EU Scientists
Use Kepler's Third law to calculate the radius of Jupiter's orbit given that the mass of the sun is 1.989x103 0 kg and that the period of Jupiter's orbit is 11.86 earth years. Compare with both the accepted value and with the Bode's law prediction.
(T^2 / r^3) = (4pi^2 / GM) ((T^2 * GM) / (4pi^2))^(1⁄3) = rr = (((11.86^2 * (6.7 x 10^-11)*(1.989x10^39)) / (4pi^2))^(1⁄3) = 7.78 x 10^6 km
What is the 19th century answer to the question, with respect to what does light move at speed c? Why did physicists of the 19th century answer this question in the way they did?
19th century physicists believed that light moved at speed c with respect to the ether. They hypothesized the existence of the ether because Young concluded that the wave nature of light requires a medium.
According to Einstein, with respect to what does the speed of light move at speed c?
According to Einstein, he stated that the speed of light, c, is constant and independent of the motion of the light source. Therefore, with respect to any uniform moving body, c is constant.
In what frame of reference are the laws of electromagnetism valid, according to Einstein?
According to Einstein, the laws of electromagnetism are valid relative to the laws of relativity because the laws of physics must be the same in all uniform moving frames of reference.
What was the natural state of motion according to Newton and Galileo?
According to Newton and Galileo, the natural state of motion is not rest, but it is instead uniform velocity.
What is an electromagnetic wave?
An electromagnetic wave is a wave that is created by vibrations between an electric field and a magnetic field. They do not require a medium to travel.
What is an event in relativity?
An event in relativity is an event that occurs at a point x in space at a specific time t.
Summarize how Aristarchus measured the relative distance to the Sun.
Aristarchus built on Anaxagoras' ideas. He concluded that the half Moon must occur when the Sun, Moon, and Earth form a right-angled triangle, and measured the angle between the lines connecting these 3 figures. He measured the angle to be 87 degrees, meaning that the Sun was about 20 times farther away than the moon, even though the actual correct angle is 89.85 degrees and the Sun is actually 400 times away farther than the Moon. Even though his calculations weren't accurate, the method he used is valid and opened the door to more discovery.
Experimenters counted the number of muons moving at 0.995c past the top of a mountain 2,000 meters above sea level. If they knew nothing of relativity theory, based solely on the mean life of muons, how should the number of muons that reached the base of the mountain compare to the number passing the top of the mountain?
Assuming the experimenters know nothing about the theory of relativity, they should regardless expect a lot more muons on the top of the mountain than the base of the mountain because of their short life span.
How did knowing the size of the Earth allow for the size of the Moon to be determined?
By comparing the size of the Earth's shadow cast on the Moon during a lunar eclipse, it is possible to figure out the size of the Moon.
What is the source of all magnetism?
Electric current — aka moving electric charge — is the source of all magnetism.
Summarize how Eratosthenes measured the diameter of the Earth.
Eratosthenes noticed that on June 21 every year, the sun would shine into the bottom of a well in a town called Syene. Given this, that means the sun must be directly overhead Syene. Using the fact that the sun can't be directly overhead Syene and Alexandria at the same time (because of the curvature of the earth), on the next 21st of June, Eratosthenes stuck a stick into the ground in Alexandria and measured the angle between the Sun's rays and the stick. Since this angle measured 7.2 degrees, that means the distance between Alexandria and Syene is 7.2/360 of the Earth's circumference. Eratosthenes concluded that the circumference was 250,000 stades, and this can be used to calculate the diameter of the earth.
List the properties that the ether must have and why it must have them. Identify any apparent contradiction between these properties.
Fluid but strong enough: It must be solid enough to support waves of light, but must also be fluid enough to fill all space. Weightless and transparent: It is not visible, which explains why we can't see this medium and why it doesn't physically interact with any entity. Little to no density: It must have this property so it doesn't impact the motion of planets or anything else in space. Permeates all space and matter so it doesn't affect any movement
Which of the seven axioms Copernicus proposed in his 1514 pamphlet, Commentariolus ("Little Commentary") do we now know are incorrect?
For the most part, Copernicus' claims in his pamphlet were correct. However, his idea that the Sun was the center of the universe is false, because we in fact don't know where the center of the universe is.
Describe Faraday's experiment that demonstrated another connection between electric current and magnetism.
