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The Copernican Revolution. Figure 2-1 Stonehenge. Figure 2-2 Observatories in the Americas. The Greek Frame of Mind. Much of the Greek method of thinking revolved around philosophy instead of scientific reasoning
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The Greek Frame of Mind • Much of the Greek method of thinking revolved around philosophy instead of scientific reasoning • Greeks valued perfection and therefore any model of the universe should involve the perfect shape, the circle • Greek also had no reason to believe that the Earth was not the center of the universe. Egotistical, yes - but completely reasonable at the time • The only 'scientific' data they had available to them was the motion of the Sun, Moon, and planets, which were monitored heavily at the time Ptolemy ~140 AD
What is this? Retrograde Motion within a Planetarium Ceiling – We will do this!
The Motion of the PlanetsRetrograde Motion • A model of the universe would be very simple except for the fact that the planets undergo a looping motion in their orbits • Remember, in one night, all planets still rise in the east and set in the west • However, if you keep track of the planet's position versus the background stars night to night, you will see the planet 'move' • The word 'planet' means wanderer in Greek Retrograde Motion Jupiter and Saturn (6/2000 - 5/2001)
Ptolemaic Model • In order to produce the retrograde motion of the planets, Ptolemy created a model with epicycles • All the planets orbited the Earth in a perfect circle • The planet itself made a smaller orbit centered upon the larger orbit around the Earth • With the right timing, this model can reproduce the retrograde motion seen from Earth Deferent = larger circular orbit around Earth Epicycle = smaller circular orbit around the deferent
Ptolemaic Model • In Ptolemy's complete model, each planet had its own orbit around the Earth with its own epicycle • By changing the period of the orbit and the epicycle, the model could match observations relatively well • The Sun and the Moon traveled around the Earth in perfect circles • The entire model was composed of more than 80 circles and was very complicated Simplified Ptolemaic Model
The Ptolemaic Model Survives • Since the Ptolemaic model matched observations sufficiently and no contrary evidence was produced, it was supported for nearly 1,500 years! • After all, if the Earth was moving, shouldn't we feel it? • Also, the Greeks were smart enough to realize that if the Earth was orbiting the Sun, it would produce stellar parallax • The Greeks didn't believe it existed because they didn't have telescopes to observe such small variations in a star's position • On top of all this, the Dark Ages provided relatively little advance in any sciences for Europe
The Copernican Revolution • At the end of the Dark Ages, a Polish cleric name Copernicus devised a new model of the universe where the Earth was no longer at the center • The heliocentric (Sun centered) model placed the Earth out of its central position, yet still maintained many of the observations we see • The beauty in his model was its simplicity over the Ptolemaic • Occam's Razor The simplest solution is the best Nicolaus Copernicus (1473-1543)
The Copernican Model In the Copernican model, retrograde motion is an apparent effect caused by the Earth 'overtaking' an outer planet in its orbit
The Copernican Revolution • Despite the fact that the Copernican model was a better representation of the solar system, it was not widely accepted • While it did provide a much simpler description compared to Ptolemy, it did not necessarily improve the predictive power of the model • The religious dogma of the time insisted upon Earth being the center of the universe • Copernicus published his works in Latin, which was unreadable by the common public
Galileo - The Observer • A century after Copernicus' work, other scientists began to make strides toward popularizing the heliocentric model • Galileo was the first to use a telescope to make detailed observations of the sky • Though he did not invent the telescope, he made many working prototypes and trained them on a variety of celestial bodies Galileo Galilei (1564-1642)
Galileo's Observations - I • Galileo used his telescopes to make observations of many heavenly objects • The sketch to the right shows Galileo's observations of the moons of Jupiter • He noticed that the position of these four moons changed night to night, as if they were rotating around Jupiter • These moons now bear his name • The Galilean moons are: • Io • Europa • Ganymede • Callisto
Galileo's Observations - II • Galileo also noticed that Venus was not simply a point of light, but actually a disk • He watched Venus go through complete phases, just like the Moon • This cycle of phases can only be satisfied by the heliocentric model, not the geocentric The phases of Venus
Galileo's Observations - III • Galileo also pointed his telescope toward the Sun • NEVER DO THIS • He discovered that the disk of the Sun was not perfect and was occasionally dotted with small black spots • By making daily sketches of these spots, he was able to determine that the Sun itself was rotating
Galileo - Acceleration of Gravity • Galileo discovered that the higher an object is dropped, the greater its speed when it reaches the ground • All falling objects near the surface of the Earth have the same acceleration (9.8 m/s2) • The acceleration of gravity on the surface of other solar-system bodies depends on their mass and radius • Mars and the Moon have a smaller acceleration of gravity • Saturn is about the same as Earth • Jupiter is more than Earth
Astronaut Alan Bean Performed Galileo’s experiment on the Moon
Galileo's Conclusion • All of Galileo's observations were pointing towards a heliocentric view of the universe • Galileo published his observations and conclusions in multiple works, including some published in Italian to appeal to a wider audience • Galileo was threatened with torture, forced to deny his beliefs in the heliocentric model, and sentenced to house arrest for the rest of his life • The seeds of the Copernican Revolution had been planted
Tycho Brahe - An Observer • Tycho Brahe was a prominent scholar and aristocrat in Denmark in the mid-late 1500's • He made a huge number of observations of the stars and planets, all with the naked eye • Even without a telescope, he was very accurate in his measurements • Also recorded the appearance of comets and supernovae Tycho (1546-1601)
Brahe’s Model • Geo-Heliocentric • Wanted to please the church and his observations simultaneously. • Let Earth still be most important with other planets orbiting sun.
