Lec 5

Question 1

Copernican revolution

Answer 1

shift from the Earth-centered (geocentric) model of the universe to the Sun-centered (heliocentric) model, initiated by Nicolaus Copernicus in the 16th century

fundamentally changed astronomy and science by challenging the authority of ancient views and laying the groundwork for modern scientific thinking

changed the way we perceive our place in the universe

Question 2

Who is Tycho Brahe and what did he declare?

Answer 2

Tycho Brahe was a Danish astronomer who made precise observations of the stars and planets

He declared a geoheliocentric model, where the Earth stayed still at the center, the Sun orbited the Earth, and the other planets orbited the Sun

Observed the nova “new star” and supernova, concluded that the nova was much farther away than the moon

Question 3

Who was Johannes Kepler and what did he declare?

Answer 3

Johannes Kepler was a German astronomer who declared that planets move in elliptical orbits around the Sun, not perfect circles, and formulated three laws of planetary motion that described how planets travel faster when closer to the Sun

believed that understanding the geometry of the heavens would bring him closer to god

Question 4

Kepler’s key discovery

Answer 4

planetary orbits are not circles but instead are a special type of oval called an ellipse

In drawing an ellipse, you must stretch the string around two tacks
–the locations of the two tacks are called
the foci (singular, focus) of the ellipse
–the long axis of the ellipse is called its major axis, each half of which is called a semimajor axis
–the short axis is called the minor axis

Question 5

eccentricity

Answer 5

a quantity that describes how much an ellipse is stretched our compared to a perfect circle

A circle is an ellipse with zero eccentricity, and greater eccentricity means a more elongated ellipse

Question 6

kepler’s 3 laws of planetary motion

Answer 6

■Kepler’s first law: The orbit of each planet about the Sun is an ellipse with the Sun at one focus
–This law tells us that a planet’s distance from the Sun varies during its orbit
–Its closest point is called perihelion (from the Greek for “near the Sun”) and its farthest point is called aphelion (“away from the Sun”)
–The avg of a planet’s perihelion and aphelion distances is the length of its semimajor axis
—refer to this as the planet’s avg distance from Sun

■ Kepler’s second law: A planet moves faster in the part of its orbit nearer the Sun and slower when farther from the Sun, sweeping out equal areas in equal times
–The “sweeping” refers to an imaginary line
connecting the planet to the Sun, and keeping the areas equal means that the planet moves a greater distance
(and hence is moving faster) when it is near perihelion than it does in the same amount of time near aphelion

■ Kepler’s third law: More distant planets orbit the Sun at slower average speeds, obeying the precise mathematical relationship

p^2=a^3

Question 7

explain the variables in keplers 3rd law

Answer 7

The letter p stands for the planet’s orbital period in years and a for its average distance from the Sun in astronomical units

the square of each planet’s
orbital period p2 ( ) is indeed equal to the cube of its average distance from the Sun a3 ( ).

Because Kepler’s third law relates orbital distance to orbital time (period), we can use the law to calculate a planet’s average orbital speed.*

confirms that more distant planets orbit the sun more slowly

Question 8

how was the force of gravity identified?

Answer 8

The fact that more distant planets move more slowly led Kepler to suggest that planetary motion might be the result of a force from the Sun

He even speculated about the nature of this force, guessing that it might be related
to magnetism.

(This idea, shared by Galileo, was first suggested by William Gilbert [1544–1603], an early proponent of the Copernican system.)

Kepler was right about the existence of a force but wrong in his guess of magnetism.

A half century later, Isaac Newton identified the force as gravity

Question 9

simplified explanation of keplers 3 laws of planetary motion

Answer 9

Law of Ellipses: Planets move in oval-shaped paths (ellipses) around the Sun, not perfect circles. The Sun is slightly off-center in that oval.

Law of Equal Areas: A planet moves faster when it is closer to the Sun and slower when it is farther away. It sweeps out equal areas in equal amounts of time.

Law of Periods: Planets that are farther from the Sun take longer to go around it. The farther the planet, the slower its orbit.

Question 10

how did galileo solidify the Coperican revolution?

