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Astronomy & Astrophysics
Ingrid L.Stefanovic

So far, our model of the Universe have only looked at empirically fitting to data Definitions Kinematic model – describes motion Dynamic model – describes why things move Inertia - the tendency to resist changes in motion or the tendency of an object to maintain whatever speed and direction of motion Acceleration – a change in an object’s speed Mass - (kilograms) an object’s measure of inertia (remains the same independent of location) Mass = a property possessed by matter that represents its inertia (The mass of your body is a fixed quantity) Weight – (pounds) the gravitational force felt by an object (weight depends on location – on earth’s surface, weight is directly proportional to mass) Centripetal force - force necessary to keep an object moving in a circle Mass of the Moon = 7.3477×1022 kg Mass of the Earth = 5.9736×1024 kg Distance to Moon = 384,399 km Linear Motion – change in speed (forward or backwards) Circular Motion – change in direction (towards centre of circle) Orbital Motion – change in speed and direction (towards object being orbited) Wavelength – distance between successive peaks in a wave Frequency – number of cycles per second Wave speed – frequency x wavelength Radial velocity – a star’s velocity towards or away from us Tangential velocity – velocity of a star across our line of sight Emission Spectrum – a spectrum that contains only certain definite frequ26cies Luminosity – the energy the Sun radiates into space per second (3.85 x 10 Watts) Astronomical Unit (AU) – mean distance from Earth to Sun (150 million km) Light Year – distance light travels in 1 year = 63,000 AU Other Facts: • The Sun is 330,000 times more massive than the Earth • Earth’s mass is 81 times more than the Moon • Copernicus said that stellar parallax was not observed on distant stars because they were too far away • The Sun has 99.85% of the mass of the solar system Aristotle’s Theory: • Objects move according to their internal nature: – stones fall because they seek the earth – smoke rises because it seeks the air • The celestial realm is governed by different laws than the Earthly realm Galileo: – Galileo introduced the concept of inertia – A cannon ball and a bullet should hit the ground at the same time if they were dropped at the same time from a given height – Showed that Aristotle’s theory of motion was incorrect – Objects moving on a level surface tend to continue moving at a constant speed unless disturbed CHAPTER 3 Newton - Born the year Galileo died - Applied the principle of universality (no difference between celestial and earthly realms) - Famous for three laws: 1. First Law - an object stays at rest or moving at constant speed unless acted upon by an outside force (an extension of Galileo’s law of inertia) 2. Second Law - an external force causes an object to accelerate at a rate proportional to the force and inversely proportional to its mass( F = m.a ) 3. Third Law - when object A exerts a force on object B, object B exerts an equal and opposite force back on A - Discovered the Universal Law of Gravitation while watching an apple fall from a tree - Said that gravity extended to the orb of the moon - The apple falls because of the gravitational attraction between the apple and earth - The moon stays in orbit around earth because of the gravitational attraction between earth and moon - Newton’s Law of Universal Gravitation states that every object in the universe gravitationally attracts every other object I. Force of attraction is proportional to masses of both objects II. Force of attraction is inversely proportional to square of the distance between objects (inverse square law) - This is given by F = (G.m1.m2) / d 2 where ‘m1’ & ‘m2’ are masses of the two objects and ‘d’ is the distance between the objects. G is a constant number. - Newton showed that the gravity on the earth’s surface is 9.8 m/s2 and the moon’s centripetal acceleration is 0.0027 m/s2 - Newton not only proved Kepler’s laws with his laws of motion and law of gravity, but he expanded upon them. - He proved Kepler’s first law by: using calculus he showed that the planetary orbit will be elliptical, if and only if, the centripetal force varies as 1/ d from the Sun which is located at one foci. - He proved Kepler’s second law by: the gravitational force acting on an object orbiting the Sun always points towards the Sun. [See page 83 for explanation of proof without using math] - He modified Kepler’s third law which now can be used for any two objects orbiting each other as a result of their mutual gravitational attraction. [See page 85 for formula of this law] - From Newton’s third law (for every action, there is an equal and opposite reaction), one object cannot be still while another is orbiting it. Instead, the two objects orbit about a point between them called the centre of mass. - For example, to balance a see-saw, a person 3 times the mass of another person must sit 3 times closer to the pivot (balancing point) than the other. - Since the Earth is 81 times the mass of the Moon, their centre of mass is 81 times closer to the Earth. - Note that it is the centre of mass of the Earth-Moon system that follows the elliptical path Importance of Newton’s Laws:  Kepler’s Laws can be derived from them  Explained the tides  Neptune was discovered by predicting the gravitational forces on Uranus  Showed that nature is understandable General Theory of Relativity: - Newton proposed that mass is not only the measure of an object’s inertia, but it also determines the strength of gravitational attraction. - To explain this, Einstein came up with the theory of relativity more than 200 years after Newton. - Einstein’s principle of equivalence states the similarity between gravity and acceleration (book drop on Earth and spaceship example) [inertial mass = gravitational mass] (Gravitational force is proportional to mass) - When a beam of light is sent through a spaceship, it will curve linearly if constant velocity and curve exponentially if accelerating. To an outside observer, the beam of light follows a straight path. - Space itself must be warped - More massive objects warp space more (objects with mass curve space) - Time and space cannot be considered separately – therefore, need to consider 4-D spacetime st - The following is what Einstein said with respect to Newton’s 1 Law: Newton: objects don’t move or change their motion in a straight line unless acted upon by an external force [Einstein: objects follow a geodesic unless acted upon by an external force – geodesic means path of least resistance in curved space] - General relativity is mostly concerned with 4-D geometry - Earth does not pull on the Moon – the Moon simply follows the path of least resistance in curved