Astronomy Test 2: Part 3

The Telescope

-1608 Hans Lipperhey, Dutch spectacle-maker found distant objects could be seen closer when looked through a combination of lenses. -built a small telescope. -1609 Galileo was able to build better quality telescopes, using lenses he ground himself, with magnifications 8-30, and apertures about 1 inch. -August that year, Galileo demonstrated telescope to the Venetian Senate. -impressed and understood the military potential -His professorship at Padua was confirmed for life and salary was doubled (as Galileo requested.)

Principia

-All those results on the laws of motion and gravitation were published in his book "Mathematical Principles of Natural Philosophy" or Principia published in 1687. -regarded as one of the most important works in the history of science. -It was in three books. -Book I: Laws of motion -Book II: Hydrostatics and hydrodynamics, -Book III: Law of universal gravitation. -According to the story, Edmund Halley visited Newton in 1684 and asked what would be the shape of a planetary orbit, if the force between it and the Sun changes as inverse square of the distance. -Newton had replied that it would be an ellipse, and that he had worked it out years ago. He had promised Halley to send the details. -Newton later reworked the proof for Halley, in the course of which he began developing a book-length discussion on the subject of motion of bodies in orbit. This was what written out into Principia during 1685-1686.

First Law

-An object remains at rest or moves along a straight line with constant speed as long as no net external force acts on it. -This implies that all objects have a tendency to resist changes in their state of motion. (to change speed or direction of motion) -This property of matter, resistance to change its state of motion is called inertia. Hence the 1st law is also called the law of inertia. -Larger the mass of an object, it has a higher inertia (more resistance to change of motion) -Friction due to surface roughness: Surfaces have tiny microscopic ridges and bumps, as one surface slides across another those irregularities catch and lock into each other causing friction. -Why we do not see this everyday? -objects in motion slowing down and becoming motionless seemingly without an outside force. -In fact there is a force, the friction: -Frictional forces act against the motion of an object.

Falling Objects on the Moving Earth According to Galileo

-Suppose a ball is dropped from a tall tower (on the moving Earth) -According to Galileo: -Both ball and the tower are moving horizontally with the same speed. -When the ball is dropped, while it is moving downward, it continues to move horizontally with the same speed with the Earth as before. -(since there is no force acting horizontally to stop it) -Ball falls vertically and strike ground right bellow where it was dropped. -An observer in the tower does not see any horizontal movement of the ball.

Falling Objects on the Moving Earth according to Aristotle

-Suppose a ball is dropped from a tall tower (on the moving Earth) -According to Aristotle: -Before the ball is dropped everything was moving with the Earth. -When the ball is dropped, its horizontal movement ceases (no horizontal force) -Ball moves vertically down while the tower moves with the Earth. -So if the earth is moving the ball has to strike the ground away from the tower.

Motion of a Projectile

-Suppose a ball is thrown horizontally (ignore air friction for now): -According to Galileo, vertically it has a uniformly accelerated motion so the vertical speed and the distance it moves vertically in a given time interval increases with time. -since there is no force acting horizontally on the ball, it will move at a uniform speed horizontally, moving a same distance in a given time interval. -Combining those two motions Galileo came to the conclusion that path of a projectile would be a parabolic curve.

Free falls and weightlessness

-Suppose few objects were dropped from an airplane and falling freely (ignore the air resistance for now). -Everything falls at the same rate (acceleration) under gravity. -Therefore they will stay together while falling. -For somebody falling with them, they would appear as floating right next to him all the time. -No other support or force is needed keep them together. -as if they are weightless. -Jumping from a diving board is a free fall and one could experience weightlessness. -Jumping with an open parachute is not a free fall.

