Cosmic Visions Midterm

Jupiter Moons

- called "Medici Stars"; - Jupiter is another center of motion, which opposed Aristotle as he said Earth was the center of the universe

Pros of Copernican System

-aesthetically pleasing; -can begin realistically measuring distances in the cosmos

Cons of the Copernican System

-doesnt explain why dont feel earth moving about sun -stellar parallax not observed -Heliocentric theory contradicts Aristotle's physics

Planets

-rise in east, set in west; -appear to move from one constellation to another from week to week; -appear to move at different rates and are not fixed in places in celestial sphere -usually lag behind stars (prograde motion) and Sometimes return faster than stars (retrograde)

Stars

-rise in east, set in west; -do NOT move with respect to each other from night to night; they seem to be fixed in respect to one another -they circle around celestial pole, but they never rise or set near celestial pole -positions can be plotted on the celestial sphere;

Moon

-rises in east, sets in west, -lags behind Sun by about 12 degrees per day on average, -one moonrise to the next = about 24 hrs 48 min -Moons monthly orbit about Earth is titled about 5 degrees with respect to the ecliptic

Planet is in opposition to the Sun if...

... it is 180 degrees away from the Sun -directly across from it

Planet is in conjunction with the Sun if...

... it is about 0 degrees away from the Sun

Values of Eccentricity: Ellipse

0 < e< 1

Equator (position)

0 degrees latitude

Problems with Eudoxus and Aristotle Models

1) don't explain shapes of retrograde motions well; 2) don't explain why planets vary in brightness --> in their model, planets would have the same distance from the Earth

Why was Brahe's observation of Great Comet of 1577 important?

1) it was the first time the parallax of a comet had ever been measured, and they realized that the comet was at least 3x as far away as the moon is from the earth. 2) The comet seemed to be cutting across orbits of planets, like Venus. Aristotle was convinced that the comet was something in the upper atmosphere of earth while Brahe said it was a celestial object that crosses planetary orbits

Summer Solstice

1) point on celestial sphere where the Sun appears to be farthest north in the sky 2)we have most hours of daylight and fewest hours of darkness (June 22)

Winter Solstice

1) point on celestial sphere where the Sun appears to be farthest south in the sky 2) we have the most hours of darkness and least hours of daylight (Dec 22)

Vernal Equinox

1) point on the celestial sphere where the Sun rises exactly in the East while it is going northward in its annual apparent path 2) date about March 21 when the Sun is directly overhead at Earth's equator at about noon. 12 hours daylight, 12 hours night

Autumnal Equinox

1) point on the celestial sphere where the Sun rises exactly in the East while it is going southward in its annual apparent path 2) date about Sep 21 when the Sun is directly overhead at Earth's equator at about noon. 12 hours daylight, 12 hours night

Ecliptic

1) the yearly apparent path of the Sun with respect to the stars on the celestial sphere; 2) the geometric plane that passes through the centers of the Sun and Earth 3) titled 23 and a half degrees in respect to the eqautor

Problems with Aristarchus Model

1) why don't we feel Earth move; 2) Aristotle's physics didn't agree; 3) parallax of stars not observed

Order of planets from the sun (Men Very Easily Make Jugs Serve Useful Needs, Perhaps)

1. Mercury 2. Venus 3. Earth 4. Mars 5. Jupiter 6. Saturn 7. Uranus 8. Neptune

Isaac Newton

1. Newton's laws; 2. developed calculus; 3. explained gravity

Model of Nicolaus Copernicus

1473-1543; 1. heliocentric model; 2. Earth rotates daily and revolves yearly about Sun; 3. Sun is near the center, but not completely in the center 4. used epicycles, deferents, eccentric --> Earth varies in distance from sun because of epicycles and deferents 5. did NOT use equant; 6. used uniform circular motion 7. allowed us to measure relative distances between sun and planets

Tycho Brahe

1546-1601; 1. BRAHE'S MODEL: sun revolves around earth, but all planets revolve about the sun 2. built large, high-precision astronomical instruments 3. obtained most accurate observations by naked eye 4. observed Great Comet of 1577 and measured its distance with parallax

Galileo Galilei

1564 - 1642; 1. one of the first to observe celestial objects frequently with telescope 2. advocated Copernican model 3. Jupiter has moons, it is another center of motion 4. Venus has phases, which disproves Ptolemaic model 5. Law of Inertia: If there is no net force acting on an object, the object remains in the same state of motion, 6. Law of Falling Bodies: all bodies fall with the same acceleration, independent of their mass.

