Equations to memorize Equations I will give you

speed=distance/timemomentum=massvelocityang. mom.=massvelocity radius

force=mass acceleration

p2=a3

distance2

size physical

360

sizeangular

3

21

22

)(

4a

MMGp

221

d

MGMFg

R

GMvescape

2

c=3 108 m/sG=6.67 10-11 m3 /(kg s2)

2

2

1.. mvEK

Moon Rise/Set by Phase• The different phases also rise and set at different times:

– At full moon, the moon is opposite the sun, so it rises at sunset, culminates at midnight, and sets at dawn

– At new moon, the moon is on the same side as the sun, and so is only in the sky during the day (rises at dawn, sets at dusk)

– First quarter rises at noon, culminates at 6pm, and sets at midnight– Last quarter rises at midnight, culminates at 6am, and sets at noon

• Note: the moon spends as much time in the sky in daytime as at night!

Moon Rise/Set by Phase

Time the Moon Rises and Sets for Different Phases

• Now let’s step through the Universe in powers of 10:

Zooming Out or Zooming In 26 Orders of Magnitude

Tides and Phases

Size of tides depends on the phase of the Moon.Note spring tides means extreme high and low tides

Tides

http://www.youtube.com/watch?v=PtUmLLlm7S0&feature=relatedhttp://maps.google.com/maps?hl=en&ie=UTF8&ll=51.64359,-2.622986&spn=0.755036,1.779785&t=p&z=9

The sky varies with latitude but not longitude.

What causes the seasons?

Seasons depend on how Earth’s axis affects the directness of sunlight.Note - not because one hemisphere is closer to the sun!!!

Axis tilt changes directness of sunlight during the year.

Why Does Flux Sunlight Vary

Kepler’s Third Law

Kepler's 3rd Law

100 billion stars

Where do we sit?

How did we come to be?

Are we ever sitting still? Earth rotates on axis: > 1,000 km/hr

Earth orbits Sun: > 100,000 km/hr

Solar system moves among stars: ~ 70,000 km/hr

Milky Way rotates: ~ 800,000 km/hr

Milky Way moves in Local Group

Universeexpands

100 billion stars

Momentum=mvAng Momentum=mvr

p2=a3

2

2

1.. mvEK

100,000 ly diameter

M

ap

aMMG

p

32

3

21

22

)(

4

in m, s, kg

in A.U., years, Solar masses yearsp

M

ap

33

33

32

in 1 second it accelerates 10 m/safter 5 seconds it is at 50 m/sThe change of mass has no effect

See over

1parsec = 3.26ly = 206,265 AUdistance2

size physical

360

sizeangular

360

distance2 sizeangular size physical

1arcsec=1/60/60 degrees = 2.7810-4 degrees

10A.Uparsecs1084.4360

10parsecs2 102.78 size physical 5

-4

Angular Size

distance 2

degrees 360 size physical = sizeangular

An object’s angular size appears smaller if it is farther away.

We see apparent retrograde motion when we pass by a planet in its orbit.

Mars Retrograde Motion

• How did Copernicus, Tycho, and Kepler challenge the Earth-centered idea?—Copernicus created a Sun-centered model; Tycho provided the

data needed to improve this model; Kepler found a model that fit Tycho’s data.

• Kepler’s three laws of planetary motion1. The orbit of each planet is an ellipse with the Sun at one focus.2. As a planet moves around its orbit it sweeps our equal areas in

equal times.3. More distant planets orbit the Sun at slower average speeds:

p2 = a3.

• Galileo solidified the Copernican revolution.—His experiments and observations overcame the remaining

objections to the Sun-centered solar system.

• Newton’s Three Laws of Motion1. An object moves at constant velocity if no net force is

acting.2. Force = mass acceleration.3. For every force, there is an equal and opposite reaction

force.

221

d

MGMFg 3

21

22

)(

4a

MMGp

Conservation Laws

• Conservation of momentum

• Conservation of angular momentum

• Conservation of energy

Measurements:Nyene to Alectown • distance ≈ 1300km• angle difference = 90°- 81°• angle difference = 9°

• CN * 9/360 = 1300• CN = 1300 * 360/9 = 52000 = 5.2 104

You are an astronomer on planet Nearth, which orbits a distant star. It has recently been accepted that Nearth is spherical in shape, though no one knows its size. One day, while studying in the library of Alectown, you learn that on the equinox your sun is directly overhead in the city of Nyene, located 1300 due north of you. On the equinox, you go outside in Alectown and observe that the altitude of your sun is 81 .

Equations to memorize Equations I will give you

speed=distance/timemomentum=massvelocityang. mom.=massvelocity radius

force=mass acceleration

p2=a3

distance2

size physical

360

sizeangular

3

21

22

)(

4a

MMGp

221

d

MGMFg

R

GMvescape

2

c=3 108 m/sG=6.67 10-11 m3 /(kg s2)

2

2

1.. mvEK