as the lighter car.
E: no motion whatsoever.
Escape Velocity
Velocity needed to completely escape the gravity of a planet.
The stronger the gravity, the higher the escape velocity.
Examples:
Earth
Jupiter
Deimos (moon of Mars)
11.2 km/s
60 km/s
7 m/s = 15 miles/hour
Consider Helium Gas at room temperature (300 K)
E = kT = 4.1 x 10-14 erg
E = 0.5 m v2 = 4.1 x 10-14 erg
so v = 1 km/sec on average, but sometimes more
Newton's Law of Gravity
For two objects of mass m1 and m2, separated by a
distance R, the force of their gravitational attraction is
given by:
F=
G m1 m2
R2
F is the gravitational force.
G is the "gravitational constant".
An example of an "inverse-square law".
Your "weight" is just the gravitational force
between the Earth and you.
1.4 Newton’s Laws
Gravity
For two massive objects,
the gravitational force is
proportional to the product
of their masses divided by
the square of the distance
between them.
1.4 Newton’s Laws
Gravity
On Earth’s surface,
the acceleration due
to the force of gravity
(Newton’s 2nd Law)
is approximately
constant, and
directed toward the
center of Earth.
1.4 Newton’s Laws
Gravity
The gravitational pull
of the Sun keeps the
planets moving in their
orbits.
Newton’s Laws and Gravity
Massive objects actually orbit around their
common center of mass; if one object is much
more massive
than the other, the
center of mass is not far
from the center of the
more massive object.
For objects more equal
in mass, the center of
mass is between the two.
1.4 Newton’s Laws
Kepler’s laws are a
consequence of
Newton’s laws.
The orbit of a planet around the Sun
has the common center of mass
(instead of the Sun) at one focus.
For a planet:
M = a3 / P2
Where M is in solar masses
P is in Earth years
and a is in AU
Throwing a ball into orbit
What happens if ball is thrown harder than
what is needed to go into circular orbit?
Escape Velocity
Velocity needed to completely escape the gravity of a planet.
The stronger the gravity, the higher the escape velocity.
Examples:
Earth
Jupiter
Deimos (moon of Mars)
11.2 km/s
60 km/s
7 m/s = 15 miles/hour
Consider Helium Gas at room temperature (300 K)
E = kT = 4.1 x 10-14 erg
E = 0.5 m v2 = 4.1 x 10-14 erg
so v = 1 km/sec on average, but sometimes more
Question 5
Newton’s law of
gravity states that the
force between two
objects
a) increases with distance.
b) depends on the state of matter
(solid, liquid, or gas).
c) can be attractive or repulsive.
d) increases with mass.
Question 5
Newton’s law of
gravity states that the
force between two
objects
a) increases with distance.
b) depends on the state of matter
(solid, liquid, or gas).
c) can be attractive or repulsive.
d) increases with mass.
The attractive force of gravity
INCREASES with greater mass,
and DECREASES QUICKLY
with greater distance.
The force doesn’t depend on the
kind of matter.
Clicker Question:
Suppose Matt weighs 120 lbs on his
bathroom scale on Earth, how much will his
scale read if he standing on a platform 6400
km high (1 Earth radius above sea-level)?
A: 12 lbs
B: 30 lbs
C: 60 lbs
D: 120 lbs
E: 240 lbs
Chapter 2: Light and Matter
Electromagnetic Radiation
(How we get most of our information about the cosmos)
Examples of electromagnetic radiation:
Light
Infrared
Ultraviolet
Microwaves
AM radio
FM radio
TV signals
Cell phone signals
X-rays
Other Examples of waves
Examples:
Sound – Pressure Waves
Water Waves
Waves on a string, cable, or spring
Traffic – Wave analysis can help understand traffic flow
Radiation travels as waves.
Waves carry information and energy.
Properties of a wave
wavelength (l)
crest
amplitude (A)
trough
velocity (v)
l is a distance, so its units are m, cm, or mm, etc.
Also, v =  f
Period (T): time between crest (or trough) passages
Frequency (n): rate of passage of crests (or troughs), n =
(units: Hertz or cycles/sec)
1
T
Properties of a wave
wavelength (l)
crest
amplitude (A)
trough
Context: Example from Sound waves
Amplitude => Volume
Frequency (n) => Pitch, determines which note you hear
Shape of wave => what makes a piano sound different from a trumpet
velocity (v)
Waves
Demo: making waves - wave table
Demo: slinky waves
Demo: standing waves - resonance
Question 2
The distance between successive
wave crests defines the ________
of a wave.
a) wavelength
b) frequency
c) period
d) amplitude
e) energy
Question 2
The distance between successive
wave crests defines the ________
of a wave.
a) wavelength
b) frequency
c) period
d) amplitude
e) energy
Light can range from
short-wavelength
gamma rays to longwavelength radio
waves.
Things that waves do
1. Refraction
Waves bend when they pass through material of different densities.
air
water
swimming pool
prism
air
glass
air
2. Diffraction
Waves bend when they go through a narrow gap or around a corner.
3. Interference
Waves can interfere with each other
4. Wave Speed depends on medium
– mechanical waves must have a medium to travel in
Example: Speed of sound
In air
340 m/s or 760 MPH at 20 deg C
In Water
1497 m/s at
(varies with temperature)
Sound speed depends on elasticity (stiffness) of the material
=> Bell Jar Demonstration
The Doppler Effect
Applies to all kinds of waves, not just radiation.
at rest
velocity v1
velocity v2
velocity v1
velocity v1
velocity v3
you encounter
more wavecrests
per second =>
higher frequency!
fewer wavecrests
per second =>
lower frequency!
Doppler Effect
Demo: buzzer on a moving arm
Demo: The Doppler Ball
The frequency or wavelength of a wave depends on the
relative motion of the source and the observer.
Radiation travels as Electromagnetic waves.
That is, waves of electric and magnetic fields traveling together.
Examples of objects with magnetic fields:
a magnet
the Earth
Clusters of galaxies
Examples of objects with electric fields:
Power lines, electric motors, …
Protons (+)
"charged" particles that
make up atoms.
Electrons (-)
}
Scottish physicist James Clerk Maxwell showed in 1865
that waves of electric and magnetic fields travel together =>
traveling “electromagnetic” waves.
The speed of all electromagnetic waves is the speed of light.
c = 3 x 10 8 m / s
or c = 3 x 10 10 cm / s
or c = 3 x 10 5 km / s
light takes 8 minutes
Earth
Sun
c= ln
or, bigger l means smaller n
Refraction of light
All waves bend when they pass through materials of different densities.
When you bend light, bending angle depends on wavelength, or color.
The Electromagnetic Spectrum
1 nm = 10 -9 m , 1 Angstrom = 10 -10 m
c= ln