Johannes Kepler

1571-1630; 1. tried to fit Brahe's data to Copernicus' model; rejected Copernican model and restarted 2. Created Kepler's Laws 3. NO CIRCULAR ORBIT, NO EPICYCLE AND DEFERENT Legacy: -3 laws of planetary motion are correct -Chose data over the model and casted aside Copernicus's model and modified model to fit data -Believed there is a simplicity in physical laws -Created Simple mathematical equation as knowledge

Galileo's Trial

1633 - tried for heresy before the Inquisition, forced to recant Copernican model, sentenced to house arrest until death

The Book of Later Han

185 BC - appearance of a "guest star" not previously seen which appeared for 8 months until it disappeared

Hipparchus of Nicaea

190 BC - 120 BC; suggested magnitude scale for apparent brightness of celestial objects ranging from: +1 (very bright) to +6 (very dim)

Shiji (Records of the Grand Historian)

240 BC - recorded the appearance of a "broom star" (Halley's Comet)

Models of Eudoxus and Aristotle

300s BC; 1. geostatic: earth doesnt move (translational or rotatational) 2. geocentric 3. two homocentric spheres associated with Sun, Moon and each planet -Planets had 4 spheres and moon had 3 -One sphere describes daily motion and the other describes the yearly motion

Model of Aristarchus

320 BC - 250 BC; 1. heliocentric, 2. Earth rotates daily, 3. Earth revolves yearly about Sun

Plato

427 BC - 347 BC; how can we "save the appearances" of the planets' motions using uniform circular motion? --> how to use uniform circular motion to describe retrograde and prograde

Ellipse

A elongated circle, or oval shape, the shape of the planets orbit -The sum of the two distances (legs of triangle) to focal points (two dots), are constant

Question 1.4: Why does a lunar eclipse last for a longer time than a solar eclipse?

A lunar eclipse is longer than a solar eclipse because the moon is smaller than the Earth. During a lunar eclipse, it takes much longer for the earth to completely move past the sun than for the moon to move completely past the sun.

Ptolemy

AD 100s; 1. geostatic 2. modified geocentric/eccentric model: The Earth couldn't be exactly in the center, it was a little off-center 3. used deferents, epicycles, eccentric, equant Wrote: "Almagest" (The Greatest) Ptolemy's model agreed with: 1) "common sense" (can't feel Earth move); 2) observations within 5 degrees; 3) much of Aristotle's physics

Question 1.3: Why don't a solar eclipse and a lunar eclipse occur every month?

ANS: A solar eclipse and a lunar eclipse don't occur every month because the it is very difficult time wise for the earth to cover the moon or the moon to cover the earth. The moon's orbit around the earth and the earth's orbit around the sun do not fall on the same plane. Since the Moon's orbit is tilted five degrees from Earth's orbit around the Sun, the Moon passes below or above the shadow.

Question 5.2: A minor planet has been discovered. The radius of its orbit about the Sun is four times the radius of Earth's orbit about the Sun. How long does the planet take to revolve around the Sun? (A) 1 Earth year; (B) 2 Earth years; (C) 4 Earth years; (D) 8 Earth years; (E) None of the above.

ANS: D. 8 years. I assumed that the radius of Earth's orbit about the Sun was measured by 1 A.U. If the minor planet's radius of its orbit about the sun is 4 times that of earth's, then it's measured by 4 A.U. When plugged into the equation for Kepler's 3rd Law, I used D=4. Therefore, D^3=4^3=64. To find T, I took the square root of 64, which equals to 8 or 8 years.

Question 5.3: How did Galileo's observations of Venus disprove Ptolemy's model of planetary motion?

ANS: Galileo discovered that Venus has phases like the moon. When Venus was in a crescent, its diameter appeared larger, which meant it must be closer to earth. When Venus was at full size, its diameter appeared smaller, meaning it was farther away from Earth. Therefore, Galileo believed that Venus must orbit the sun and not the earth because the size of its diameter was affected. If Venus were orbiting earth, its diameter would stay about the same because it would be in a more equally distanced orbit from the Earth. This disproved the Ptolemaic model as that model was based on the fact that all planets revolved around Earth.

