|Moon’s orbit is 5° off of the Sun-Earth ecliptic plane; what does this explain regarding eclipses?||The moon’s path is always near the ecliptic, sometimes slightly north or south of it.|
|Lunar Sidereal Month = how long it takes for the moon to circle the sky and return to the same position||27.3 days = true orbital period of the Moon.|
|Synodic Month||“Together; path” -calendar month based on Sun = 29.5 days (this is expressed as the Lunar Phase Cycle, which is Sun-based|
|Why are the 2 extra days of the synodic period needed?||Remember, that each month, we move 30° of arc around the sun as the moon orbits, so two extra days are needed in the synodic (calendar) month to account for this shift in position.|
|“Face on the Moon” -What does this mean?||lunar rotation synchronous with its orbital revolution around Earth (same side faces Earth constantly = Tidal Lock).|
|Tidal Lock||Only see one side of the moon; experience tides by gravity of the moon (water, rocks); tides create friction and rate of rotation|
|Lunar Eclipses||Shadow of Earth on Moon (more frequently observed because Earth is larger than Moon).|
|Umbra||full shadow (darkest). On Moon, an observer in the umbral area would not see the Sun. –>Totality|
|Peneumbra||Sun partly occulted by the Earth. The Sun would be partially visible by an observer on the Moon. At such time, the full shadow covers only a part of the moon’s face –>Partial Eclipse|
|During complete lunar eclipse, the Moon appears reddish orange, not black. Why is this so?||The red glow is from a ring of sunrises and sunsets around the circumference of Earth that shines into the umbra of Earth’s shadow.|
|As viewed from the umbral zone, how would the Earth appear?||coppery- red color|
|Solar Eclipses||Sun is occulted by the Moon, the disc of which is nearly the same size as that of the Sun.|
|Total Solar Eclipses||rare events owing to the small size of the umbral area (narrowness of the umbral path) due to the Moon’s smaller size.|
|Description of Total Solar Eclipse||(average 2-3 minutes, up to 7.5 minutes duration) = migration of shadow 1700 km/hour across face of Earth.|
|What are we in during Penumbra?||We are in Penumbra during partial eclipse; sun becomes an arc (hazardous to observe).|
|What happens to Sun's photosphere during? What can now be seen? What also becomes visible?||Sun’s photosphere covered during full Solar Eclipse. Solar Chromosphere can now be seen. Stars become visible|
|relationship between Eccentricity of Earth and Lunar orbits|
|the phenomenon of Annular Eclipses|
|Thales of Miletus (500 B.C.E. in present day Turkey) ; How did he view the world? What does it contrast with?||viewed the Universe as RATIONAL (that is, it can be UNDERSTOOD). This contrasts with early mystical view that the universe is unknowable.|
|Plato; What did he discover? How were problems solved during this time? What were the path of planets?||Perfection concept (spheres of Euxodus)
Problems at this time solved through philosophy; string of deductive conclusions following from a “First principle” (self-evident truth):
Paths of planets elegant circles with planets at uniform speeds
|Aristotle (384-322 B.C.E.) ; What model did he follow? Stellar Parallax? How did he describe heaven? Inside of Earth? What did he think of Earth?||Geocentric Universe Model
Earth stationary = no Stellar Parallax
Heavens perfect; imperfection below level of the Moon
Inside of Earth = greatest imperfection
Earth = sphere; casts circular shadow on Moon
|Aristarchus (2nd-3rd centuray B.C.E.); What model did he follow?
Who was he challenged by? What 3 things did he claim?
|Heliocentric Universe Model = Sun-centered
Challenged by contemporary astronomer + earlier Aristotle:
No Stellar Parallax seen by Aristotle
No colossal winds associated with a moving Earth
Aristotle “wrong for the right reasons”
|Eratosthenes (Alexandria). What did he do? Where is sun at summer solstice? Where is it in Alexandria and what was the Sun degree difference?|| computed circumference of Earth.
At Summer Solstice, Sun directly overhead at Syene (Aswan)-
illuminated a deep well
At Alexandria (on same day-and same longitude), the noonday
Sun was at 83°. 7° difference = 1/50 of 360°)
|How can this be solved?||Knowing distance between Syene and Alexandria (5000 Stadia),
one can compute circumference of entire Earth.
5000 X 50 = 250,000 stadia (Circumference of Earth); divide this
value by 2 phi (3.1416 X 2 = 6.28), this yields 40,000 stadia.
|What was the historical consequence of Christopher Columbus’s use of Aristotle’s calculations rather than Eratosthenes’s calculations in assessing his discovery?||Aristotle’s diameter- was thought that Earth was so small that he could sail west and reach Japan. Eratosthenes’s calculations-would have never risked the voyage. Crew would starve to death|
|Claudius Ptolemy (2nd century Alexandria). How was Earth? Any stellar parallax? What did he envision?||Worked from First Principle that Earth was stationary.
