Renaissance Astronomy, Kepler's Laws, and Universal Gravitation

Approximately how much time passed between the end of the Greek era (Ptolemy) and the beginning of the Renaissance era (Copernicus? What was this period called?

About 1300 years since Ptolemy, known as the Middle Ages

What culture was extremely instrumental during this time in bridging that long gap of time? Why?

During and after the dark ages Arabic cultures resurrected and extended Ancient Greek astronomy during dark ages by translating Almagest around 827 CE. Many stars names are Arabic, Europeans began to trade with Arab nations

Specifically, what does "Copernican Revolution" refer to?

Shift from geocentrism to heliocentrism

T/F: Copernicus was the first person in history to propose the idea of heliocentrism.

False, Aristarchus was the first to create a heliocentrism model

What model of the solar system/universe was widely accepted during the life of Copernicus? How long had it been the accepted model? Whose model was it?

A geocentric model (Ptolemaic), had been accepted for over 1,000 years, it was Ptolemy model

What exactly was Copernicus's main motivation in proposing his heliocentric model?

to fix the mathematical and philosophical problems with the traditional Ptolemaic geocentric model. His model explained retrograde motion without the use of epicycles or complicated geometry which was Ptolemys work

What was the English title of Copernicus's book? How did it end up coining a new meaning for a
certain word, and what is that word:

On the revolutions of the heavenly spheres, revolution before Copernicus just meant revolve around, new meaning was a sudden change

How confident was Copernicus in publishing his book? Give evidence to support your answer.

Not confident, he decided to publish his book during his death bed

Give 3 - 4 common objections to his model. Which was the most significant?

Philosophical Objections:

• Complicated with Catholic Doctrine Aristotelian “Common Sense) arguments

Physical/Scientific Objections:

• If earth is spinning:

• It should rip apart

• We should feel it’s motion; objects shouldn’t fall straight down

• We should see stellar parallax or change in star brightness in a year

The biggest scientific objection was the inaccuracy in predicting planetary positions due to assuming circular orbits — even though conceptually, the heliocentric idea was revolutionary

What is an important corollary of Copernicus's model?

A corollary of his model: Universe is EXTREMELY vast- accounts for lack of stellar parallax

Corollary: a proposition that logically follows another

What were 2 problems with his model?

• Sill used circles (as divine and perfect)

• Sun at center of entire universe

What is Tycho Brahe known for? Where did he do most of his work?

developing the geo-heliocentric model of the universe and for making the most accurate astronomical observations of his time without a telescope. Gifted his own island by king of Denmark

What was one of Brahe's flaws, which prevented him from drawing more significant conclusions from his work? How did he eventually attempt to overcome this weakness?

He was not great at math which meant he couldn’t explain his data well, has an assistant, Kepler, to do the math part for him

Describe the model of the universe which Brahe proposed. Give some of his reasoning.

a. Was Brahe a geocentrist or a heliocentrist? Explain.

Torn between Copernicus heliocentric model and Ptolemaic geocentrism; proposed an alternative model

Tychonian Model

• though the earth was simply too big to be moving (Common Sense…)

• Hybrid Geocentric/Heliocentric

How is Kepler connected to Brahe? How did that connection happen?

Kepler was Brahe’s assistant when he moved to germany due to being kicked out by the new king because the king that favored him had died

T/F: All of Kepler's significant contributions to astronomy came from analysis of his own
observations and data

False, Kepler's most significant contributions to astronomy, his three laws of planetary motion, came from his analysis of data collected by his predecessor, Brahe

What was Kepler's biggest contribution to the Copernican Revolution? Why was it culturally
significant?

The 3 Laws of Planetary motion, consequences are it debunked the idea that earth is “special” and that the heavens are perfect (no circles). Hinted at the force holding the planets in orbit (gravity)

What is Kerler's 1st law of planetary motion?

a. According to the first law, where exactly is the sun in the shape of the orbit of a planet?

b. What is the definition of an ellipse?

Keplers First Law: each planets orbit about the Sun is an ellipse.

A. Planetary orbits are elliptical with the sun at one focus

B. an oval-shaped orbit that describes the path of a celestial body, such as a planet, around a central star, like the Sun (d1 + d2 is always constant)

What is eccentricity (e)? What is the range of its values? What do they mean?

a. Planet A has an eccentricity ot 0.33. Planet B has an eccentricitv ot 0.08. Describe the difference between the orbits of these two planets

In astronomy, eccentricity (e) describes how “stretched out” or elliptical an orbit is. It tells us the shape of a planet’s or comet’s orbit around the Sun.

1⃣ Range of values:

e=0 → perfectly circular orbit

0 < e < 1 → elliptical orbit (oval-shaped) e = 1 → parabolic trajectory (object escapes the Sun, not a closed orbit)

2⃣ What the values mean:

Low eccentricity (~0) → orbit is almost a circle. Example: Earth e ≈ 0.017 e≈0.017

High eccentricity (close to 1) → orbit is very stretched out. Example: Halley’s Comet e ≈ 0.967 e≈0.967

✅ Simple summary: Eccentricity measures how round or stretched an orbit is:

0 → circle

Close to 1 → very elongated ellipse

What is Kepler's 2nd law? What significant conclusion can be drawn from it?

