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Fully explain/describe/define the following terms. Give a viable application of each term. Provide graphs, photographs, tables, etc. where appropriate to facilitate your understanding. a) Stefan-Boltzmann Law It states that, the thermal energy radiated by a blackbody radiator per second per unit area is proportional to the fourth power of the absolute temperature. This is given by the following formula: π = ππ 4 πβπ2 π π΄ π = 5.6703 × 10β8 π€ππ‘π‘/π2 πΎ 4 b) Wien's Law It is a law of physics that is used to describe the scale of thermal radiation. Wien's displacement law states that the black body radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature. c) Hubble's Constant/Law Hubbleβs law describes the relationship between velocity of recession and the distance of a Universe. His findings showed that there is direct or linear relationship between a galaxyβs velocity of recession and its distance. The law simply means that galaxies farther away from us are moving away faster from us. A galaxy twice as far away is moving away twice as fast. d) Relativity In physics, the theory of relativity or simply relativity usually comprises two theories by Albert Einstein: special relativity and general relativity. Concepts introduced by the theories of relativity include: Measurements of various quantities are relative to the velocities of observers. e) Tully-Fisher Law It describes the luminosity of spiral galaxies and their speed of rotation. The law states that the fourth power of the circular velocity of stars around the core of the galaxy is proportional to the luminosity. Tully-Fisher relation is a correlation of spiral galaxies between their luminosity and their speed of rotation. The bigger the galaxy, the faster it rotates and vice versa. f) Roche's Limit The smallest distance to which a large satellite can approach its primary body without being damaged by tidal forces is called the Rocheβs Limit. The limit is theoretically two and half times the radius of a larger body if the satellite and primary are of similar composition. g) Drake's Equation It is a probabilistic argument derived from Bayes, and which is used to arrive at an estimate of the number of active, communicative interplanetary civilizations in the Milky Way galaxy. π = π β . fπ . nπ . fπ . fπ . fπ . L Where N = Number of civilizations in the Milky Way, Rβ = rate of star formation, fp = fraction of stars with planetary systems, ne = number of planets per solar system that can support life, fl = fraction of plantes where life appears, fi = fraction of life bearing planets on which intelligent life emerges, fc = fraction of civilizations that develop a technology that releases detectable of their existance in space, and L = the duration with which such civilization releases detectable technologies into space. h) Kepler's Laws These laws were developed by Johannes Kepler. The three Kepler laws are: Law of Orbits- It states that all planets move in elliptical orbits, with the sun at one center. Law of Areas β the law states that a line that connects a planet to the sun sweeps out equal areas in equal times. The Law of Periods β according to this law, the square of the period of any planet is proportional to the cube of the semi-major axis of its orbit. i) Newton's Laws Isaac Newton came up with three laws of motion: First Law (Law of Inertia) β the law states that unless an external force is applied to an object, every object in a state of uniform motion has the tendency of remaining in that state of motion. Second Law of Motion β according to Newton, the relationship between mass of an object, m, its acceleration, a, and the applied force, F is F=ma. The direction of force vector is the same as the acceleration vector. Third Law of Motion β Newtonβs Third Law of Motion states that for every action, there is an equal and opposite reaction j) Rayleigh's Law This law was derived by Lord Rayleigh in 1871, applies to particles that are smaller than the wavelength of the light being scattered. The law states that the percentage of light that will be scattered is inversely proportional to the fourth power of the wavelength. Small particles scatters a much higher proportion of short wavelength light than long wavelength light. k) Fraunhofer lines Named after the German physicist Joseph von Fraunhofer (1787β1826), Fraunhofer lines are a set of spectral lines. The lines were originally observed as dark features (absorption lines) in the optical spectrum of the Sun. l) Hertzprung-Russell diagram The diagram was developed independently in the early 1900s by Ejnar Hertzsprung and Henry Norris Russell. HR diagrams are of two forms: the theoretical HR diagram which plots the temperature of stars against their luminosity, and the observational HR diagram (color-magnitude diagram) that plots the color of stars (or spectral type) against their absolute magnitude. m) Inverse Square Law According to physics, an inverse-square law is any physical law stating that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source of that physical quantity. Since it is strictly geometric in its origin, the inverse square law applies to diverse phenomena. Inverse law is obeyed by point sources of gravitational force, electric field, light, sound or radiation. n) Mass-luminosity relation This is an equation giving the relationship between the mass of a star and its luminosity. The relationship is represented by the equation: where Lβ and Mβ are the luminosity and mass of the Sun and 1 < a < 6. The value a = 3.5 is commonly used for mainsequence stars o) Mass-radius relation According to this law, if both the radius R and mass M of a main-sequence star are in solar units, then R = M 0.8. p) Nebular theory It is an explanation of how the solar system was formed. First developed in 18th century by Emanuel Swedenborg, Immanuel Kant, and Pierre-Simon Laplace, the Nebula Theory was first developed by Kant, then Laplace and later by astronomer Victor Safronov who built his nebular theory on Laplaceβs findings. Despite numerous challenges from numerous theorists, the attempt to replace it did not succeed. It was not until the 1970βs with Soviet that the modern (and widely accepted) Solar Nebular Disk Model (SNDM) came into being. Our solar system was formed 4.568 billion years ago when a small part of a giant molecular cloud experienced a gravitational collapse, according to the modern nebula theory. The Sun was formed by the collapsing mass collected in the center, while the rest of the material flattened into a protoplanetary disk, out of which the planets, moons, asteroids, and other small Solar System bodies formed. The Solar System has evolved considerably since its formation as a result of collisions between objects, planetary migration and the capturing of extra-solar objects by our own system. q) Olber's paradox Named after a German astronomer Heinrich Wilhelm Olbers, Olbers' paradox, also called the "dark night sky paradox", is the argument that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. r) Standard Solar Model The standard solar model (SSM) is the treatment of the Sun mathematically as a spherical ball of gas (in varying states of ionization, with the hydrogen in the deep interior being completely ionized plasma). s) 21-cm radiation 21-cm Line Radiation is the wavelength of the hyperfine transition of hydrogen. Most of the hydrogen gas in the interstellar medium is in cold atomic form or molecular form. In 1944 Hendrik van de Hulst predicted that the cold atomic hydrogen (H I) gas should emit a particular wavelength of radio energy from a slight energy change in the hydrogen atoms. It is useful in that when the 21cm radiation undergoes red-shifting, astronomers and scientist can judge distances very nicely, thanks to the hydrogen flip-flop.