The Second Law

-The 2nd law describes how the state of motion of an object changes when a force is applied. -When a force is applied on an object it will accelerate in the direction of the applied force. -The acceleration is proportional to the applied force and inversely proportional to its' mass. - larger force ⇒ larger acceleration. - Larger mass ⇒ less acceleration -m:mass -a: acceleration -F: force -the force is measured in Newtons (N); when mass in kilograms, distance is in meters, and time is in seconds we get the force in Newtons (N) -Weight of 1 kg object is about 10 Newtons -Weight of 1 lbs is about 4.5 N

Centripetal Force

-The force needed to move an object in a circular (or curved) path

Galileo on falling objects

-This implied if an object is dropped it would fall at a constant speed determined by its weight and nature -Heavier objects fall faster, lighter objects slower, according to Aristotelian view. -Galileo showed that it was wrong. He showed that all objects falls at the same rate regardless of the weight. -Contrary to the popular belief, it is unlikely that he showed this by dropping two different sized objects off the tower of Pisa. (Not mentioned in his writings). -Galileo did a number of experiments to study the nature of motion of falling bodies. -He came to the conclusion that a freely falling body has a uniform accelerated motion regardless of its nature. -its speed increases at a uniform rate, regardless of the weight of the object.

Newton's laws of Motion

1. An object remains at rest or moves along a straight line with constant speed as long as no net external force acts on it. 2. When a force is applied on an object, it will accelerate in the direction of the applied force. The acceleration is proportional to the applied force and inversely proportional to its' mass. 3. To every action, there is an equal and opposite reaction

Mass:

a measure of the amount of matter in an object.

Newton's law of universal gravitation

-Any two objects in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. -F : gravitational attractive force between two objects m1 : mass of the first object -m1 : mass of the second object -r : distance between the two objects -G : gravitational constant -Gravitational attraction between ordinary objects is very weak. -EX: gravitational attraction between two iron balls each 10kg, at a distances of 30 cm (1 foot): -on cosmic scales gravitational force is significant because objects are massive, eg. Earth 6x1024 kg, Sun, 2x1030 kg -Matter from different parts of the earth are at different distances from the object. -They pull on the object by different strengths according to the gravitational law. (stronger pull from nearby matter than far away matter) -Total gravitational force is equivalent to the pull of the mass of the whole earth at the center of the Earth -Though very weak, the gravitational attraction between two movable objects can be measured in sensitive experiments. -This was how the value of the gravitational constant G was first measured by the British physicist Henry Cavendish in 1798 using a torsion balance. -Once the value of G is known, using the gravitational formula, mass of the Earth, the Sun or anything which has an object orbiting around it can be estimated.

Isaac Newton

-English physicist and mathematician, -One of the most influential scientists of all time. -Made seminal contribution in mechanics, optics, mathematics. -Born in Lincolnshire, England, 1643. -In 1661, Entered Trinity College of Cambridge, graduated in 1665. -In 1665 the university was closed due to a plague epidemic. -Newton spent much of the next two years back at the family farm, reading and thinking and working on his theories on nature. -It was during this time he began to think about gravity, made initial discoveries on optics and calculus. -In 1667 Newton returned to Cambridge as a Fellow, in 1669 was appointed the Lucasian Professor in mathematics. -In 1705 he was knighted. By this time Newton had become one of the most celebrated persons of his time. -In 1727 Newton died and was buried in the Westminster Abbey.

Weightlessness in outer space

-For the same reason inside an spacecraft in outer space things appear to be floating and experience no gravity. -But 300-400km above, Earth's gravity is not very different from what it is on the ground (about 90%) -What really happens is that the spacecraft is in a perpetual free fall to Earth (or whatever gravity it is subjected to) with everything in it. -Since everything is falling together, no support or force is needed to keep them in place. -Just like we do not feel the gravitational pull of the Sun since Earth is always falling to the Sun. -Same can be experienced inside an airplane if allowed to fall freely. -In general in outer space there is nothing to resist to motion due to gravity, so everything is in a free fall (unless rockets are fired) whether they are orbiting earth or in a different trajectory -For the same reason in outer space things appear to be floating and experience no gravity. -In outer space there is nothing to resist to motion due to gravity, so everything is in a free fall (unless rockets are fired)

Galileo on the laws of Motion

-Galileo made extensive contributions to the understanding of the laws governing the motion of objects. -He published those finding in 'Dialogues Concerning Two New Sciences', the book he wrote during the final years of his life while under house arrest. -Prevailing ideas of the time on motion were mainly Aristotle's ideas: -Each object has a natural motion, the tendency to move toward their natural place with a speed decided by its nature. -Earthly objects fall because they move towards the center of the Earth (universe), their natural place. -Air and fire move (rise) linearly upward.

