# Lab 11_Rotation Curves, Mass Distribution, and Dark Matter_2013.pdf

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Rowan Introduction to AstronomyLab 11 / Rotation Curves, Mass Distribution,and Dark MatterName:________________________________________________Score:____________________SummaryIn this exercise, you will compare the mass distribution found in the solar system with thatfound in galaxies.BackgroundMost astronomers are convinced that there is matter in the universe which we have neverseen because it is dark and does not emit or reflect light. It appears that over 90% of thematter in the universe may be dark matter. The existence of this dark matter has hugeimplications for the future of the universe.Whether the universe continues to expand indefinitely (becoming less and less dense, andcolder and colder) or starts contracting again as the force of gravity pulls the masses in theuniverse back together depends on how dense the universe is. Current research indicates thatthere is not enough dark matter plus regular matter to halt indefinite expansion. Our currentknowledge of dark matter comes from its gravitational effect on regular matter.Part 1: Orbital Speeds of the Planets in the Solar System [27 pts total]Procedure [Note rounding instructions!]Though the orbits of the eight planets are ellipses, the orbital paths have rather low eccentricities. In other words, their orbits are fairlyclose approximations of a circle. We can calculate the length of a circular orbital path using the simple formula for the circumferenceof a circle:r, whereris the radius or, in the case of the solar system, the average distance from the planet to the Sun.1.Using the radius of orbit data in column 3 (see table below), calculate the length of each planet’s orbitand place in column 4.(Round each answer to2decimal places.)*Express in appropriate scientific notationNext, calculate the number of seconds in a year (use 3 decimal places and scientific notation): ______________________________PlanetMass(kg)Radius of orbit(×108km)Length of Orbit(×108km)Orbital PeriodOrbital Period(s)*Orbital Speed(km/s)Mercury3.3×10230.5887.969 days =0.2408 yearVenus4.9×10241.08224.700 days =0.6152 yearEarth6.0×10241.50365.25 days =1.0 yearMars6.4×10232.28686.971 days =1.8808 yearsJupiter1.9×10277.7911.859 yearsSaturn5.7×102614.3329.457 yearsUranus8.7×102528.7784.323 yearsNeptune1.0×102645.03164.79 yearsGravitational lens created by a galaxy clusterreveals the presence of dark matter. (NASA)
Lab 11 / Rotation Curves, Mass Distribution, and Dark Matter22.For column 5, convert the orbital periods in years to seconds. Write those values in column 6. (Round answers to 2 decimalplaces and use scientific notation.)3.Finally, calculate the orbital speed by dividing the length of orbit (km) by the orbital period (s). Your answers go in column 7 andwill be in km/s. (Express as regular numbers round to 2 decimal places).[Table is worth 12 pts]4.Go toand check each planet’s listed orbital speed (see data box to the right under “Orbital Characteristics”)against your calculated speed. Do any of the listed values differ from your calculated ones by more than 1%?[1 pt]yesnoIf “yes,”

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