We returned to our consideration of the heliocentric versus geocentric models in Galileo's time. Why was the geocentric predominant? The Church supported it because it fit well with certain statements from the Bible -- for instance, in Genesis 1:3 - 2:4 the separation of land and sea (third day) occurs before the two great lights, the sun and moon (fourth day) or the central role played by man in creation or Joshua 10:13 "So the sun stood still ...." (if the sun stood still in this account, that implied that ordinarily it was moving). Furthermore, the Church had also adopted many ideas from the classical period -- one of them the geocentric model. But there was also the presumably common sense notion that we "know" when we are moving.

We considered how do we know when we are moving. One idea was about our visual perspective -- that the objects around us change relative to us -- we make an assessment based on whether most of the things around us are fixed relative to us (then we are still) or most of the things around us changing relative to us (then we are moving). We mentioned that with our eyes closed in a car we could sense changes in speed for example by feeling pushed back into the seat or feel ourselves tilting when the car turned. But as these last two involved accelerations, that raised the questions of whether we could sense a constant velocity motion. In a convertible one can feel the wind blow in one's face or through one's hair, but with the top up and windows closed, this method would not be available since the air would move with the observer. 

We next envisioned being on a plane that had reached its cruising speed when there was no turbulence. "You are now free to move about the cabin" -- does it feel any different from being stuck on the runway? If you drop something on a plane it falls "straight down". But from the perspective of an observer on the ground the object would also move horizontally with the plane. We considered the situation from these two "frames of reference". What would change and what would be the same? Vertically they would be the same: same height (vertical distance), same acceleration, same amount of time. Horizontally they would be different: on the plane there is no horizontal motion, from the ground there is a constant horizontal velocity. The relavant equations would be constant acceleration in the vertical y direction and constant velocity in the horizontal x direction.

y = y₀ + v_0y t + a_y t² / 2

x = x₀ + v_0x t

Of course, Galileo did not talk about cars or planes but he did talk about the hulls of ships, asking questions like would a bird know if it was a calm day at sea or was the ship tied to the dock.

YouTube: Projectile Motion & Reference Frames

Newton Illustration
xkcd: Kepler

We finished with Galileo by discussing his Dialogue Concerning the Two Chief World Systems. The dialog features three characters: Salviati, who presents the heliocentric theory and basically serves as a stand-in for Galileo; Simplicio, who presents the geocentric theory; and Sagredo, an intelligent character who starts out neutral but is ultimately persuaded by the heliocentric theory. It was thought by some that the character of Simplicio represented the Pope (Urban VIII). There were arguments about whether Galileo had previously been ordered not to teach heliocentrism. The "just a thoery" trick did not work this time, Galileo was forced to recant and spent the rest of his life under house arrest. It was during this time that Galileo wrote Two New Sciences covering his work on motion. (It was pblished in the Netherlands.)

The year Galileo died, Isaac Newton was born -- though it's a little contrived since the two countries were on different calendar systems. Newton went to Trinity College in Cambridge (slightly ironic since he didn't believe in the Trinity). Under normal circumstances to become a fellow at the college, he would have had to be ordained. But Newton managed to keep his position and even get promoted to the Lucasian Chair without doing so. (until recently the same chair was held by Stephen Hawking.)

We played a round of "Contemporary: Friend or Foe". Newton mostly had foes.

• Edmond Halley (as in Halley's comet). Friend. Encouraged Newton to write and helped to publish (i.e. finance) the Principia
• Gottfried Leibniz. Foe. "Co-inventor" ? of Calculus.
• Robert Hooke (as in Hooke' Law). Foe. When Newton put together many aspects of mechanics, he often failed to give credit to those reponsible for the pieces he was putting together.
• Voltaire. ???. "I was herein greatly mistaken; Sir Isaac Newton had a pretty niece, called Mrs. Conduite, who had the good fortune to please the lord high treasurer, Halifax. Had it not been for this handsome niece, his doctrine of gravitation and infinitesimals had been wholly useless to him, and he might have starved with all his talents."
• Christiaan Huygens. Foe. Disagreed on the nature of light.

We mentioned Newton's contributions to physics -- mechanics (his laws of motion and the universal law of gravitation) and optics (light, colors, prisms, reflecting telescope, etc.). He also spent a considerable amount of time pursuing alchemy and Biblical studies. Newton worked for the mint and ruthlessly pursued counterfeiters.