Answer 10

-kepler’s laws matching Tycho’s data provided strong evidence in favour of copernicus’s placement of the sun at the center of the solar system

-used a telescope to make discoveries—like Jupiter’s moons and Venus’s phases—that provided strong evidence that not everything orbits the Earth, supporting the Sun-centered (heliocentric) model

Question 11

what is the copernican view and what were the objections of it?

Answer 11

The Copernican Revolution was the SHIFT from the Earth-centered view of the universe (geocentric) to the Sun-centered view (heliocentric), proposed by Nicolaus Copernicus
–changed how people understood the structure of the cosmos

There were objections because it challenged long-held beliefs from the Church and ancient philosophers like Aristotle and Ptolemy. Many thought it contradicted the Bible, lacked proof at the time, and defied common sense (e.g., people didn’t feel the Earth moving)

1.Aristotle had held that Earth could NOT be moving because, if it were, objects such as birds, falling stones, and clouds would be left behind as Earth moved along its way

2. The idea of noncircular orbits contradicted Aristotle’s claim that the heavens—the realm of the Sun, Moon, planets, and stars—must be perfect and unchanging
3. No one had detected the stellar parallax that should occur if Earth orbits the Sun

(galileo answered all 3 objections)

Question 12

major steps in the copernican revolution

Answer 12

1) Night by night, planets usually move from west to east relative to the stars. However, during periods of apparent retrograde
motion, they reverse direction for a few weeks to months

2) Most ancient Greek people assumed
that Earth remained FIXED at the center of
the solar system
–the Greek geocentric model explained apparent retrograde motion by having planets move around Earth on small circles that turned on larger circles

3) By the time of Copernicus (1473-1543), predictions based on the Earth-centered model had become inaccurate
–copernicus revived the sun-centered idea (didn’t succeed but inspired a revolution continued over next century)

4) Tycho exposed flaws in both the ancient Greek and copernican models by observing planetary motions with accuracy
–his observations led to kepler’s breakthrough insight that planetary orbits are elliptical, not circular and let kepler develop his 3 laws

5) Galileo’s experiments and telescopic observations overcame remaining scientific objections to the sun-centered model
–his discoveries and the success of kepler’s laws in predicting planetary motion overthrew the earth-centered model

Question 13

kepler’s 3 laws

Answer 13

1) a planet’s orbit is an ellipse with the Sun at one focus

2) as a planet moves around its orbit, it sweeps out equal areas in equal times

3) more distant planets orbit at slower avg. speeds, obeying p^2=a^3

Question 14

pseudoscience

Answer 14

Pseudoscience is a set of beliefs or practices that claim to be scientific but lack evidence, cannot be tested, or don’t follow the scientific method
–often relies on personal anecdotes, ignores contradictory evidence, and doesn’t change when new information is found

Question 15

bias

Answer 15

tendency twd a particular result

Question 16

critical

Answer 16

right on edge, near boundary

Question 17

deviation

Answer 17

change or difference

Question 18

conclusions about astronomy BEFORE copernicus

Answer 18

The earth is the center of the universe and feels fixed
Everything revolves in circles around it
Stars don’t seem to change

Question 19

assumptions before copernicus

Answer 19

Heavens are perfect and incorruptible
Circles are perfect

Question 20

geocentric universe

Answer 20

A model of the universe, with the earth at the centre, and the celestial object around it (not correct or current)
Called the planets “wandering stars”

Question 21

prograde motion

Answer 21

Prograde motion(normal motion)- the apparent west to east motion of objects (over many nights) as compared to the stationary background stars

Question 22

retrograde motion

Answer 22

Retrograde motion- the apparent east to west motion of objects (over many nights) as compared to the stationary background stars

Question 23

how is prograde and retrograde motion a problem for geocentrism?

Answer 23

geocentrism=(the Earth-centered model)

problem because planets sometimes appeared to move backward (retrograde) in the sky, which didn’t make sense if everything orbited Earth in perfect circles

To explain this, ancient astronomers added complicated loops called epicycles, but it still didn’t fully work

The heliocentric model (Sun-centered) explained it more simply—retrograde motion happens naturally as Earth passes slower-moving outer planets

Question 24

prograde vs retrograde motion

Answer 24

Prograde motion is when a planet appears to move eastward across the night sky (its usual direction), while retrograde motion is when a planet appears to move westward, or backward, for a short time.

