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SMA Negeri 1 Lemahabang2016 Astronomy Olympiad Practice

An Introduction to CosmologyBy Maman Rukmana1What is the Cosmology?In cosmology, we will learn about:Einsteins RelativityUniverseHubbles LawModel of Universe

Einsteins RelativityThe first is Special RelativityThat the light velocity is constant. So, if we move nearest with light velocity, we can have time dilatation.

The second is General RelativityThat the gravitational force is curve of space and time, not a attract between two things.3The show that Einsteins Relativity theory are:Presition of Mercurys orbitCurve the light by gravitational filedGravitational redshiftMuon particle in atmosphereThe show that Einstein Relativity4Lorentz TransformationAssume a vector in r = xi + yj + kz. And assume an observation in K calculate the event at t. In the assume, we can find the four dimension coordinate. All points are space-time.If other observation is K, two coordinate is different but the space-time coordinate is representstive same place and time.That statement is a tranformation concept, are the arrangement that relation two coordinate (x, y, z) and (x, y, z).

5Long contraction is:Long Contraction and Time Dilatation

Time dilatation is:6Big Bang TheoryUniverse was created from big bang which flung many matter to all space.Cosmolog: Georges Lemaitre, Albert Einstein, Alexander Friedmann and Stephen HawkingStart of Universe

7Steady State TheoryUniverse not start and not end, but in steady state with expansion by constant velocity and create the new matter where that matter as galaxies.Cosmolog: Fred Hoyle, Herman Bondi and Thomas Gold8Radial velocity for sky object which keepa away from us is approximately with distanceRelation Vr = H0 dWhere: Vr = radial velocity (km/s)H0 = Hubbles Constant (km/s/Mpc)d= distance to us (Mpc)

Hubbles Law9Find Radial Velocity (Spectroscopy)In spectrum of sky object (0), object that keep away from us, will show the redshift

So:Vr = z cwhere c is light velocity (3 x 105 km/s)But, for relativity:

10Hubbles ConstantHubbles Constant is a constant which show a parameter of age universe, is young or old.With the time is not stop, value of Hubbles Constant is to smallWhy?Analysis with your argument!Model of UniverseIn cosmology, model of universe are:Single componentMultiple componentHow the model of universe by simple and multiple component?Read and learn together!

Single ComponentAccording single component, model of universe are:Curvature onlySpatially flat universeMatter onlyRadiation onlyLambda onlyCurvature onlyA particularly simple universe is one which is empty (no radiation, no matter, no cosmological constant, no contribution to of any sort).Relation:

Splatially flat universeSetting the energy density equal to zero is one way of simplifying the Friedmann equation.Relationa:

In a flat universe dominated by matter (w = 0) or by radiation (w = 1=3).15Matter onlyLet's now look at specific examples of spatially flat universes, starting with a universe containing only non-relativistic matter (w = 0). The age of such a universe isand the horizon distance is

Radiation onlyThus, at early times - long before the time of radiation matter equality - the universe was well described by a spatially flat, radiationonlymodel. In an expanding, flat universe containing only radiation, the age of the universe isand the horizon distance isLambda onlyIn a Steady State universe, the density of the universe remains constant because of the continuous creation of real particles. If, in a flat, lambda-only universe, you see a light source with a redshift z, the proper distance to the light source, at the time you observe it, is (upper panel)

And lower panelMultiple componentAccording multiple component, model of universer are:Matter + CurvatureMatter + LambdaMatter + Curvature + LambdaRadiation + MatterBenchmark Model

Matter + CurvatureIn a curved universe containing nothing but matter, the ultimate fate of the cosmos is intimately linked to the density parameter 0. The Friedmann equation in a curved and matter:Given this parametric form, it is easy to show that the time that elapses between the Big Bang at = 0 and the Big Crunch at = 2 is

Matter + Lambda

and will collapse back down to a = 0 at a cosmic timeThe Friedmann equation for the flat matter plus lambda" universe reduces toMatter + Curvature + Lambda

By choosing different values of m,0 and ,0, without constraining the universe to be at, we can create model universes with scale factors a(t) which exhibit very interesting behavior. Start by writing down the Friedmann equation for a curved universe with both matter and a cosmological constant:

Radiation + Matter

In our universe, radiation-matter equality took place at a scale factor arm = 2,8 x 10-4. The Friedmann equation around the time of radiation-matter equality can be written in the approximate form

The time of radiation-matter equality, trm, can be found by setting a = arm in equation

Benchmark Model

Large-Scale Structure of the Universe

25ExampleIn this table is date of a objec from the universe.

With date of the table, estimate age of universe for:Flat OnlyMatter OnlyRadiation Only

ObjectRedshiftDistance (Mpc)Galaxy5.74000Supernova Ia5.94250Quasar6.24500Hypernova6.45000AnswerRedshift Distance (Mpc) VrHoHo-H(Ho-H)^25.7400028692571.731316.37968240.70034685.9425028765767.683972.3323365.439789196.2450028864564.14333-1.208311.460003156.4500028924057.84792-7.5037156.3056939AVERAGE Ho65.3516SUM (Ho-H)^2103.905833STANDARD DEVIATION5.096710535HUBBLE CONSTANT65.35 +- 5.1Assume the Hubble constant is 65,35 km/s/Mpc. Flat onlyt = 1/H = 1 / (65,35 km/s/Mpc) = 3,086 x 1019 / 65,35 = 19, 34 Billion YearsMatter onlyt = 2/3H = 2 / 3 (65,35 km/s/Mpc) = 2 * 3,086 x 1019 / 3 * 65,35 = 12,89 Billion YearsRadiation onlyt = 1/2H = 1 / 2 (65,35 km/s/Mpc) = 3,086 x 1019 / 2 * 65,35 = 9,67 Billion Years

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