Telescopic Observations of the Sky

-Galileo turned his telescope to sky, his first target was the Moon. -Contrary to the belief that Moon was a perfect sphere, what he saw was a rugged mountainous surface. -He estimated the height of mountains from the length of their shadows. -Galileo's observations of rugged mountainous, Earth like moon surface directly contradicted Aristotle's cosmological descriptions of perfect and unchanging heavenly bodies.

Sunspots

-In 1612 Galileo (and many others) observed sunspots, dark patches on the surface of the Sun. -Those "blemishes" on the Sun refuted the basic principles of Aristotelian doctrine of an unchanging perfect nature of the heavenly objects. -Galileo observed motion of the sunspots indicating that the Sun was rotating. -This made it less strange that the Earth might rotate on an axis too, as required in the Copernican model. -Christopher Scheiner, an astronomer and a priest who supported the geo- centrism, also observed sunspots. -He claimed the spots must be tiny undiscovered planets circling close to the Sun, which would occasionally pass in front of its disk. -Galileo showered that it was wrong, since spots were not permanent and their shape changed.

Dialogues

-In 1623 a Galileo's supporter and friend, Cardinal Maffeo Barberini, who generally held a favorable view on the art and science, was elected Pope Urban VIII. -Soon Galileo met with Pope Urban III, during which they discussed the Copernican theory. -Pope gave permission to Galileo to write about the Copernican theory as long as: -he gives a balanced view for and against the helio-centrism. -treats Copernican theory only as a mathematical hypothesis. -Galileo completed the book 'Dialogues" in 1629. It was published in Florence in 1632. All 1000 copies were sold out within months. -It was a witty and brilliant work. The book was presented as a series of Dialogues over a span of four days among three participants - Salviati, Sagredo and Simplicio: -Salviati: An intellectual, with keen insights who seems to speak for Galileo and argues for the Copernican theory. -Sagredo: An intelligent layman who is seeking truth. Initially impartial, gradually comes to accept Salviati's arguments. -Simplicio: A follower of Aristotelian ideas, presents arguments against the Copernican theory. Speaks for Galileo's opponents, who puts up ineffectual, simplistic arguments for Salviati to knock down, often contradicting himself. -In spite of scrutiny by the Church officials, book was biased and supported Copernican ideas. -Shortly afterwards the sale of the book was banned, Galileo was summoned by the Roman Inquisition. -After a two week trial he was condemned. -Galileo agreed to plead guilty to a lesser charge in exchange for a lenient sentence. -He had to confess that the Copernican case was made too strongly in his book Dialogue and agreed to modify his opinions in his next work, and he believed and always will believe that what church recognizes and teaches was true. -Galileo was sentenced to prison for an indefinite term, later was allowed to return to his house in Florence, where he lived under house arrest until his death in 1642. -Papal Inquisition was abolished in 1822 -In 1835 Galileo's book Dialogue was taken off the Vatican's list of banned books. (later published as Dialogue Concerning the Two Chief World Systems) -Heliocentrism gradually gained acceptance, but still there were many accepted geocentric theory on religious grounds. In the US both Yale and Harvard had taught the geocentric theory until early eighteenth century. -In 1992 Vatican formally admitted that Galileo's views on the solar system were correct.