Prograde = normal, forward motion

Retrograde = temporary, backward motion

Retrograde motion is an illusion caused by Earth’s movement as it overtakes another planet in its orbit

Question 25

heliocentric model

Answer 25

The sun is at the center of the universe Planets orbit the sun in circles The moon orbits the Earth Still not accurate

Question 26

copernicus

Answer 26

Believed the sun is the center of universe Planets orbit the sun in circles Moon orbits the Earth

Question 27

apparent retrograde motion

Answer 27

Apparent retrograde motion is the illusion that a planet is moving backward (westward) in the sky instead of its usual forward (eastward) path This happens when Earth, which orbits the Sun faster, passes by a slower outer planet From our viewpoint, the planet seems to reverse direction for a short time before continuing forward again

Question 28

tycho brahe

Answer 28

1546-1601 Got funding from the king of denmark to build the first large european observatory Made extremely precise measurements of the motion of mars Observed a supernova, discarded the idea of the cosmos as unchanging Usd parallax to constrain distances From his data, current models clearly had problems

Question 29

johannes kepler

Answer 29

1571-1630 Worked from Brahe’s data Was concerned with the inaccuracy of the current models for theological reasons Correctly predicted transit of Mercury Discovered a fix for copernicus’ model (ellipses)

Question 30

keplers 3 laws

Answer 30

The orbit of each planet about the sun is an ellipse with the sun at one focus A planet moves faster in the part of its orbit nearer the sun and slower when father from the sun, sweeping out equal areas in equal times More distant planets orbit the sun at slower average speeds, obeying a precise mathematical relationship (P^2=a^3) (mass has no impact on orbit)

Question 31

perihelion

Answer 31

closest point to the sun

Question 32

aphelion

Answer 32

farthest point from the sun

Question 33

semimajor axis

Answer 33

the avg of a planet's perihelion and aphelion distances

Question 34

eccentricity

Answer 34

A value measuring how “squashed” or offset an ellipse is from a perfect circle Aka how much an ellipse deviates from a perfect circle 0=perfect circle, highly eccentric=stretched oval

Question 35

galileo

Answer 35

1564-1642 Pioneer in the design, manufacture and use of telescopes Experimented with laws of motion and gravity Correctly predicted the transit of mercury Using telescopes he observed that: -the moon has craters (so not everything are perfect circles) -jupiter has moons that orbit it (so not everything orbits the Earth) -venus has phases (consistent with the heliocentric (sun-centered) model and inconsistent with the geocentric (earth-centered) model: --size of venus changes through the year --the ‘new’ phase happens when venus appears largest --the ‘full’ phase happens when venus is in line with the Sun (and when venus appears smallest)

Question 36

What did Copernicus, Kepler and Galileo teach us about astronomy and what was different about their contributions?

Answer 36

Moved from Earth centered to Sun centered model

Question 37

how does the word eccentricity apply to the orbits of heavenly bodies?

Answer 37

Eccentricity Definition: A measure of how stretched out or oval an orbit is. Application: An eccentricity of 0 means a perfect circle. The higher the number (up to 1), the more elongated the orbit. For example, Earth’s orbit has low eccentricity (almost circular), while some comets have very high eccentricity (very stretched orbits).

Question 38

how does the word orbital period apply to the orbits of heavenly bodies?

Answer 38

Orbital Period Definition: The time it takes a celestial body to complete one full orbit around another body (e.g., a planet around the Sun or a moon around a planet). Application: Earth’s orbital period is one year. Distant planets like Neptune have longer orbital periods because they travel slower and have farther to go.

Question 39

how does the word orbital semimajor axis apply to the orbits of heavenly bodies?

Answer 39

Orbital Semimajor Axis Definition: Half the longest diameter of an elliptical orbit. It measures the average distance between the orbiting body and the object it orbits. Application: The semimajor axis helps determine how far a planet is from the Sun and is directly related to its orbital period by Kepler’s 3rd Law—larger semimajor axes mean longer orbital periods.