In Faraday's experiment, he created an electromagnet by winding a coil of wire and passed an electric current through it. He then placed another coil nearby and connected a meter to it that registered the flow of current in this second coil. Nothing happened until he interrupted the current in the first coil (which changes the magnetism), and there was a deflection in the meter. This means that changing magnetism produces electric current, and the name of this is electromagnetic induction.
What experiment, done by Oersted, demonstrated a connection between electric current and magnetism?
In his experiment, the needle of a compass pointed to a right angle to the wire when a current was passed through the wire. This means that the electric current deflected the magnetic compass. This implies that the current had produced a magnetic field that made the needle turn.
What observations were made by Galileo to support the Sun-centered model of the Universe?
In the sun-centered model, both Earth and Venus orbit the sun. Even though Venus is always half-lit by the Sun, from Earth's perspective it is seen to go through a cycle phases, from a crescent to a disc.
Describe the early 19t h century experiment by Young that argued for a wave model of light.
In this experiment, Young passed sunlight through two pinholes in a darkened room, illuminating a screen opposite of the holes. Rather than observing 2 bright spots on the screen, Young found a series of alternating bright and dark spots on the screen. This occurs because each hole makes the light that goes through it diffract, and this makes the waves meet and interfere. This shows that light travels in waves.
What property of light waves does the Michelson-Morley interferometer directly demonstrate?
It directly demonstrates the interference of waves, and that constructive and destructive waves only depended on the distance of the mirrors.
What is the significance of the Michelson-Morley experiment for the question does the Earth move with respect to the ether?
It discredited all theories about the ether. The experiment showed that there is either no medium, and if there is, it is very negligible.
What are Kepler's three laws of planetary motion? How did one of Kepler's laws provide an improvement of Copernicus' Sun-Centered model of the Universe?
Kepler's first law of planetary motion states that planets move in ellipses, rather than circles. His second law states that the line between a planet and the sun sweeps out equal areas in the plane of the planet's orbit over equal times. His third law states that the ratios of the squares to the periods of two planets are equal to the ratio of cubes of the average distance from the sun. Kepler's first saw is an improvement over Copernicus' model because Copernicus' model claimed that planets had constant motion, whereas Kepler's first law shows that planets do not have consistent motion.
How did Kepler's laws of motion support the Sun-centered model of the Universe over the Earth-centered-model?
Kepler's laws of motion supported the Sun-centered model of the Universe because it claimed that a planet's orbit was an ellipse around a certain point. SinceEarth was a planet, that meant that the Earth orbited around the Sun, making it more appealing to the Sun-centered model
Why and how did Maxwell modify one of the four fundamental statements about electricity and magnetism?
Maxwell suspected that a changing electric field would create a magnetic field. He noticed that the equations were not consistent with the idea that electric charge is conserved. However, consistency could be regained if he added the term "changing electric field" in the equation for the source of magnetic fields.
The muon is an unstable particle with a mean life of 2.2 x 10- 6 seconds. What is meant by mean life?
Mean life is the average lifetime. For an unstable particle, mean life is the average lifetime until it completely decays.
Describe the analogy between the two light beams in a Michelson interferometer and the two people swimming up and downstream and across and back in a river.
Michelson believed that when comparing the speed a swimmer is moving against the current to a swimmer moving with the current, the speed is different because the mediums are providing different levels of resistance which the body must go through. This is the medium that he called the ether.
In what two ways can motion change?
Motion can change by having a different speed, or having a different direction (both can happen simultaneously too).
What entities respond to magnetism?
Moving charges not only respond to magnetism, but they also create magnetism.
State Newton's three laws of motion.
Newton's three laws of motion: 1. Objects in motion tend to stay in motion and objects at rest tend to stay at rest unless acted upon by an unbalanced force. 2. Force = Mass x Acceleration 3. For every action there is an equal and opposite reaction
What is retrograde planetary motion?
Retrograde planetary motion is a theory of circles within circles. To make a path of retrograde motion, the main circle is the deferent, and it has a rod attached that served as a pivot, which. This explains the occasional "backwards motion" of the planet's as seen from Earth's sky, which is an illusion.
How did the number of muons reaching the base of the mountain really compare to the number passing the top of the mountain?
Surprisingly, more than half of the muons at the top were also detected at the bottom. This occurred because the muons clock moves slower than our regular clock, so they are able to travel longer distances than expected. This is time dilation.
