1. Homework #3
An asteroids closest approach to the Sun (perihelion) is 2 AU, and farthest distance from the Sun (aphelion) is 4 AU.
What is the semi major axis of its orbit?
What is the period of its orbit?
What is it’s eccentricity?
Calculate the energy required to raise an electron in a Hydrogen atom to the 2nd excited state:

2. Homework #3 continued
A set of keys is dropped from the top of the Empire State building in New York. How fast will they be going when they hit a poor tourist on the ground 9 seconds later?
How tall is the Empire State Building?
An astronaut drops his set of keys from the same height as the Empire State Building on the Moon (1/6th the gravity of Earth), how fast is it going when it hits the Lunar surface?

3. Homework #4
A set of keys is dropped from the top of the Empire State building in New York. How fast will they be going when they hit a poor tourist on the ground 9 seconds later?
How tall is the Empire State Building?
An astronaut drops his set of keys from the same height as the Empire State Building on the Moon (1/6th the gravity of Earth), how fast is it going when it hits the Lunar surface?

4. You can also go over wavelength, frequency, and speed with this tool from the Light and Spectroscopy tutorial.
Anatomy of a Wave

5. Light as a Wave For a wave, its speed is: v =  f [distance/time]
But the speed of light is a constant
c = 3 x 108 m/s
For light:  f = c and
f = c / 
The higher f is, the smaller  is, and vice versa.
Our eyes recognize f (or ) as color!

6. 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)
E = hf = hc /  (h = 6.6 x J s)
Bluer light carries more energy per photon.

7. Interaction of Light with Matter
Remember that each electron is only allowed to have certain energies in an atom.
Electrons can absorb light and gain energy or emit light when they lose energy.
Hydrogen
It is easiest to think of light as a photon when discussing its interaction with matter.
Only photons whose energies (colors) match the “jump” in electron energy levels can be emitted or absorbed.

8. Light as Information Bearer
We can separate light into its different wavelengths (spectrum).
By studying the spectrum of an object, we can learn its:
Composition
Temperature
Velocity

9. This tool from the Light and Spectroscopy tutorial.

10. Dividing Light Into a Spectrum
Astronomers separate out light into its individual components using a diffraction grating or using a prism - then they analyze each part independently!

11. blue 460 nm 81
Filter
Detector 81

12. blue 460 nm 81
green 530 nm 85
Filter
Detector 85

13. blue 460 nm 81
green 530 nm 85
yellow 580 nm 83
Filter
Detector 83

14. blue 460 nm 81
green 530 nm 85
yellow 580 nm 83
orange 610 nm 78
Filter
Detector 78

15. blue 460 nm 81
green 530 nm 85
yellow 580 nm 83
orange 610 nm 78
Filter
red 660 nm 70
Detector 70
The spectrum is continuous. UV IR

16. Natural Spectra ????

17. Änuenue (rainbow)
Light from the Sun
Water droplet

23. Shine Light through Hydrogen…

24. Shine Light through Hydrogen…

25. Shine Light through Hydrogen…
410

26. E = hn = hc/l g l = hc/E E = hn E = hn = hc/l l (mm) = (mm=10-6m)
h=Planck’s constant; n=frequency [Hz=1/s]; l=wavelength [m]
l (mm) = (mm=10-6m)
E [eV]
1.24 [mm eV]

27.
410
E(3 g 2) =
= 1.89 eV

28. l (mm) = (mm=10-6m)
E [eV]
1.24 [mm eV]
l(3 g 2) = ~ mm
1.89
1.24

29. Shine Light through Hydrogen…
410

30. Thermal Radiation

31. Rules for Emission by Opaque Objects
Hotter objects emit more total radiation per unit surface area.
Stephan-Boltzmann Law:
E = T4 (s = 5.7 x [Watt/m2Kelvin4])
Hotter objects emit bluer photons (with a higher average energy.)
Wien Law:
max = 2.9 x 106 / T (K) [nm]

32. What have we learned? What is the escape velocity of the Earth?
If an object travels fast enough, it will escape the gravitational pull of the Earth. The speed needed can be calculated by setting the gravitational potential energy at the surface of the Earth to the expression for kinetic energy and solving for the speed necessary to overcome the pull of the Earth.
½ mv2 = mgh
remember 7/11 (7 m/s or 11 km/s)

33. What have we learned? What is universal law of gravity?
F = G m1m2 r2
What does this formula mean? If you double a mass what happens to the force? If you half the distance, how does the force change?

34. What have we learned?
How are speed, wavelength, and frequency related for a wave?
The wavelength is equal to the speed divided by the frequency
What is meant by the dual nature of light?
Light sometimes behaves like a particle (photon) and at other times like a wave. This is a first hint that all things have a dual nature – behaving both as particles and waves.
What is the relationship between the energy for light and its amplitude, frequency, or speed?
The energy associated with light is independent of its amplitude. Also, since all light travels at the speed of light, Energy is also independent of speed. The energy is however directly proportional to the frequency (color) of the light.