Phases of Venus

-In December 1610 Galileo observed Venus with his telescope. -After few months of observations, he was able to observe that Venus was going through a full cycle of phases. -This was not allowed in the Ptolemaic system. -Angular separation between Venus and the Sun never exceeds ~48o. -Ptolemaic geocentric system explained this by putting Venus on an epicycle, and the epicycle goes around the earth at the same rate as the Sun. (center of epicycle is always in the same direction as the Sun). -But if that was true, Venus would never be in full phase, only crescent phase would be visible from the Earth. -In December 1610 Galileo observed Venus with his telescope. -After few months of observations, he was able to observe that Venus was going through a full cycle of phases. -This was not allowed in the Ptolemaic system. -Angular separation between Venus and the Sun never exceeds ~48o. -Ptolemaic geocentric system explained this by putting Venus on an epicycle, and the epicycle goes around the earth at the same rate as the Sun. (center of epicycle is always in the same direction as the Sun). -But if that was true, Venus would never be in full phase, only crescent phase would be visible from the Earth. -Copernicus' heliocentric system allowed all phases of Venus visible from the Earth. -Full phase cycle of Venus thus ruled out the Ptolemaic geocentric system. -By that time Church, which embraced the geocentric view and Aristotelian doctrine, viewed the Copernican idea as a hypothesis, -A mathematical device to calculate positions of planets, not as the real picture and a threat to the views of the church. -But more and more evidence were gathering in favor of the Copernican view through telescopic observations: -Craters and mountains on the Moon, and sunspots refuted the Aristotelian view of unchanging perfect nature of the heavens. -Phases of Venus could not be explained in terms of the Ptolemaic/Aristotelian system. -Moons of Jupiter showed that planetary bodies could move around objects other than the Earth. -Rotation of the Sun showed planetary objects could rotate as required in the Copernican model. -Resolution of the Milky way to stars proved that stars were at a greater distance than earlier thought. -Still many rejected the heliocentric theory, and refused to believe what was seen though telescopes were real. They considered them as just artifacts due to optical defects in his telescope. -Frustrated by this, Galileo began openly expressing his ideas in supportive of the Copernican system. -"The Bible was written to show us how to go to heaven, not how the heavens go" - Galileo in a letter to the Grand Duchess of Tuscany in 1615 (Galileo was a devoted catholic all his life.) -Alarmed by the growing activism, in 1616 Galileo was summoned to Rome - He was cautioned against speaking out on behalf of the Copernican claim and was forbidden to discuss the theory orally or in writing. -Copernicus' book "The Revolutions" was banned as the Sun centered system was contrary to the teachings of Scripture, a heresy.

Galileo on Motion

-In addition to vertical motions(falls and rises), Aristotle described another type of motion, Forced Motions. -Produced by external forces (pushes and pulls) on objects. -In such motions objects only moved as long as a force is applied. -It was on this ground that Aristotelians rejected the idea that the Earth was rotating or moving around the Sun. -Again Galileo pointed out that it was wrong. Moving objects stop because of friction. -according to Galileo, if there is no friction a moving object would keep moving at the same speed. -no other force is needed to keep it moving as Aristotle envisioned.

Gravitation: The thought before

-In reality, it was an idea Newton developed over time. Probably he began to think about it after seeing an apple falling from a tree in the garden. -He had also been trying to understand the orbit of the Moon those days. -He may have thought like this: -For the apple to fall, there must be a force pulling it towards the Earth. -There is an attractive force pulling everything towards the Earth, that is why objects fall. -The Moon goes around the Earth. There has to be a force pulling the Moon towards the Earth for it to keep doing that. (otherwise moon would have moved away from the Earth) -The Moon is located at a greater distance, does the force which causes apples to fall on ground extends up to the Moon and keeps it moving around the Earth? -Newton realized, in fact it does. -The same force which pulls things to ground is the same force that pulls the Moon towards the Earth and keeps it going around the Earth. (just like the tension of a string keeps a ball in a circular path)

Galileo Galilei

-Italian astronomer, physicist, mathematician, & natural philosopher. -referred to as "father of modern astronomy and physics". -Born in Pisa 1564. -1581: University of Pisa for medical degree. -made famous discovery on pendulums watching a chandelier swing back & forth at Cathedral of Pisa (noticed regardless how far it swung, the time it took to swing back and forth was always the same. -principle used to build pendulum clocks. -While at University of Pisa, became interested in mathematics & began studying mathematics on his own. -dropped out in 1585. -Appointed to Chair of Mathematics at Pisa in 1589. -Became the Chair of Mathematics at the University of Padua in 1592. Remained at Padua for the next 18 years