Summarize the key strengths and weaknesses of the Sun-Centered and the Earth-Centered models of the Universe, as understood in 1610.
The Earth Centered models were viewed as common sense, had very good predictability of planetary orbits, and explained that everything fell to the ground due to the centrality of Earth. These models, however, were complicated, could not predict phases of Venus, and lacks explanations for blemishes on the Sun and Moon and the orbiting of Jupiter's moons. The Sun-centered models could perfectly predict planetary orbits, the phases of Venus, and tolerates the Moons of Jupiter due to multiple centers. It was seen as a very simple model. However, these models were viewed as imagination and did not have any obvious explanation for why things fell to the ground.
Outline how the distance to the Sun was estimated in ancient Greece.
The Greeks showed how knowing the distance to the Sun depended on knowing the distance to the Moon, which depended on knowing the diameter of the Moon, which depends on knowing the diameter of the Earth.
What is the Michelson-Morley experiment? What was it designed to measure? Did it succeed in measuring what it was designed to measure? Include a description of a Michelson Interferometer.
The Michelson-Morley experiment was an experiment where light was sent towards a half silvered mirror (half of the light goes through while the other half bounces off) and bounced the reflections off another mirror (where some of this light would bounce back towards the light source while other parts bounce back through the half silvered mirror). This showed that if there was an ether, then the light would be going faster once it was deflected and slower when coming back because it was passing through a medium. It was designed to measure the absolute velocity of the Earth within the ether. Using the velocity of light through the ether would depend on the velocity of Earth through the ether. The experiment did not succeed because the interference of the waves did not change, and this implies the ether had no effect. They had believed there was an ether, but this experiment proved that even if it did exist, it had no effect. The Michelson Interferometer is used to merge multiple sources of light in order to obtain an interference.
Summarize Ptolemy's Earth-centered model of the Universe. What was the motivation to change the original Earth-centered model to that described by Ptolemy?
The Ptolemaic Earth-centred model of the universe was constructed to comply with the beliefs that everything revolves around the Earth and that all celestial objects follow circular paths. The best analogy for this model is a fairground, where different objects have circular motions, but these motions have some differences. The motivation for this model was the looping planetary orbits, since there was no solution for the reasoning behind this, since it was initially thought that all orbits were supposed to be circular.
Why was the field concept introduced? Contrast the field concept (and the idea of local conditions) with the action-at-a-distance concept.
The field concept was introduced as a response to the action-as-a-distance concept. The action-at-a-distance concept claimed that an object can be affected without being physically touched by another object. The action-at-a-distance concept required the moon to be aware of what's happening at the location of Earth, but physicists were not convinced by this and thought it would make more sense if the moon only needed to be aware of its immediate vicinity and responded only to local conditions. This is what caused the field concept to be introduced.
What are Einstein's two postulates of special relativity?
The first one is that the laws of physics apply to all uniform moving bodies. The second one is that the speed of light when in free space will have the same value in any inertial frame of reference, therefore meaning that the speed is independent of the motion of the light source.
In which frame of reference is the length of an object longest?
The length of an object is longest in the frame of reference where the object is at rest.
Aristarchus proposed a model of the Universe that placed the Sun at the center, rather than the Earth. What arguments were proposed against the Sun-centered model?
The main argument was that it just seemed completely obvious the Sun revolved around the Earth. It was claimed that if the Earth revolved around the Sun, we would feel a constant wind blowing against us, and since there is no constant wind, the Earth must be stationary. Another reason was that a moving Earth was incompatible with the Greek understanding of gravity. The last reason is the lack of shift in the position of the stars. It was claimed that if the Earth was moving around the Sun, then the position of the stars would change because the Earth would be in a different position.
An experiment testing the prediction of time dilation was done in the early 1960's with an unstable subatomic particle called the muon, a negatively charged particle with a mass greater than that of the electron. How were the muons used in this experiment created?
The muons in this experiment were created by the decay of mesons that were separated from nuclei that were affected by cosmic rays.
What is in the preface to Copernicus' book De Revolutionibus that leads scholars to suspect that he did not write it (the preface)? What motivation would Copernicus (or whoever was responsible for the preface) have to include such a statement?
The preface of the book makes scholars suspect Copernicus didn't write it because it invalidates the content of the book. The motivation for this is because if Copernicus' claims were perceived to be serious, this could have led to persecution from the religious and scientific community.