Question 1.1: If the expected sunrise is 6:51 AM and the sunset is 5:06 PM in Boston on a certain day, what time will the sun be at its highest altitude in the sky?

ANS: It will be highest at about 11:58PM. The time when the sun will be at its highest is midway between sunrise and sunset (there is symmetry). Since the amount of time between 6:51AM and 5:06PM is 10 hours and 15 minutes, the midpoint time is 11:58PM

Question 5.1: According to Kepler's "heliocentric" model, why does Earth have seasons?

ANS: Kepler's heliocentric model states that the earth's axis of rotation is NOT perpendicular to the ecliptic, but is actually tilted about 23.5 degrees. Seasons are a result of this tilt. When the northern hemisphere is tilted closer toward the sun, it receives more direct sunlight, making it experience summer. While this is occurring, the southern hemisphere is titled further away from the sun, preventing it from receiving direct rays of sunlight. Therefore, the southern hemisphere is experiencing winter. It is important to note that the northern hemisphere is not closer to the sun during summer; the earth's axis is just tilted closer as it moves around the ecliptic.

Question 3.3: Does Earth's moon have retrograde motion in its monthly motion about the celestial sphere? How could Ptolemy's model avoid retrograde motion for the moon?

ANS: Moon doesn't move in retrograde. (Sun also doesnt move in retrograde). How can an object that lacks retrograde motion be modeled in Ptolemy's system? If the period that the moon goes around the epicycle is the same as the period that the epicycle goes around the deferent is the same, then retrograde motion isn't modeled.

Question 3.2: Describe in some detail how Ptolemy's model explained the retrograde motion of a superior planet.

ANS: Ptolemy's model explains the retrograde motion of a superior planet through the use of epicycles. The motion when a planet reaches the side of the deferent closest to the Earth, the counterclockwise motion of the epicycle makes the planet appear as if it moving backward in the sky, or is in retrograde. Once the planet crosses the deferent back to the far side of the epicycle, it continues its prograde motion because the epicycle and orbit are in sync again.

Question 4.2: According to the Copernican model, why does a superior planet always have a retrogression when it is in opposition to the sun?

ANS: The Copernican model places the sun in the center of the solar system, whereas the other planets orbit the sun. A superior planet always has a retrogression when it is in opposition to the sun because a faster-moving earth on an inside orbit will speed by an outer planet which appears to move backwards. Inner planets are always going to move faster than outer planets around the sun. For example, if the earth is moving around the sun and so is Mars, the earth will pass Mars in its orbit and it will seem that Mars is moving backward as earth moves forward.

Question 4.1: According to the Copernican model, why is a sidereal day shorter in length than a mean solar day?

ANS: The sidereal day is the true period of rotation that the earth has relative to the distant fixed stars, which is 23 hours and 56 minutes. Additionally, while the earth rotates on its axis, it also revolves around the sun, moving about 1 degree per day. The earth therefore must rotate a tiny bit more, about 4 minutes in time duration, for the sun to be in the same exact position.

Question 3.1: Suppose you use parallax to estimate the distance to two objects, one of them much closer to you than the other object. Assuming both measurements use the same baseline, which measurement will have a higher percentage of error? Why?

ANS: The star that's farther away would have a higher percentage of error. When an object is farther away, it will shift less than an object that's closer. When we're dealing with error, it's harder to tell when things are subtly different than when things are wildly different. When we did th experiment of the object that is closer, the object shifted a lot. We are able to measure it. With the object that's far away, we weren't able to to tell the difference, so it's hard to tell the error.

4.3: Why was Tycho Brahe's measurement of parallax of the Great Comet of 1577 important?

ANS: Tycho Brahe's measurement of parallax of the Great Comet of 1577 was important because it was the first time the parallax of a comet had ever been measured, and they realized that the comet was at least three times as far away as the moon is from the earth. The comet seemed to be cutting across orbits of planets, like venus, which had never been observed in that manner before. Aristotle was convinced that a comet was something in the upper atmosphere of earth while Brahe said it was a celestial object that crosses planetary orbits.

Question 2.2: An observer at Earth's equator sees a planet overhead at midnight. Which of the following planets must it NOT be: (a) Venus, (b) Mars, (c) Jupiter, (d) Saturn, or (e) "Not enough information has been given to answer the question."

Ans: Venus. There is no way it could be Venus because Venus is always less than or equal to 48 degrees from the sun, so if the sun isn't out/visible, Venus can't be either.

