PHY1033C/HIS3931/IDH 3931 : Discovering Physics: The Universe and Humanity’s Place in It

Fall 2015

Prof. Peter Hirschfeld, Physics

Announcements

• HW 2 due Sept. 15 • Turn in lab writeups • Reading: Gregory Chs. 2,3 Wertheim

(coursepack), Lindberg (coursepack)

Last time

Last time • Review of position, velocity from modern perspective (slides on web) • Development of medieval scientific thought: attempt to reconcile a rediscovered Aristotle with church teachings. • Medieval critiques of Aristotle’s theories of motion: idea of “impressed force” to keep an arrow moving after it has left the bow. •Possibility of “infinitite rectilinear motion” if one can remove resistance understood in 1300s.

Clicker quickies Which of the following mathematical devices for describing planetary motions discussed in the Almagest was the contribution of Ptolemy himself? a. homocentric spheres b. epicycles on deferent c. eccentric circles d. equant point e. all of the above

Introduction of mathematics into discussion of moving bodies (1300s): Mertonians (Oxford) : definitions of velocity and acceleration

Nicole Oresme (U. Paris) graphical representation and theorems

Velocity was the rate of change of the position of an object. What's the rate of change of the velocity called?

Def: acceleration-- rate of change of the velocity of an object.

Acceleration

average acceleration a = ∆v/∆t

A: Yes, when something is going in a circle at constant speed, it is continuously changing the direction of its velocity, so a ≠ 0.

Q: Can you have a ≠ 0, v = constant?

A: Yes, e.g. when you throw a ball up and it is at the very top of its trajectory before starting back down: a=-9.8m/s2, v=0.

Q: Can you have a=0 and v ≠ 0?

A: Yes, when object has constant velocity!

Q: Can you have a ≠ 0 and v = 0 ?

v

In this course, we have referred to “uniform circular motion” where a planet moves at constant speed

From modern perspective, since it’s velocity direction is changing, it is accelerating. Greeks & medievals would not have called this acceleration.

time 1 later time 2

v

Already know one special equation for something moving at constant velocity, ∆x = v ∆t. If we measure with respect to the origin of the coordinate system at t=0 (choose xi=0 and ti=0), then we just write x = v t. What about if acceleration is constant? This would occur if you are keeping the gas pedal depressed at a fixed angle for a few seconds, or when an object is in free fall near the Earth's surface.

Equations of motion

The same kind of reasoning as above leads to v = a t, The velocity increases at a constant rate! You might be tempted to substitute this into our x-equation, but this is wrong, because x = v t is only good for constant velocity, not changing velocity. It turns out for the special case of constant a, we get

v =a t x = ½ a t2

Constant acceleration a

constant acceleration only!

Marco Polo’s journey

Pace of exploration quickened in the 1400s

1. New navigational techniques

2. Royal funding

Traditional Navigation techniques

The cross staff

If latitude of a location was known, it could be reached

Location 1

Location 2

N New technique: The magnetic compass

A captain could not always control where the ship went

Numerous islands were discovered when a ship was blown about by storms

Pace of exploration quickened in the 1400s

1. New navigational techniques

2. Royal funding

Why did kings start supporting travel?

Ottoman ruler

Sultan of Egypt

Food in medieval times was very bland

So the West began to be interested in exploration

Prince Henry of Portugal 1394-1460

Encouraged geographical exploration

Heard of a gold trade south along Africa’s coast

Wanted to find Prester John

Cape Nun

By 1450

Lucrative slave trade established Portugal was secretive, but Spain began to be interested A new king got Pope Sixtus IV to issue a bull in 1481 confirming Portugals’s right to lands south of the Canary Islands

1487 Bartholomeu Diaz

Cape of Good Hope

The success of Columbus forced the creation of a new papal treaty

1494

Vasco da Gamma 1497

Encountered Arabs

Returned, 1499

By 1509 Portuguese were in the Spice Islands

Now that India had been reached by sea, was there another route to the East?

Columbus had studied Ptolemy’s Geography and Marco Polo’s Travels Distance from Africa to China not great Read Paolo Toscanelli –

distance = 5000 miles Reduced distance to 3500 miles Began trying to persuade Portuguese in 1480s

After rejection, turned to Spain

Left for Canary Islands August, 1492 Used dead reckoning, not celestial navigation

Gold ornaments the of inhabitants of the islands convinced him he had reached islands off China

Columbus underreported the distances he calculated to the crew

Others became convinced that what Columbus had revealed was a new world

One who used these words was the Italian geographer Amerigo Vespucci Inspired by the voyages of Columbus, he visited the Gulf and the eastern coast of the U.S. in a voyage of 1497

Other voyages to the east coast of South America convinced him that this territory represented a new continent

World map of 1507 Martin Waldseemüller

The world at the beginning of the 16th century was a different place from what it had been

The goals were the same as they had been in the East – spices, gold, and Christians

Ironically as the world became new, Europeans looked backwards to regain lost wisdom In the process they stumbled upon a new vision of the cosmos Before Copernicus there was another world shaking event

Ferdinand Magellan

From the lesser Portuguese nobility In 1505 he signed on at 24 to a 20-ship fleet the king commissioned to take over spice trade

Expected resistance from the Sultan of Egypt and the Indian rajahs

(~1480-1521)

Cannanore

Malacca

Magellan was promoted for his actions in these campaigns Back in Portugal he fell out of favor at court Was not able to persuade the king to search for shorter route to the Spice Islands Frustrated by the rejections, he turned to the king of Spain

18-year old Emperor Charles I found the idea intriguing But after being disappointed with Columbus, the king’s advisors were against it He also reported a geographer’s conclusion about the Treaty of Tordesailles Magellan claimed to have learned about the existence of a pass from a document in the Portuguese archives

A fleet of 5 ships set off September 20, 1519 with Magellan in command Other 4 ships had Spanish captains who did not trust the Portuguese admiral The first location of the supposed pass was just the mouth of a wide river Magellan pushed farther and farther south – he was caught in a bind But the farther south he went, the more his hopes waned

Three ships arrived in the Philippines in the spring of 1521

He knew he could not be far from the Spice Islands

Magellan determined to take the land for Spain

When the Victoria stumbled into port in Spain there were but 18 crew left Since those left behind in Malacca were later captured these were the only survivors of the original 265 Then cargo of spices did pay for the voyage