Outline how the size of and distance to the Moon was estimated.
The relative sizes of the Earth and Moon can be estimated by observing the Moon's passage through the Earth's shadow during a lunar eclipse, and the size of the Earth's shadow is pretty much the same as the size of Earth itself. Using the size of the Earth, the Moon's diameter was calculated as 1⁄4 of the diameter of the Earth. To figure out the distance, a person must stare up at a full Moon, close one eye and stretch out their arm. Then, they cover the moon with the end of their forefinger, and this forms a triangle with their eye. The ratio between the arm length and height of the fingernail is about 1:100, and this is the same proportion as the ratio between the distance to the moon and the moon's diameter. The diameter is 3,200 km, so the distance must be 320,000 km.
In what frame of reference is the time interval between two events the shortest?
The time interval between two events is the shortest in the frame of proper reference. This occurs when two events occur at the same point.
Why isn't the wave nature of light (visible electromagnetic radiation) obvious to us?
The wavelength of light is incredibly small (20 millionths of an inch), so it requires very closely spaced holes to make Young's interference pattern noticeable.
What are characteristics of the force between electric charges?
There are two types of charge: Positive and negative. Charges with the same type repel from each other, and charges with opposite charges are attracted to each other.
Why do physicists believe that the muon experiment verified time dilation?
This experiment verified time dilation because if there was no time dilation, then the base of the mountain should have had little to no muons. Time dilation is what allows the muons to travel longer than what one would expect, because of a different frame of reference and clock speed.
What great contribution to astronomy was made by Tycho Brahe? What instrument now common, was not at Tycho's disposal during the late 16t h century?
Tycho Brahe's most significant contribution was his observatory on the island of Hven. This observatory cost more than 5% of Denmark's GDP and had instruments that minimized the amount of errors when calculating angular positions of stars and planets. Tycho, however, did not have a telescope at his disposal.
Today, most scientific research is funded through government grants. How was Tycho's research funded?
Tycho's research was funded by King Frederick II of Denmark and Emperor Rudolph II of Prague.
In Newton's view what is needed to change motion?
Unless there is a net force acting on an object, an object will maintain its motion. The presence of net force means that one external force is stronger than another external force.
A person in a spaceship flies past the Earth at half the speed of light. A person at rest on Earth says the clock in the spaceship runs slower than the clock at rest on Earth. How much slower?
Using the provided formula, the person at rest on Earth will claim that the clock on the spaceship is .866 times slower than the clock on Earth.
What is wave interference?
Wave interference occurs when two waves meet while traveling along the same medium. It results in a "combined" wave of either greater, lower, or the same amplitude.
List four numbers that characterize a wave.
Waves have multiple properties, but some of the significant ones are: 1. Amplitude 2. Frequency 3. Period 4. Wavelength
What observations did Greek philosophers make to support the idea that the Earth is round?
When ships would sail out to see, the tip of the mast would be the last part of the ship that could be seen, so they concluded that the surface of sea curves away, and since the surface of the sea curves, so does the entire Earth.
Which model of the Universe made more accurate predictions, the Aristarchus Sun-Centered model or the Ptolemy Earth-Centered model? Describe the key strengths and weaknesses of the two models, as understood by the ancient Greeks.
While one can argue the Aristarchus Sun-Centered model is more accurate than the Ptolemy Earth-Centered model because the Sun is indeed the center of the solar system, the Ptolemy model endured while the Aristarchus didn't because only the Ptolemy model predicted with motion of the planets with such precision. The sun centered model was seen as a leap of imagination because of the claim the sun was in the center, and the lack of motion felt on Earth. The Earth centered model attracted more agreements, since it claimed the Earth was the center and this was an explanation for the lack of motion of Earth. Also, the planetary motion prediction was considered "the best yet."
Use Bode's law to calculate the radius of the orbit of Jupiter. Compare with the accepted value.
a = .4 + .3(2^n) .4 + .3(2^4) = 5.2 AU
Battlestar Gallactica is cruising above the earth at a speed of 0.8c. The commander launches fighters at 4 second intervals. How much time elapses between launches according to an earth observer?
t' = t * sqrt(1-(.8c/c)^2) = t * .6 t' = .6t4s = .6t so t = 6.67s t = 6.67s