astro RQ 2
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Mathematics
Date
Feb 20, 2024
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3
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11. Describe at least three characteristics of Greek thinking that helped pave the way for the
development of modern science.
The first is that the greeks developed a tradition of trying to understand nature without resorting
to supernatural explanations. By not assuming everything was done without reason, they
opened the discourse to rational thought. Second was the development of geometry. Geometry
allowed them to make sense of the stars movements. The third is that they were willing to
discard theories if they didn’t coincide with reality.
12. What do we mean by a model of nature? Summarize the development of the Greek
geocentric model, from Thales through Ptolemy.
A model is a conceptual representation whose purpose is to explain and predict observed
phenomena. The first step was Anaximander who suggested that the heavens must form a
complete sphere around earth and that the earth’s surface must also be curved. This is the
geocentric model. Eventually they ended at the ptolemaic model which had the planets move
around earth on small circles that turned into larger ones.
13. What is apparent retrograde motion, and why was it so difficult to explain with the
geocentric model? What is its real explanation?
Apparent retrograde motion is when planets appear to reverse direction. It is difficult to explain
because there was a generally accepted notion that said all heavenly objects moved in a circle.
14. Who first proposed the idea that Earth is a planet orbiting the Sun, and when? Why didn’t
this model gain wide acceptance in ancient Greece?
Aristarchus in about 260 BCE. There were many arguments against the model that included
philosophical ones but the largest one was that it seemed inconsistent with the observations of
stellar positions in the sky.
15. Briefly describe and contrast the different views of the atomists and the Aristotelians on the
subject of extraterrestrial life.
The atomists believes that both the earth and the heaven were made from an infinite number of
indivisible atoms of each of the four elements while the aristotelians believed that the four
elements were confined to earth while the heavens were made of another element.
16. What was the Copernican revolution, and how did it change the human view of the
universe? Briefly describe the major players and events in the Copernican revolution.
Copernicus wrote a book that revived aristarchus’ suggestion of a heliocentric system and
included enough mathematical detail so that it was not easily dismissable causing much
scientific debate. The idea spread wildly but didn’t gain too many converts because it didn’t work
very well. This is because it maintained that heavenly objects moved in perfect circles. The
copernicus revolution was a centuries long movement that lead to the development of different
models for space.
17. Why didn’t Copernicus’s model gain immediate acceptance? Why did some scientists favor
it, despite this drawback?
It didn’t gain immediate acceptance because it was also inaccurate and people didn’t want to
abandon tradition for something else that was also inaccurate. Some scientists accepted it
because it seemed to fix some of the earlier problems.
18. State and explain each of Kepler’s laws of planetary motion. Why did they gain acceptance?
First: the orbit of each planet about the Sun is an ellipse with the Sun at one focus. This means
that the planet’s distance varies throughout its orbit
Second: 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.
Third: : More distant planets orbit the Sun at slower average speeds, obeying the precise
mathematical relationship p2 = a3. P is the orbital period in years and a is the semimajor axis
from the sun in astronomical units. They gained acceptance because they were mathematically
sound laws.
19. Briefly describe three reasonable objections to the Sun-centered model that still remained
even after Kepler’s work, and explain how Galileo’s work overcame each of these objections.
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. Galileo answered
this with rolling balls to demonstrate that a moving object remains in motion unless a force acts
to stop it.
2. The idea of noncircular orbits contradicted the view that the heavens—the realm of the Sun,
Moon, planets, and stars—must be perfect and unchanging. Galileo built a strong telescope to
prove that the sun and moon had imperfections
3. No one had detected the stellar parallax that should occur if Earth orbits the Sun.
Galileo provided strong evidence that the stars were much farther away than previously thought
20. How did Newton’s discoveries about the laws of motion and the universal law of gravitation
put the Sun-centered model on an even stronger footing?
21. How did the Copernican revolution affect scholarly thought regarding the question of life
beyond Earth?
Because now we know that we are not the center of the universe so life might be possible on
other worlds
22. What is the difference between a hypothesis and a theory in science?
A hypothesis is similar to an educated guess while a theory is a tested explanation backed by
evidence
23. Describe each of the three hallmarks of science, and give an example of how we can see
each one in the unfolding of the Copernican revolution.
1:Modern science seeks explanations for observed phenomena that rely solely on natural
causes. Tycho’s measurements of planetary motion influenced kepler
2:Science progresses through the creation and testing of models of nature that explain the
observations as simply as possible. This is seen in the multiple models that were tested and
compared.
3. A scientific model must make testable predictions about natural phenomena that would force
us to revise or abandon the model if the predictions did not agree with observations. Each
model could make precise predictions about the movement of heavenly objects
24. What is Occam’s razor? Give an example of how it can be applied.
Occam’s Razor says that no more assumptions should be made than necessary. In the
copernican model, they liked it because of the simple explanation for retrograde motion.
25. Why doesn’t science accept personal testimony as evidence? Explain.
Because personal testimony is not necessarily accurate and in order for science to turn
something into a theory, it needs to be tested and verifiable by anyone.
26. In what sense is gravity both a fact and a theory? Explain clearly.
Gravity is a fact because we know that there is some force that pulls us down to earth, but
gravity is also a theory because the theory of gravity explains why gravity pulls us down to
earth.
27. What is Newton’s universal law of gravitation? Write it in equation form, and clearly explain
what the equation tells us. What do we mean when we say that the law is an inverse square
law?
Every mass attracts every other mass through the force called gravity.
The strength of the gravitational force attracting any two objects is directly proportional to the
product of their masses. For example, doubling the mass of one object doubles the force of
gravity between the two objects.
The strength of gravity between two objects decreases with the square of the distance between
their centers. That is, the gravitational force follows an inverse square law with distance. For
example, doubling the distance between two objects weakens the force of gravity by a factor of
22, or 4.
The equation is F = G *(M1 * M2) / d^2
28. How did Einstein’s general theory of relativity change our view of gravity?
Einstein gave us a framework for understanding how gravity could be affecting objects over
incredibly large distances.
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