Law of equal areas: a line connecting the sun and a planet sweeps out equal areas in equal time

What is perihelion?

a. Where would you find a planet's speed is the SLOWEST?

The point at which a planet is CLOSEST to the sun in its orbit

What is aphelion?

The point at which a planet is FARTHEST from the sun in its orbit

Where would you find a planet's speed is the SLOWEST?

Aphelion

What is Kepler's 3rd law, specifically? In more basic terms, what does it mean?

Law of Harmonies: square of a planets period of orbit is proportional to cube of its semi major axis

(Basically the farther a planet is from the sun, the longer it takes to orbit)

How are Kepler's 2nd and 3rd laws different?

Law of equal areas (2nd Law): focus on how speed changes during orbit

Law of Harmonies (3rd Law): relationship between orbit size and time

T/F: Kepler adequately described the underlying physical mechanism which explained his 3 laws.

False, It was Isaac Newton who later provided the explanation through his law of universal gravitation, showing that Kepler’s laws are a natural consequence of gravitational force and the laws of motion

Where was Galileo from? What important device is he known for "inventing"?

Italy, “invented” refracting telescope

What are some notable things Galileo observed with his telescope?

• moons surface features

• Sunspots; sun rotates

• Jupiters moons; they revolve

• Uncountable stars in Milkyway

• PHASES OF VENUS

Was Galileo a heliocentrist or a geocentrist? What happened as a result of him teaching what he believed to be true based on evidence?

Staunchly defended heliocentric, which brought him under fire from the Catholic Church. Brought before the inquisition and put under house arrest from the remainder of his life

Where did Newton live? Give 5 significant contributions he made to science/math.

a. Which of these contributions is most significantly connected to Kepler? Why?

London

• 3 laws of motion (explain why we don’t feel like we’re moving)

• Law of Universal Gravitation

• Discovered Calculous to explain and describe elliptical orbits

• Invented REFLECTING telescope

a. Law of Universal Gravitation gave the mechanism behind Keplers Laws

What are the two factors that determine the amount of gravitational force between 2 objects?

Product of the masses, Moon has less mass: less mass = less Gravitational force (Fg)

distance between them, They are much closed to the moon: less distance = greater gravitational force

Explain why you weigh less on the moon even though you have the same mass

The Moon’s gravity is much weaker than Earth’s (only about 1/6 as strong). That means the Moon pulls on you with less force, so your weight is smaller — but your mass (how much matter you have) stays exactly the same. Moon has less mass: less mass = less Gravitational force (Fg)

Explain why astronauts on the moon do not fall toward the earth or the sun.

They are much closed to the moon: less distance = greater gravitational force

The gravitational force is an attractive force between two obiects because of their ____.

Mass, every mass attracts every other mass

The earth attracts the moon with a gravitational force. and the moon is also pulling on the earth
Which force is greater - the moon pulling on the earth of the earth pulling on the moon? Explain.

Both forces are EQUAL (Newtons 3rd Law). They don’t seem equal due to different accelerations due to HUGE differences in mass (Newtons 2nd Law)

Your gravitational pull on the earth is equal to the earth's gravitational pull on you. Why is it you always accelerating toward the earth when you fall, and not the earth accelerating toward you?

You fall toward Earth because you accelerate much more than Earth does. The forces are equal, but your mass is small, so your acceleration is large, while Earth’s acceleration is practically zero.

How is the gravitational force between two objects related to their mass?

Gravitational force is directly proportional to the mass. Gravitational force increases with mass — bigger masses mean a stronger pull between them.

How is the gravitational force between two objects related to the distance between them?

Gravitational force is inversely proportional to distance r . Gravitational force gets weaker with the square of the distance — the farther apart two objects are, the much smaller the force of gravity between them.

T/F: There's no gravity in space. Explain.

There is gravity in space, it’s just weaker the farther you are from a massive object, astronauts feel weightless because they’re falling along with their spacecraft, not because gravity has disappeared.

As an object's mass increases, the gravitational force between it and any other object ______.

Increases

As two objects get closer together (the distance between them decreases), the gravitational force
between them ______.

Increases

Which of these would cause a greater change in the gravitational force between 2 objects? Why?

a. Doubling the product of their masses

b. Doubling the distance between them

b. Doubling the distance between them causes a greater change in the gravitational force because the force depends on the square of the distance

How does the Law of Universal Gravitation explain and verify Kepler's 2nd and 3rd laws?

Newton’s Law of Universal Gravitation provides the physical explanation behind Kepler’s observational laws:

2nd law → gravity explains changing orbital speed.

3rd law → gravity explains the precise relationship between orbit size and orbital period.

Be able to write in detail about 4 significant trends, or shifts, in astronomy from prehistoric times up to the Renaissance.

1. Nature of Explanations: The shift from supernatural explanations to physical and natural explanations

2. Paradigm, geocentrism to heliocentrism. The belief that the heavens are perfect to the understanding that the universe is complex and chaotic

3. Reasoning: Where truth is derived from pure logic or the term “Common Sense” to truth is derived and supported by Evidence and Data. Before conclusion was first followed by seeking evidence to support, the shift now is to gather evidence first to draw a valid conclusion from it. Followed by the emphasis on being right to emphasis on finding truth

4. Technology: shifts from naked eye observations, to instruments to assist to telescopes and more