Homework 3 (Chapter 4)

What is a scientific paradigm?

A commonly accepted set of scientific ideas and assumptions.

What is a scientific revolution?

A paradigm shift that reshapes our ideas and understanding of some particular aspect of nature.

Why did Copernicus have to keep small epicycles in his model?

He needed epicycles because he used uniform circular motion instead of elliptical motion

How do you know that the planet traveled faster from point A to B rather than from point A' to B' in the figure below? (The planet takes the same amount of time to move from A to B and from A' to B'.)

It moved farther along its orbit from A to B in the same amount of time.

How does Kepler's second law of planetary motion overthrow one of the basic beliefs of classical astronomy

It states that the planets do not move at a constant speed in their orbits, hence, it contradicts the idea of uniform circular motion.

How does Kepler's first law of planetary motion overthrow one of the basic beliefs of classical astronomy?

It states that the planets do not orbit Earth and also do not follow circular orbits; hence, it contradicts the idea of uniform circular motion.

When Tycho observed the new star of 1572, he could detect no parallax. Why did that undermine the belief in the perfect heavens idea of Aristotle?

Observing a new star undermined the perfect heavens idea because the starry sphere was no longer unchanging.

Why did Plato propose that all heavenly motion was uniform and circular?

Plato proposed uniform circular motion because he viewed the world as perfect, and he considered the sphere and uniform circular motion to be perfect.

Which planet has the longest duration of retrograde motion as viewed from Earth? The shortest?

The duration of the retrograde motion is shortest for our neighbor Mars and generally longest for Neptune

In Ptolemy's model, how do the epicycles of Mercury and Venus differ from those of Mars, Jupiter, and Saturn?

The epicycles of Mercury and Venus were attached to a line joining Earth and the Sun. The epicycles of Mars, Jupiter, and Saturn revolved around Earth independently of the Sun.

arly cultures believed that ultimate causes of things are mysteries beyond human understanding. Is this a first principle? Why or why not?

Yes, it was a statement that explained how things work (i.e. mysteriously) and did not require additional explanation.

Are the spheres of Eudoxus a scientific model? If so, is it entirely true

Yes, the spheres of Eudoxus are a scientific model, though we understand now that the model is not correct, because at least Earth is not at the center.

Based on the figure below, do planets with larger a take longer, shorter, or the same time to orbit the Sun?

longer