Question 2.3: Jupiter seems to vary in apparent brightness from month to month. A long-term observer of the planets at Earth's equator notes on one clear night shortly after sunset that Jupiter appears to be the brightest she has ever seen it. Jupiter must be: (a) Near the point where it sets on the western horizon; (b) About 70 degrees above the western horizon; (c) Almost overhead; (d) About 70 degrees above the eastern horizon; (e) Near the point where it rises on the eastern horizon.

E. Near the point where it rises on the Eastern Horizon. This is due to the fact that it will always be brightest when it's in opposition to the Sun. If the Sun is just setting, Jupiter has to be directly across it, which means Jupiter would be a little higher than its rising point.

Eccentricity

Eccentricity = c/a measures how stretched out ellipse is Circle Value: e=0

Question 1.2: What will be the phase of the moon if you see the moon on the eastern horizon as the sun is setting?

Full moon. The sun is fully illuminating the moon because the sun is setting and the moon is rising at the same time.

Parallax of stars

If the Earth revolves yearly about the Sun, the nearby stars should shift position with respect to the far away stars -closer stars: large parallaxes -distant stars: small parallaxes

Who was Brahe's assistant?

Johannes Kepler

Why seasons?

Kepler's heliocentric model states that the earth's axis of rotation is NOT perpendicular to the ecliptic, but is actually tilted about 23.5 degrees. Seasons are a result of this tilt. When the northern hemisphere is tilted closer toward the sun, it receives more direct sunlight rays, making it experience summer. While this is occurring, the southern hemisphere is titled further away from the sun, preventing it from receiving direct rays of sunlight. Therefore, the southern hemisphere is experiencing winter. It is important to note that the northern hemisphere is not closer to the sun during summer; the earth is just tilted closer as it moves around its orbit.

Superior Planets

Mars, Jupiter, Saturn; -vary from 0-180 degrees away from Sun; -ALWAYS in retrogression when in opposition to Sun and always appear brightest when opposite

Inferior Planets

Mercury and Venus; -always < 48 degrees away from Sun; -are in retrogression when in conjunction with Sun

Did everyone think the Earth was flat until Columbus?

NO - WRONG, ABSOLUTELY WRONG! (believed Earth spherical since Pythagoreans - 500 BC up) Aristotle also thought it was spherical 250 BC

North pole position vs South Pole position

North pole: +90 degrees south pole: -90 degrees

Scientific Method

Observations (Data) = Model (Theory)

Question 2.1: A certain star rose at 10:00 p.m. Eastern Daylight time on September 15. What time will the same star rise on September 17?

Stars don't rise at the same time every day ANS: 9:52 PM. If a sidereal day is about 23 hours and 56 minutes, it will rise at 9:56PM on September 16 and if you add 23hrs and 56 mins to that, it will rise at 9:52PM on September 17. Sidereal day is the time from when a star rises and rises again the next day

Kepler's Second Law

a line drawn from the Sun to a planet sweeps out equal areas in equal times so a planet travels faster when closer to the Sun and slower when farther away -Explanation: the time it takes for the planet to travel from C to D and A to B is the same, which means the planet has to travel at a faster pace from C to D because the distance is greater (at its perihelion: when its closest). Moves slower when it is at its aphelion (when its furthest)

Kepler's Third Law

a precise relationship exists between a planet's distance from the Sun and its orbital time : D^3 = K x T^2 where D = average distance of the object from the Sun; T = the planet's orbital period; K = a constant

Acceleration

acceleration = change in velocity/change in time - it is a vector: includes speed and direction (NSEW) -Things fall at CONSTANT ACCELERATION of 9.8 m/s^2 down, NOT VELOCITY

Galileo's Law of Inertia

an object in motion on a horizontal plane will remain in motion at the same speed unless affected by an outside influence

Parallax

apparent displacement of an object as seen from two different points NOT on a straight line with the object → objects shift position -distant object= smaller angle of parallax --> will lead to more error if you are trying to figure out its position since it's a very minimal difference -closer object= larger angle of parallax -If you observe from two different places, there is an apparent shift of nearby objects with respect to distant objects

Mean solar day

average time from one sunrise until the next = 24 hours

Velocity

average velocity = change in position/change in time - it is a vector: includes speed and direction (NSEW)