Measuring actual mass

-Measuring the actual mass (inertial mass) is more challenging. -Inertial property of objects has to be used: - i.e. higher the mass (inertia) a larger force is needed to change its motion. -Newton's 2nd law: F=ma force = mass x acceleration -Apply a known force and measure the acceleration to estimate the mass of an object

Planetary orbits and Conic Sections

-Newton showed that it was possible to mathematically deduce all three of Kepler's laws of planetary motion according to his theory of gravitation. -A complete mathematical analysis showed that orbits could generally be conic sections (circular, elliptical, parabolic or hyperbolic orbits). -Circle and ellipse are bounded (enclosed) curves, a planet orbiting on such orbit continues to go around the sun. -Parabola and hyperbola are unbounded (open) curves extend to infinity. An object on such orbit eventually leaves the solar system. -Some comets follow such orbits, so they are seen only once, do not reappear.

Newton's cannonball experiment - Orbits

-Newton suggested an ingenious thought experiment to explain orbital motion. -Suppose somebody is firing cannonballs form the top of a mountain horizontally, gradually firing at faster and faster speeds. -The cannonball will hit the ground at a distance depending on its initial speed. -As the speed of the cannonball is increased, it will hit the ground at a location farther and farther away from the mountain A,B,C... -At some speed it moves so fast that it will not hit the ground. It travels in a circular path and return to the firing point, and continue circling the Earth. (that speed is about 8 km/s) If the speed is increased further, it will go into an elliptical orbit. -If the speed is increased even further it will follow a parabolic or hyperbolic orbit and move away (escape) from the Earth. -escape velocity: It is about 11 k/s from the Surface of the Earth. -So all objects orbiting the Earth are perpetually falling to the Earth. But the orbital velocity keeps them from ever actually hitting! -In the same way the Earth and planets are in a perpetual free fall to the Sun under Sun's gravity.

Inertia balance:

-Object moves back and forth (oscillates) due to the restoring force of the spring. -More massive objects accelerates/moves slower and takes a longer time to complete an oscillation. -That can be used to estimate the mass of an object regardless of the gravity at the location.

friction

-Restraining force generated from the rubbing action between objects or media (water, air) when there is a contact between them

Escape Velocity

-Speed needed to overcome the Earth's gravity and leave Earth. -This limiting speed that a projectile will follow a parabolic orbit and escape

Galileo on Falling Objects

-Speed of a freely falling object increases at a rate 10 m/s each second (9.8 m/s more accurately). -EX: an object accelerates 9.8 m/s per second when they fall freely (without air resistance)

Gravitation

-Thus Newton realized that all objects in the universe orbit around each other due to an attractive force between them, he called the Gravitation -The Earth's gravitational attraction on the moon provides the centripetal force needed to keep Moon going around the Earth. -In the same way planets must be pulled by the Sun's gravitational attraction towards the Sun, which keep them moving around the Sun. -This was a major revelation: -The force pulls us to the ground, or cause apples to fall is the same force which holds the whole solar system (and the universe) together and causing them to move in orbits around each other. -Since ancient times various ideas had been suggested what holding the Sun Moon and planets in the sky and keep them moving. -Finally Newton found the answer. He expressed his findings in the law of universal gravitation. -In 1916 Albert Einstein explained what causing this attraction in his general theory of relativity.

Third Law

-To every action, there is an equal and opposite reaction This simply says that interaction forces comes in pairs, and the action and reaction are of the same magnitude in opposite directions. -When an object is sitting on a table, weight of the object pushes the table down, and table pushes the object upward equally hard. -When rowing a boat one pushes water backward with oars. And water pushes the oars (and the boat) forward. -A rocket pushes burned gases down, gas pushes the rocket up by an equal force. -Gun pushes the burned gas (and the cannonball) forward, gas in turn push the gun backward.