Question 40

how do kepler's laws describe how bodies move in the solar system

Answer 40

Near circular orbits around the Sun, where orbital period increases as distance from the Sun increases

Question 41

Geocentric model

Answer 41

(Earth-centered) Definition: The geocentric model places Earth at the center of the universe. All other celestial bodies—including the Sun, Moon, stars, and planets—were believed to revolve around Earth. Key Supporters: Aristotle: Argued that Earth was the natural center of the universe due to gravity and perfection in circular motion. Ptolemy: Developed the Ptolemaic model, which used complex systems of circles upon circles (epicycles and deferents) to explain planetary motion, especially retrograde motion. Key Features: Planets and the Sun move on perfect circular paths around Earth. Retrograde motion was explained using epicycles (small circles that planets move on, which in turn orbit Earth). This model dominated Western thought for almost 2,000 years. Limitations: While it predicted positions of planets with reasonable accuracy, it became increasingly complex and less intuitive.

Question 42

Heliocentric model

Answer 42

Definition: The heliocentric model places the Sun at the center of the solar system, with Earth and the other planets orbiting around it. Key Supporters: Aristarchus of Samos (early proposer, c. 3rd century BCE). Nicolaus Copernicus: Revived the model in the 16th century and provided geometric reasoning for it. Kepler: Improved the model using elliptical orbits (Kepler’s Laws). Galileo: Provided telescopic evidence (e.g., phases of Venus, moons of Jupiter) that supported the Sun-centered model. Key Features: Explained retrograde motion naturally: planets appear to move backward from Earth’s point of view when Earth overtakes them in orbit. More accurate and simpler than the geocentric model once elliptical orbits were adopted. Laid the foundation for modern astronomy and Newtonian physics. Scientific Impact: Marked the start of the Copernican Revolution, a critical shift toward modern scientific thought and methods.

Question 43

Ellipse

Answer 43

Ellipse: An ellipse is a special type of oval that describes the shape of most planetary orbits. It is defined by two points called foci (singular: focus). To draw one, you place a string around two pins (the foci) and pull it tight with a pencil — the path the pencil traces is an ellipse. A circle is a special case of an ellipse where the two foci are in the same place, so the eccentricity is zero. "Kepler’s key discovery was that planetary orbits are not circles but instead are a special type of oval called an ellipse"

Question 44

eccentricity

Answer 44

Eccentricity (e) describes how much an ellipse is stretched out compared to a perfect circle. It is calculated by the ratio: e= c/a where c is the distance from the center of the ellipse to one focus, and a is the length of the semi-major axis. A perfect circle has eccentricity 0. A more elongated ellipse has a higher eccentricity (closer to 1). “A circle is an ellipse with zero eccentricity, and greater eccentricity means a more elongated ellipse

Question 45

semi major axis

Answer 45

The semi-major axis (a) is half the longest diameter of an ellipse — it stretches from the center to the farthest edge. It represents a planet’s average distance from the Sun over the course of an orbit. It's the key distance term used in Kepler’s third law of planetary motion. “The average of a planet’s perihelion and aphelion distances is the length of its semimajor axis

Question 46

orbital period

Answer 46

Orbital period (p) the time a planet takes to complete one full orbit around the Sun. In Kepler’s third law, this is related mathematically to the semi-major axis: p^2=a^3 Where: p is in years, a is in astronomical units (AU). “Kepler’s third law: More distant planets orbit the Sun at slower average speeds, obeying the precise mathematical relationship: p^2=a^3

Question 47

copernicus

Answer 47

Copernicus: Simpler Explanation for Retrograde Motion Problem with Geocentric Model: Explaining retrograde motion required complicated epicycles (circles on circles). Heliocentric Solution: Copernicus showed that retrograde motion occurs naturally when Earth overtakes another planet in its orbit (no epicycles needed). Limitation: He still used perfect circles, so his model wasn’t much more accurate than Ptolemy’s.

Question 48

brahe

Answer 48

Tycho Brahe: Accurate Observations Without a Working Model Contribution: Tycho made extremely accurate naked-eye measurements of planetary positions (within 1 arcminute). Important Observation: He saw a nova (supernova) in 1572 and a comet in 1577, both lacking measurable parallax, proving they were far beyond the Moon. Impact: This contradicted Aristotle’s idea of unchanging, perfect heavens.

