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 Planets Retrograde 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 wellBy 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 positionThe 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 RazorOccam'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: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 THISNEVER 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 - 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/s 2 ) 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 gravityMars and the Moon have a smaller acceleration of gravity Saturn is about the same as EarthSaturn is about the same as Earth Jupiter is more than EarthJupiter 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 measurementsEven 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 circleEccentricity, e ~ 0 for a circle 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 SunC, 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 gravitational force is always attractive The strength of the attraction decreases with increasing distance The strength of the attraction decreases with increasing distance
The Gravitational Force G is the gravitational constant G = 6.67 x 10 -11 N m 2 /kg 2G = 6.67 x 10 -11 N m 2 /kg 2 m 1 and m 2 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 variablesWe 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 metersReplace 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
PTYS/ASTR 206Keplers Laws and Gravity 2 1/27/09 The same concept holds for planetary orbits about the Sun
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 3 rd law for the orbits of the planets about the Sun is:
…which is one of these… …and there are about 40 billion other galaxies in the universe.
How are we going to get a handle on this BIG Universe of ours???
Units of Distance Astronomers use (and mix together) units of distance. Metric:1 meter = 1 m 1 centimeter = 1cm 1 kilometer = 1 km Astronomical Unit (AU) – Earth-Sun distance = 1.496 x 10 11 m Light Year – Distance light travels in 1 year = 9.46 x 10 12 km Parsec (pc) = = 3.08 x 10 16 m ….kiloparsec (kpc), megaparsec (Mpc)
So…how big is IT anyway? (the Universe that is….) …about 10 billion-billion-billion centimeters in diameter or 10,000,000,000,000,000,000,000,000,000 cm or 10 28 cm or 10 billion l-y or 6000 Mpc
Scale of the Universe 1) The Earth is the Size of a clenched fist - or…. 12,800 km = 10 cm 2) The Moon is 3500 km in Diameter - or….the size of the tip of your THUMB - or….the size of the tip of your THUMB 3) The Moon is 384,000 km away -or…. 3 meters from the fist 4) The Sun is 1,400,000 km in diameter - or…. 11 meters in diameter - or…. 11 meters in diameter 5) The Sun is 150,000,000 km away - or…. 1.2 km from the fist
The Earth and the Sun EarthSun Diameter12800 km1.5 million km (117x Earth) Mass6x10 24 kg2x10 30 kg (333,000x Earth) Compositionrocksgas (75% hydrogen 25% helium) Rotation period=1 day~25 days
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