Kepler's 2nd Law and Gravitation

-Universal gravitational law explains the reason for the Kepler's second law planetary motion. -Since gravitational attraction from the Sun depends on the inverse square of the distance. -When the planet gets closer to the sun on its orbit, it feels a stronger gravitational pull from the Sun. -So it has to move faster to overcome the stronger pull towards the sun and vice versa.

Circular motion:

-When an object is moving in a circle, every moment its direction of motion is changing. -So we know (from 1st law) it has to be under influence of some force. -EX: when one swing a tethered ball in a circle feels the tension of the string. -That is because natural tendency of the ball is to move in a straight line. -In a circular motion the ball is always changing its direction towards the center. -the string has to apply a force to pull the ball towards the center from the straight path of motion ball is trying to maintain. Tension of the string provides that force. -Centripetal Force -If a force is needed to keep an object move in a circle, is it accelerating? -Yes, an objects moving in a circle is always accelerating towards the center. -acceleration towards the center -v: speed of the object -r: radius of the circle

Weight and Mass

-both used loosely -People often use "weight" to mean "mass", and vice versa. --It is technically wrong. On the Earth gravity makes 1 kilo gram mass to exert about 9.8 Newton force. - That is what most scales measure. ie weight. - What scales really show is an estimate of mass (in kilograms or pounds) based on the weight of the object. - As long as we only work with objects on the Earth that works most of the time. But it cannot be used universally. -Weight depends on the gravitational strength at the location. -On Earth weight of an object is the gravitational pull by the Earth (say 100kg) -On the Moon it would weight less because gravitation pull on the Moon is weaker (1/6 of Earth's) -so a scale calibrated to read weight in kg on Earth would read about 17 kg on the Moon. -On Jupiter it would weight more (about 250 kg) because gravitational pull on Jupiter is stronger. -In all above locations mass of the object is the same, 100kg. -You have to apply a force of same strength to accelerate (horizontally) at the same rate on the Moon as well as on the Earth.

perihelion

-closest to Sun gravitational pull from the Sun is strongest -planet moves fastest

aphelion

-farthest to Sun gravitational pull from the Sun is weakest -planet moves slowest

Galileo on falling objects- Friction

-if we drop a stone and a feather stone falls faster. -Galileo correctly identified that such differences were due to friction. -When an object moves it rubs against a surface, and rub against air. The force due to rubbing action acts against the motion is called the friction. -This is what makes the difference in motion for different types of objects. -When a stone and a feather are dropped, feather falls slower because due to its shape it is subjected to more drag(friction) from air. -If a stone and a feather are dropped in a vacuum, they would fall at the same rate.

Weight:

-is the amount of gravitational pull on an object. -It is a force so has to measure in Newton

Moons of Jupiter

-on January 7, 1610 when Galileo pointed his telescope at Jupiter He saw three tiny stars very close to it, strung out in a line. -When he observed again next day he saw the same stars, but their positions had changed. -He continued to observe Jupiter and the stars. On January 13, a fourth star appeared. -After a few weeks, Galileo noticed that the stars were moving along with Jupiter across the sky, while changing their positions with respect to Jupiter. -Soon, he realized those were not stars, but planetary bodies that were orbiting around Jupiter. -Thus Galileo discovered the four largest satellites (moons) of Jupiter. -Galileo observed the Milky Way through his telescope: -He saw that the Milky Way was made up of countless stars. -He explanted that the Milky way looked nebulous to the naked eye because there were so many stars, far away than anyone previously imagined. -This eliminated a main argument against heliocentric theory since Greek times: -non observability of stellar parallax. -Stars do not show parallax as the Earth goes around the Sun because stars are very far away. -The earth's orbit is vey small in comparison to their distances.

Velocity

-rate at which an object change its position in a given direction. -is speed with the direction, so have to provide magnitude of rate of change (a number), as well as the direction. -Circular motion is an example where there is a constant speed, but changing velocity (because direction of the motion is always changing).

Speed

-rate at which an object changes its position. -given as a number, distance per unit time. Ex. 40 miles/hour -Speed taken with the direction of motion is called velocity. -Circular motion is an example where there is a constant speed, but changing velocity (because direction of the motion is always changing).