Question 49

kepler

Answer 49

Kepler: Elliptical Orbits Match Observations Breakthrough: Kepler abandoned circles and used ellipses based on Tycho’s data. Kepler’s Laws: Planets move in elliptical orbits with the Sun at one focus. Planets sweep out equal areas in equal times (move faster when near the Sun). p^2=a^3: Orbital period squared equals semi-major axis cubed. Result: His model matched planetary motion far more accurately than the geocentric one.

Question 50

galileo

Answer 50

Galileo: Telescopic Evidence Galileo's telescope revealed multiple phenomena that directly challenged the geocentric model: Moons of Jupiter: Proved that not all objects orbit Earth (some orbit another planet). Phases of Venus: Venus shows a full set of phases only if it orbits the Sun. Sunspots and Lunar Craters: Showed the heavens were not perfect and unchanging. Support for Inertia: Disproved Aristotle’s argument that objects would be left behind on a moving Earth.

Question 51

Kepler’s First Law:

Answer 51

The Law of Ellipses "The orbit of each planet about the Sun is an ellipse, with the Sun at one focus." In Non-Technical Language: Planets don’t orbit in perfect circles — they follow oval-shaped paths called ellipses. The Sun isn’t in the exact center; it’s slightly off to one side at a point called a focus. Conditions: Applies to all planetary orbits around the Sun. The semi-major axis gives the average distance of the planet from the Sun.

Question 52

Kepler’s Second Law:

Answer 52

The Law of Equal Areas "A planet moves faster when it is closer to the Sun and slower when it is farther from the Sun, sweeping out equal areas in equal times." In Non-Technical Language: Imagine drawing a line from the Sun to a planet. As the planet orbits, this line sweeps out an area. In the same amount of time, the area swept is always the same, even if the planet moves faster near the Sun and slower farther away. Conditions: This law explains the changing speed of a planet during its orbit. Applies to each full orbit individually — it's not uniform speed, but uniform area coverage per unit time.

Question 53

Kepler’s Third Law:

Answer 53

The Law of Harmonies "The square of a planet’s orbital period (p²) is proportional to the cube of the semi-major axis of its orbit (a³): p^2=a^3 where p = orbital period in years, a = average distance from the Sun in astronomical units (AU). In Non-Technical Language: The farther a planet is from the Sun, the longer it takes to go around once. There is a mathematical relationship between how far a planet is and how long it takes to complete an orbit. Conditions: Only applies to objects orbiting the Sun. Assumes orbits are not significantly affected by other gravitational forces (e.g., big moons or nearby planets).

Question 54

Apply Kepler's first law to describe the motions of objects in the solar system

Answer 54

Kepler’s First Law: The Law of Ellipses Description: Each planet moves around the Sun in an elliptical orbit, with the Sun at one of the two foci of the ellipse. Application in the Solar System: This law explains why planets do not move in perfect circles but instead in slightly stretched orbits. For example, Earth is closest to the Sun (perihelion) in early January and farthest (aphelion) in early July, though its orbit is nearly circular. Other bodies like comets have highly eccentric orbits that bring them very close to the Sun at perihelion and extremely far away at aphelion.

Question 55

Apply Kepler's second law to describe the motions of objects in the solar system

Answer 55

Kepler’s Second Law: The Law of Equal Areas Description: A line connecting a planet to the Sun sweeps out equal areas in equal times. This means that a planet moves faster when it is near the Sun and slower when it is farther from the Sun. Application in the Solar System: This explains why a planet like Mars speeds up as it approaches perihelion and slows down near aphelion. This variation in orbital speed helps explain why seasons have different durations on Earth and why the orbital motion appears irregular when viewed from Earth.

Question 56

Apply Kepler's third law to describe the motions of objects in the solar system

Answer 56

Kepler’s Third Law: The Law of Harmonies Description: The square of a planet’s orbital period 𝑝 (in years) is proportional to the cube of its average distance 𝑎 (in astronomical units, AU) from the Sun: p^2=a^3 Application in the Solar System: This law quantitatively explains why outer planets move more slowly. For instance: Earth’s orbital period is 1 year at 1 AU. Jupiter is about 5.2 AU from the Sun and takes about 11.9 years to orbit it. Neptune, about 30 AU away, takes 165 years to orbit the Sun. This law allows scientists to calculate how long it takes for any object—whether planet, dwarf planet, or asteroid—to orbit the Sun based solely on its distance.