Johannes Kepler - A Theorist • Shortly before his death, Tycho began working with another scientist named Kepler • Kepler was put to the task of creating a model to fit all of Tycho's planetary data • Kepler spent the remainder of his life formulating a set of laws that explained the motion of the planets Kepler (1571 - 1630)
Kepler's First Law • Kepler first noted that the orbital path of a planet around the Sun is an ellipse, not a perfect circle • The Sun lies at one of the foci of the ellipse • The eccentricity of an ellipse is a measure of how 'squished' from a circle the shape is • Most planets in the Solar System are very close to a perfect circle • Eccentricity, e ~ 0 for a circle Focus Focus Kepler's 1st Law: The orbital paths of the planets are elliptical with the Sun at one focus.
Kepler's First Law =closest to the Sun =farthest from the Sun
Kepler's Second Law • Kepler also noticed that the planets sweep out equal areas in their orbit over equal times • Notice that this means the planet must speed up and slow down at different points • If it takes the same amount of time to go through A as it does C, at what point is it moving faster? • C, when it is closest to the Sun Kepler's 2nd Law: An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse over equal intervals of time.
Kepler's Third Law • Finally, Kepler noticed that the period of planet's orbit squared is proportional to the cube of its semi major axis • This law allowed the orbits of all the planets to be calculated • It also allowed for the prediction of the location of other possible planets Kepler's 3rd Law Simplified NOTE: In order to use the equation as shown, you must be talking about a planet in the Solar System, T must be in years, and a must be in A.U. !!!
Kepler's Third Law - Examples • Suppose you found a new planet in the Solar System with a semi major axis of 3.8 A.U. • A planet with a semi major axis of 3.8 A.U. would have an orbital period of 7.41 years years
Kepler's Third Law - Examples • Suppose you want to know the semi major axis of a comet with a period of 25 years • A planet with an orbital period of 25 years would have a semi major axis of 8.55 A.U. A.U.
Isaac Newton • Kepler's Laws were a revolution in regards to understanding planetary motion, but there was no explanation why they worked • That explanation would have to wait until Isaac Newton formulated his laws of motion and the concept of gravity • Newton's discoveries were important because they applied to actions on Earth and in space • Besides motion and gravity, Newton also developed calculus Newton (1642-1727)
Newton and the Apple - Gravity • After formulating his three laws of motion, Newton realized that there must be some force governing the motion of the planets around the Sun • Amazingly, Newton was able to connect the motion of the planets to motions here on Earth through gravity • Gravity is the attractive force two objects place upon one another
Gravitational Force • The gravitational force is always attractive • The strength of the attraction decreases with increasing distance
The Gravitational Force • G is the gravitational constant • G = 6.67 x 10-11 N m2/kg2 • m1 and m2 are the masses of the two bodies in question • r is the distance between the two bodies
Gravity - Examples • Weight is the force you feel due to the gravitational force between your body and the Earth • We can calculate this force since we know all the variables 1 Newton is approximately 0.22 pounds
Gravity - Examples • If gravity works on any two bodies in the universe, why don't we all cling to each other? • Replace the from previous examples with two people and the distance with 5 meters 1 Newton is approximately 0.22 pounds
Orbits The law of universal gravitation accounts for planets not falling into the Sun nor the Moon crashing into the Earth Paths A, B, and C do not have enough horizontal velocity to escape Earth’s surface whereas Paths D, E, and F do. Path E is where the horizontal velocity is exactly what is needed so its orbit matches the circular curve of the Earth
The same concept holds for planetary orbits about the Sun PTYS/ASTR 206 Keplers Laws and Gravity 2 1/27/09
Galilean Satellites and Kepler’s Laws • Newton derived Kepler’s third law using physics and his universal law of gravitation. His form of Kepler’s 3rd law for the orbits of the planets about the Sun is:
The EARTH Is just a tiny planet
The Earth has a moon The Earth and Moon together, as seen from the departing Galileo space probe
The Sun Mass 2x1030 kg Radius 7x105 km Central temperature 15 million K Surface temperature 5780 K Composition 75% hydrogen(by mass) 25% helium