No Stellar Parallax
Problem of Retrograde Motion to explain
He envisioned epicycles (small circles) on the larger planetary
paths to keep planets at uniform speeds.
|Nicholas Copernicus 1473 – 1543 (Polish): What model does he follow? What did he learn from his Heliocentric Hypothesis?||Heliocentric Model-
Copernicus very cautiously advanced his Heliocentric Hypothesis, which explained Retrograde Motion as a relativistic perspective from a moving Earth.
|Geocentric Universe had become ruling Paradigm||Aristotelian Universe had become deeply ingrained into established religious thinking. Hellenistic “perfection” model for heavens/celestial sphere supported concept of “Heaven and Hell”; became part of religious Doctrine.|
|Why does Copernicus reject the Geocentric Model?||Copernicus rejects GEOCENTRIC model, but retains epicycles and circular motion (main hypothesis correct but general model still flawed)|
|Tycho Brahe (1546-1601); Who was he? What did he make? Did he see stellar parallax?|| wealthy Dane, extravagant-big ego, had royal favor, had access to best observatory.
Generated best star/planet maps to date using a star pointer (not telescope).
Did not see stellar parallax (universe = Earth-centered)
|Tycho’s supernova (“new star”); What does this say about the universe? What model did this challenge?||an imperfection in the universe bc it should be closer to Earth than the Moon (and should show stellar parallax, but did not). This challenged the Aristotelian model of perfection of the higher universe, bc the supernova had to be on the Celestial Sphere|
|Johannes Kepler ; What did he interpret? What did Kepler create?|| (born in 1571)
Kepler reinterprets Brahe’s data to show that planetary paths are not circular and that planetary speed varies.
Kepler's Three Laws of Planetary Motion
|Kepler's First Law of Planetary Motion||orbits of planets are ellipses with Sun at one focus
-Eccentricity: e= c/a
|Kepler's Second Law of Planetary Motion||Area-time constancy (planet closer to Sun has shorter solar distance that must be mathematically compensated by greater planetary velocity to keep area/time constancy).
-understanding concept of orbit
|Kepler's Third Law of Planetary Motion||A planets orbital period squared is proportional to its average distance from the Sun cubed.
p2 = a3
P = time (years) a = astronomical units
|More about Kepler's Three Laws||Planetary paths are elliptical (ellipse is eccentric loop with two foci)
-They are empirical
|Galileo Galilei (1564-1642): How did Galileo look at celestial observations? What did he discover about moons? Milky Way?||Galileo Galilei (1564-1642):
Applied a Dutch instrument (telescope) to celestial observations.
A, Moon displays imperfections (cratered moonscape)
B. Milky Way composed of stars
|Galileo's Jovian Moons; What will happen if moon orbits Jupiter? How fast do the four inner moons move? What law is supported?||Jovian Moons: If moons orbited Jupiter, than Earth could orbit the Sun (Jovian system = Solar System analog); Innermost of the four Galilean moons move the fastest; the outer-most one moves the slowest, supporting Kepler’s third law.|
|Galileo and the phases of Venus||Venus not seen only as crescent as predicted by Ptolemaic model,
but as a full suite of phases; this told him that Venus also had a
heliocentric orbit, like Earth.
|Galileo and the Sun||Sun displayed Sunspots, hence was imperfect. Sun revolves (this
was physically costly for Galileo.
|Galileo had “broken the dam” for observational science||Galileo had “broken the dam” for observational science and had pushing thinking “out of the envelope”, paving the way for Newton. The paradigm was now rapidly shifting.
-empirical observations; repeat experimentations
|Galileo- Acceleration of Gravity||Steady increase in velocity of a falling body|
|Galileo- Inertial Motion||visual in space–> motion continues until something changes it|
|Isaac Newton||created 3 laws of motion that describe any moving object|
|Newton's First Law of Motion||An object at rest or uniform motion in a straight line unless acted on by some force|
|Newton's Second Law of Motion||Acceleration (A) of a body is inversely proportional to its mass (M) and directly proportional to net force (F)
-Mass and weight are 2 different concepts
|Newton's Third Law of Motion||To every action, there is an equal and opposite reaction.|
|Inverse Square Law||proportional power function of increased light areal coverage and dimming of same light on surface with increasing distance from light source (recognized by Newton)
-Newton applied principle to Gravity, utilizing his third law and Keplers
|Orbit Velocity vs. Circular Velocity||orbit- lateral or sideways movement
circular- circular orbit