Why does a lunar eclipse last for longer time than a solar eclipse?

because the Earth is larger than the Moon, thus the shadow is also larger

Why don't a solar eclipse and lunar eclipse occur every month?

because the Earth is tilted 23.5 degrees, it doesn't line up every month

According to Ptolemy, why are inferior planets always <48 degrees away from Sun?

center of inferior planet's epicycle must lie on straight line between Earth and Sun

Synodic Month

complete cycle of moon phases (about 29.5 days) --> new moon to new moon

Values of Eccentricity: Circle

e = 0

Values of Eccentricity: Earth's orbit

e = 0.0167 (almost circle)

Values of Eccentricity: Parabola

e = 1

Newton's First Axiom (Constant motion)

each body remains in a state of rest or moves at constant velocity (constant speed is a straight line) unless it is compelled to change by a net external force

Kepler's First Law

each planet has an elliptical orbit with the Sun at one focus of the ellipse

Retrogression of a superior planet

faster moving Earth on an inside orbit speeds by outer planet which appears to move backwards --> Inner planet moves faster than outer planets around the sun

Galileo and Venus

found that Venus has phases like the moon disproves Ptolemaic model; proves Venus must orbit the Sun because the size of its diameter is affected when it is close and far away from the Earth. -Full venus= far, crescent venus = close -If it were orbiting earth, its diameter would stay about the same because it would be in a somewhat more equally distanced orbit from the Earth.

Why was Brahe's observation of not being able to measure the parallax of 1572 bright star important?

important because it contradicted Aristotle's idea of the celestial realm being unchanging. It seemed that a new star had arisen and was as far as the fixed stars that had been previously observed

According to Copernicus...

inferior planets = inner planets, superior planets = outer planets

Right Ascension

longitude

Galileo's Telescope

made with two lenses; best magnification = 30X; observed new features of the cosmos

Galileo and the Moon

moon has rough, uneven surface with mountains and valleys

Aphelion

point in the orbit at which planet is farthest from the Sun

Perihelion

point in the orbit at which the planet is closest to the Sun January in N Hemisphere

Sun

rises in the east, sets in the west -Appears to move from one constellation to another because it is off by a couple of degrees each day since sun day is 24 hours and star day is 23 hours and 56 mins

Earth's rotation

rotates from east to west

Equant

shows the uniform angular motion of a planet about off-center point (E'); E' is the equant; it uses a circle but is NOT uniform circular motion 1) uses a circle but is NOT uniform circular motion; Planet would move more slowly on the left because the distance is less on the left, it is not uniform circular motion 2) uniform angular motion about off center point (E'); E' is the equant 3) Sun of planet travels equal angles about E' in equal times 4) Planet moves slower near equant

Why are times different between solar day and sidereal day

sidereal day is the true period of rotation that the earth has relative to the distant fixed stars, which is 23 hours and 56 minutes. Additionally, while the earth rotates on its axis, it also revolves around the sun, moving about 1 degree per day. The earth therefore must rotate a tiny bit more, about 4 minutes in time duration, for the sun to be in the same exact position. Rotation = turning about its axis

Epicycle

smaller circle associated with motion A circle that rolls upon the external or internal circumference of another circle

Galileo and sunspots

sun is imperfect

Declination

the angular distance of a point north or south of the celestial equator (+90 to -90) AKA latitude

Deferent

the circle around earth which the center of a celestial body's epicycle moves around the circle around the earth in which a celestial body or the center of the epicycle of its orbit was thought to move

Sidereal Day

time from when a star rises until it rises again (about 23 hr 56 min) --> same time of earth's rotation

Eudoxus

used 25 homocentric spheres

Aristotle

used 55 spheres, also proposes theory of physics with two realms

Prograde Motion

when a planet lags behind the stars (move from west to east relative to stars)

Retrograde motion

when a planet moves in the opposite direction across the sky and returns faster than stars (east to west relative to stars)

Lunar Eclipse

when the Earth passes between the Moon and Sun and Earth's shadow falls on Moon, only occurs during a full moon

Solar Eclipse (Mel is Sun and loves being in the middle; mel = moon)

when the Moon passes between the Earth and Sun and the Moon's shadow falls on Earth, only occurs during a new moon -like looking at dark side of moon

Dialogue on the Two Chief World Systems

written by Galileo in 1632 contrasting Ptolemaic and Copernican systems, led to his demise