1. Universal Law of Gravitation
Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.

2. Orbital Paths from Law of Gravitation
Extending Kepler’s Law #1, Newton found that ellipses were not the only orbital paths.
All orbits are “conic sections”
ellipse (bound)
parabola (unbound)
hyperbola (unbound)
Orbital motion takes place around the center of mass

3. The Center of Mass
In Kepler's Laws, the Sun is fixed at a point in space (a focus of an ellipse) and the planet revolves around it. Why is the Sun privileged?
Kepler had mystical ideas about the Sun, endowing it with almost god-like qualities that justified its special place.
Newton demonstrated that the the Sun does not occupy a privileged postion and in the process he modified Kepler's 3rd Law.

4. The center of mass is familiar to anyone who has ever played on a see-saw. The fulcrum point at which the see-saw will exactly balance two people sitting on either end is the center of mass for the two persons.
m1d1 = m2d2

5. Recall Kepler’s 3rd law: P2 / a3 = constant
Newton realized that in the planet-Sun system the planet does not orbit around a stationary Sun (a planet exerts as much gravitational force on the Sun as the Sun does on a planet).
Instead, Newton proposed that both the planet and the Sun orbited around the common center of mass for the planet-Sun system.
This led Newton to modify Kepler's 3rd Law.
Fg = Gm1m2/d2
Recall Kepler’s 3rd law:
P2 / a3 = constant

6. Newton’s Version of Kepler’s Third Law
P2 = 42 a3 / G (m1 + m2)
G is known as the universal gravitational constant.
If you can measure the orbital period of two objects (P) and the distance between them (a), then you can calculate the sum of the masses of both objects (m1 + m2).

7. We will return to Newton and discuss his “Laws of Motion” after we learn some simple background physics

8. A Universe of Matter and Energy
What is matter?
What is energy?

9. Matter – material such as rocks, water, air; “stuff” composed of atoms
Energy – makes or has the potential to make matter move!
The history of the universe, including biological organisms, is based upon the interplay between matter and energy.

10. Three Basic Types of Energy
kinetic
energy of motion
potential
stored energy; e.g., chemical, gravitational, electrical, etc.
radiative
energy transported by light (electromagetic radiation)

11. Conservation of Energy
Fundamental law of nature
Energy can be neither created nor destroyed
It can change form or be exchanged between objects.
The total energy content of the Universe was determined in the Big Bang and remains the same today.
K.E.
P.E.
R.E.

12. (m is mass, v is velocity)
energy of motion
K.E. = 1/2 mv2
(m is mass, v is velocity)
Kinetic Energy (K.E.):

13. temperature On the microscopic level: is a measure of the
average kinetic energy
of particles within a substance

14. Temperature Scales

15. Temperature vs. Heat Temperature is the average kinetic energy.
Heat (thermal energy) is the total kinetic energy.
lower T
higher T
less heat
more heat
same T

16. Sound waves are a form of kinetic energy on a microscopic level (organized vibration of molecules)

17. Applying what we’ve learned - pizza vs. soup
caution in the kitchen

18. Potential Energy: Energy that is “stored” within an object and that has the potential of being released in a different form

19. Gravitational Potential Energy
gravitational potential energy is the energy which an object stores due to its ability to fall
It depends on:
the object’s mass (m)
the strength of gravity (g)
the distance which it can fall (d) g m d
P.E. = mgd

20. gravitational potential energy
P.E. = mgd

21. Mass-Energy Potential Energy
mass-energy: energy is stored in matter itself
this mass-energy is what would be released if an amount of mass, m, were converted into energy
E = mc2
[ c = 3 x 108 m/s
is the speed of light]

22. Chemical Potential Energy
Chemical potential energy: energy stored chemical bounds

23. There are many additional examples of potential energy. e. g
There are many additional examples of potential energy. e.g., stretched springs, …

24. Energy, while conserved, can be transformed from one type of energy to another
Potential Kinetic

25. Potential Kinetic

26. Kinetic Potential

27. Orbits & Energy Uphill Maximum Potential Energy Maximum Kinetic Energy
Downhill

28. Radiative energy: energy carried by electromagnetic radiation (light).

29. Light Light as a wave Light as a particle (photon)
A vibration in an electromagnetic field
through which energy is transported.
Light as a wave
Light as a particle
(photon)

30. Properties of Waves WAVELENGTH (: Distance between adjacent crests
FREQUENCY (f): number of crests that pass through a point each second. It is measured in units of hertz (Hz), which are the number of cycles per second.
AMPLITUDE: A measure of the strength of the wave.
SPEED (s): how fast the wave pattern moves For any wave: s = f 

31. The speed of light is a constant: s = c !!!
Light as a Wave
The speed of light is a constant: s = c !!!
Therefore, for light: f  = c
The higher f is, the smaller  is, and vice versa.
In the visible part of the spectrum, our eyes recognize f (or ) as color!

32. Light as a Particle
Light can also be treated as photons – packets of energy.
The energy carried by each photon depends on its frequency (color)
Energy: E = hf = hc/  [“h” is called Planck’s Constant]
Shorter wavelength light carries more energy per photon.

33. The Electromagnetic Spectrum
lower energy
higher energy

34. Light as Information Bearer
Spectrum: light separated into its different wavelengths.
Spectroscopy: The quantitative analysis of spectra
The spectrum of an object can reveal the object’s:
Composition
Temperature
Velocity