35. What have learned? What is light?
Light is an electromagnetic wave that also comes in individual “pieces” called photons. Each photon has a precise wavelength, frequency and energy.
Forms of light listed in increasing energy are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays

36. What have we learned?
What are wavelength and frequency for light? Wavelength is the distance between two parts of a wave that are the same and frequency is the number of waves that pass a point per second.
How do light and matter interact? Matter can emit light, absorb light, transmit light or reflect light
ln = c
E = hn …...

37. What have we learned? How does light tell us what things are made of?
Every kind of atom, ion, and molecule produces a unique set of spectral lines.
How does light tell use the temperatures of planets and stars?
We can determine temperature from the spectrum of thermal radiation

38. What have we learned? What are the possible orbits allowed by gravity?
elliptical, hyperbolic, parabolic

39. Tides
Since gravitational force decreases with (distance)2, the Moon’s pull on Earth is strongest on the side facing the Moon, and weakest on the opposite side.
The Earth gets stretched along the Earth-Moon line.
The oceans rise relative to land at these points.

40. Tides
Every place on Earth passes through these points, called high tides, twice per day as the Earth rotates.
High tides occur every 12 hours 25minutes
remember, the Moon moves!
The Sun’s tidal effect on Earth is not as strong.
the ratio Earth’s diameter : distance to Sun is much less than ratio Earth’s diameter : distance to Moon
When the Sun & Moon pull in the same direction (new & full phases)
high tide is higher than usual (spring)
When the Sun & Moon pull at right angles (first & last quarter phases)
high tide is lower than usual (neap)

41. Tidal Friction
This fight between Moon’s pull & Earth’s rotation causes friction.
Earth’s rotation slows down (1 sec every 50,000 yrs.)
Conservation of angular momentum causes the Moon to move farther away from Earth.

42. Synchronous Rotation
…is when the rotation period of a moon, planet, or star equals its orbital period about another object.
Tidal friction on the Moon (caused by Earth) has slowed its rotation down to a period of one month.
The Moon now rotates synchronously.
We always see the same side of the Moon.
Tidal friction on the Moon has ceased since its tidal bulges are always aligned with Earth.

43. aphelion
perihelion
FF’ a b 2a
e = FF’ = aphelion - perihelion 2a

44. Homework #3
An asteroids closest approach to the Sun (perihelion) is 2 AU, and farthest distance from the Sun (aphelion) is 4 AU.
What is the semi major axis of its orbit?
What is the period of its orbit?
What is it’s eccentricity?

45. Homework #3 continued
A set of keys is dropped from the top of the Empire State building in New York. How fast will they be going when they hit a poor tourist on the ground 9 seconds later?
How tall is the Empire State Building?
An astronaut drops his set of keys from the same height as the Empire State Building on the Moon (1/6th the gravity of Earth), how fast is it going when it hits the Lunar surface?

46. Homework #3
An asteroids closest approach to the Sun (perihelion) is 2 AU, and farthest distance from the Sun (aphelion) is 4 AU.
What is the semi major axis of its orbit?
What is the period of its orbit?
What is it’s eccentricity?

47. Homework #4
A set of keys is dropped from the top of the Empire State building in New York. How fast will they be going when they hit a poor tourist on the ground 9 seconds later?
How tall is the Empire State Building?
An astronaut drops his set of keys from the same height as the Empire State Building on the Moon (1/6th the gravity of Earth), how fast is it going when it hits the Lunar surface?

48. Rules for Emission by Opaque Objects
Hotter objects emit more total radiation per unit surface area.
Stephan-Boltzmann Law:
E = T4 (s = 5.7 x [Watt/m2Kelvin4])
Hotter objects emit bluer photons (with a higher average energy.)
Wien Law:
max = 2.9 x 106 / T (K) [nm]

49. Two kinds of Spectra: 1) Absorption
If light shines through a gas, each element will absorb those photons whose colors match their electron energy levels.
The resulting absorption line spectrum has all colors minus those that were absorbed.
We can determine which elements are present in an object by identifying emission & absorption lines.

50. 2) Emission Spectra
The atoms of each element have their own distinctive set of electron energy levels.
Each element emits its own pattern of colors, like fingerprints.
If it is a hot gas, we see only these colors, called an emission line spectrum.

51. Lets look at continuous, absorption line, and emission line spectra –

52. Kirchhoff’s Laws
I. A hot, dense glowing object (solid or gas) emits a continuous spectrum.

53. Kirchhoff’s Laws
II. A hot, low density gas emits light of only certain wavelengths --
an emission line spectrum.

54. Kirchhoff’s Laws
III. When light having a continuous spectrum passes through a cool gas, dark lines appear in the continuous spectrum –
an absorption line spectrum.

55. Kirchhoff’s Laws I
III II