General Astronomy - Lab Report Example

of Colorado at Denver Department of Physics Physics 1052 General Astronomy of the Experiment: Determining the Size of the Moon (Insert the date the experiment was conducted)Date of submission: (insert date)(Insert full names)The velocity of the earth using measured Doppler shift in spectrum of Arcturus star.ObjectivesTo determine the velocity of the earth using measured Doppler shift in spectrum of the star Arcturus.AbstractIt is possible to determine the orbital velocity of the earth by measuring the Doppler shift in a stellar spectrum.

The experiment utilizes the star Arcturus which is a bright star in the sky shinning a soft orange light in the northern spring skies. Arcturus is the best choice for this experiment because the earth revolves while moving towards and away from the star in its entire orbital period. Figure 1: The earth orbiting the sun and moving towards (b) and away (a) from Arcturus each half of its orbital life respectively. Equipment:i. A Transparent Ruler (with divisions at least as small as 1 mm)ii. A figure of two spectra of Arcturus (a and b) with reference lines 1 – 7 are shown above and below the spectra.

Procedure1. One line was selected from the figure of two spectra of Arcturus star as shown in the diagram below. The displacement of the line was then measured to a tenth of a millimeter. 2. The shifts on the diagram represented by filled rectangles were measured using a scale estimate to a tenth of a millimeter. Since viewing of the reading was a challenge a magnifying glass was used. The measurement made represented the shift Δ λ in mm of the line.3. The measurements were recorded in a table documented in the results.4. The same procedure was repeated for lines 1,,3,5,7 and the results documented.

Figure 2: Two spectra of Arcturus star as observed by Astronauts.Results and calculations.The table of obtained results from the measurements done.Line no.Original Wavelength Angstrom (Å)Shift Shift Vr = ( /cspectrum a ( mm)Spectrum b (mm)spectrum a (Å)Spectrum b (Å)spectrum a spectrum b 14260.48396.80393.30 936.49991.12 65,942.5765,942.5724271.16 396.90393.40 936.68991.37 65,791.0369,622.5934271.76 398.10394.10 939.52993.13 65,981.2369,746.1944282.41 410.00402.41 967.601014.07 67,784.2671,039.6754294,13413.20407.12974.681025.9468,093.8971,675.0564299.34415.50410.16980.581033.6068423.0672,122.7074307.91417.10412.34984.361039.1068550.1872,362.24The measurement obtained are in mm and 1 Angstrom (Å) = 10-10 m.

Conversion Factor (CF) =Thus for spectrum a, CF= =2.36angstrongs/millimeterAlso the CF for spectrum b, CF= =2.52 angstroms/millimeterRelative velocity that exists between the star and the earth is given by, Thus for spectrum a, relative velocity, =62,942.

57Km/sWhile for spectrum b, =65,942.57Km/sThen the average relative velocity of red-shift =67,223.75Km/sAnd for the blue-shift = -70,501.57Km/sSteps for obtaining the formula of velocity of the earth;Using the given formulae for the relative velocities of red-shift and that of blue-shift We start by making the subject of the formula in each case, then we have, also Equating the two, we have = =68862.

66Km/sBy assuming that Arcturus lies on latitude of 310, then the true =59,221.32Km/sConclusion The Earth orbits around the sun at a speed of 29.77Km/s (Glenn), the calculated value (59221.32Km/s) is almost twice the actual value because of parallax, sensitivity of the equipment used, light source and the approximation of values while recording in the table. Works CitedGlenn, Elert. "Speed of the Earth in Orbit.

" 27 March 2013. www.hypertextbook.com. 27 March 2013 .physicsrutgers. Sizes and Distance and the Small Angle Approximation. 09 November 2000. 26 February 2013 .