space - Space itself “transmits” the gravitational force - In a place with strong gravity, time moves more slowly relative to an observer in weak gravity - GPS system is in a weaker gravity than on Earth - Newton’s gravitational laws work extremely well for most applications. - Newton: Force is proportional to mass - Relativity: More mass warps space more CHAPTER 4 Light and Electromagnetic Spectrum: - Maxwell showed that the speed of light was 300,000 km/s and said that it was an electromagnetic wave. - Light emits energy - Electromagnetic spectrum contains gamma rays, x-rays, ultraviolet rays, visible, infrared and radio - Visible light falls between 400 – 700 nm in wavelengths - Black holes – extreme mass causes them to warp space (they were discovered indirectly from their gravitational effects on the orbits of nearby objects and from massive amounts of X-ray radiation emitted by gas falling in) What is Light? - According to Aristotle, light is a wave motion of aether - According to Newton, light is a stream of tiny particles - In modern day, we use light as both a wave and a particle (photon) - Roemer was the first to accurately measure the speed of light in 1675 - Newton showed that the color of light was a fundamental property using 2 prisms to separate a single color - William Herschel shone a spectrum of sunlight onto a set of thermometers and showed that there are invisible types of light outside of the visible spectrum Kelvin Temperature Scale - Absolute zero point (-273 C) - Temperature is the measure of the average kinetic energy of particles - As temperature increases, the particles move faster. At absolute zero, there is a state of minimum atomic motion. Wave Nature of Light: - Two thoughts about light came from the Greeks. One is that light is a stream of extremely small, fast- moving particles and our vision is the result of the interaction between our eyes and this stream. The second idea came from Aristotle where light was an aether movement (5 element added to his 4 elements), and our vision is the result of movement of the aether produced by the object we perceive. - Newton showed that a prism separated white light into a spectrum. Previously thought was that the prism adds color to light. He showed this by using a second prism to recombine the separated colors into white light. - He showed that color is a fundamental property of light. - Wave equation states that Wave speed = (wavelength) x (frequency) - White light is made up of light of many different wavelengths all traveling at the same speed in a vacuum - Planets absorb certain wavelengths of light and reflect others and this determines the apparent color of the planets - Mars looks red because the dusty surface reflects red light and it absorbs blue - Light of different wavelengths are defined as colors for our convenience to understand - The wavelength of the reddest red is 700 nanometers and the wavelength of violet is 400nm Electromagnetic Spectrum: - Waves longer than 700nm are called infrared waves and waves longer than 100,000nm are called radio waves. - Going the other way, waves smaller than 400nm are called ultraviolet rays and waves even smaller are called x-rays and gamma rays - All the waves including visible light are classified as electromagnetic waves. Colors of Planets and Stars: - Color of planet can be used to predict the temperature on its surface - Peak wavelength is inversely proportional to the temperature - Dense matter emits what is called a Blackbody or thermal spectrum - The reason we see a particular color of a planet (ex. Mars) is because the material on the surface of the planet absorbs some of the wavelengths of sunlight and reflects a combination of wavelengths that looks a particular color. - For example, the reason we see a red taillight is because the white light emitted by the bulb gets absorbed by the red plastic cover and only releases the red color’s wavelengths. 6 - The relationship between temperature and it’s wavelength are given as λmax = 2.9 x 10 / T (in K) - The higher the temperature of a star, the shorter the wavelength at which it emits its energy - A “white” star is hotter than a “red” star. - We can determine a star’s surface temperature by examining its intensity vs. wavelength curve (Figure 4-7, pg.108) - Blackbody Radiation: radiation that would be emitted from an object that absorbs (or emits) all wavelengths completely. 4 - Stefan-Boltzmann Law: the hotter an object is, the more radiation it emits. F = σ.T where F is the energy flux Kirchoff’s Laws 1. Hot high-density objects emit continuous spectra 2. Hot low-density gases emit spectral lines 3. If light passes through low-density matter, light is absorbed in lines Types of Spectra: - A continuous spectrum has a peak at a certain wavelength, but some energy is emitted at all wavelengths. - Such a spectrum is produced when a solid object is heated to a temperature great enough that the object emits visible light (ex. Filament of a lamp) - Kirchhoff formulated a set of rules (Kirchholff’s laws) which summarize how the three types of spectra are produced: 1. A hot, dense glowing object emits a continuous spectrum 2. A hot, low-density gas emits light of only certain wavelengths – (bright line spectrum) 3. When light having a continuous spectrum passes through a cool gas, dark lines appear in the continuous spectrum – (dark-line spectrum)  Know the difference between continuous spectrum, emission line spectrum and absorption line spectrum  Emission line spectrum has black everywhere except a few lines of certain colors in the spectrum  Absorption line spectrum has the continuous spectrum with black lines at certain spots  Elements produce lines at exactly the same wavelengths in both absorption and emission spectrum  Emission lines of Sun’s atmosphere can be seen by looking at the Sun’s corona during a solar eclipse  Helium was discovered by looking at solar emission lines  An example of the universality is that electromagnetic spectra of objects in the celestial realm and the terrestrial realm are the same The Doppler Effect: Consider waves spreading from a disturbance on the surface of water. Four important points can be made from this: 1. If a source of the waves is moving, the waves still travel at the same speed in all directions. 2. The waves in front of the moving source are shorter than they would be if the source were stationary, and the wavelengths behind the moving source are longer. The wavelength is inversely proportional to the frequency. For example, if you are in front of a car with a siren, the wavelengths are shorter and the frequency higher (high pitch). When the car passes by, the wavelengths become longer with lower frequency (low pitch). This effect is called the Doppler Effect.
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