Materials and MethodsResults/DiscussionMagnificationConclusionReferences7. Starry Night ManualAcknowledgementsAPPENDIXEunha JinFall 2002Determining the Sidereal Rotational Period of MarsIntroductionThe seemingly periodic motion of the planets and the stars captivated the interestof humans throughout history. There was a pursuit to explain the observed phenomena,the motions of celestial objects, by proposing various models –e.g. the heliocentric modelof the solar system. The planet Mars was recognized by Babylonians, Egyptians, andGreeks as a celestial body of curiosity.1 The planet’s motion is normally from east towest. However during the planet’s opposition, the Mars appears to retrograde. Despitehistorical pursuits to explain the motions of stars and planets, the study of a planet’sdiurnal motion upon its axis could not be thoroughly investigated until the advent of thetelescope. In 1781, William Herschel, a German born musician, published a treatise on theAstronomical observation on the Rotation of the Planets round their Axes, mad with aView to determine whether the Earth’s diurnal Motion is perfectly equable. His work wasa first attempt to accurately measure the axial rotation of planets, or more specifically,that of Mars. Herschel determined the rotational period of Mars to be 24 h 39 min 21.67 sutilizing a 20ft. Newtonian Reflector telescope.2 In 1830, Beer and Madler determined theMartian rotational period to be 24 h 37 min 23.7 s, which is very close to the currentlyaccepted value.3,4 Hershel’s method to determine the period of rotation of Mars involvedthe observation of the planet by monthly intervals. By accounting for the number ofrotations and the time it takes from the start of the rotation and the designated end of aseries of revolutions reduces the error introduced by not accurately observing a full 360revolution. The resulting synodic rotation period, or the rotation period measured relativeto earth, was subsequently converted to its sidereal rotation by adjusting the value to therelative geocentric positions of each planet. In the present study, Herschel’s methods will be utilized to evaluate the feasibilityof measuring the sidereal rotation of Mars to the significant figures that were historicallyreported. More specifically, computer simulations that mimic Herschel’s experimentalconditions will be attempted to determine the sidereal rotation of Mars to the second. Materials and MethodsGeneral. All computer simulations were done by Starry Night Pro.Simulation Parameters. Mars was observed from Bath, England (Latitude: 2 21’ 45”West, Longitude: 51 22’ 12” North). The times observed were at various nights betweenthe years 1777-1779, The field of view (FOV) was set to 0° 15’. The computer simulationkept the time measurements. *Results/DiscussionCertain key discrepancies between Hershel’s experimental conditions and thoseoutlined within this investigation must be acknowledged for determining the siderealrotation of mars. The most obvious point is that this study was pursued by computersimulation, which results in certain implications. Firstly, weather and atmosphericconditions would not impede on the ascertainment of experimental results. Since atelescope was not utilized for observation**, lens aberrations and the logistics oftelescopic techniques can be altogether ignored. Furthermore, there is a set limit at which* Herschel utilized a pendulum based clock.** Mars remain below the horizon during observation times between the months of October to December.Martian surface features can be seen by simulation, and all surface features observed inthe simulations are permanent. Thus, the concern of whether or not an observed feature ispermanent is eliminated. Therefore, the observational parameters set by the simulationsurpass the class of telescopes that Herschel used because Martian features must be seento determine the rotation period.Herschel used several different types of telescopes for his observations. However,the specifics of his 20 ft Newtonian Reflector power 300 (see Appendix I) will beevaluated and simulated to fully understand the observational conditions from which hederived his results. Table 1 summarizes the specifications of Hershel’s 20 ft NewtonianReflector. The key objective for calculating the actual specifications is to derive the FOVvalue for his telescope, as shown in Fig. 1. This value is a necessary parameter for StarryNight Pro to make observations. Once again, the FOV value set for this experimentalwas different because surface features could not be distinguished as shown in Fig. 1.Table 1. The Specifications of Herschel’s Telescope.5,***Magnification ObjectiveDiameterin mm.LightgatheringpowerResolvingPower, inseconds of arcFOV20ft NewtonianReflector40 138 300 0.84 1° 09’ExperimentalParameter_ - - -0° 15’Table 2. Relative Resolving Powers between Telescopes.Type Resolving*** See Appendix I for calculations.Power, inseconds of arc1 in. 4.5Herschel’s 0.846 in. 0.76Hubble 0.05The resolving power is a measure of how well the telescope can capture finedetail of astronomical features.6 Thus, the telescopes magnification is not as essential asits ability to resolve objects. In Table 2, the relative resolving powers of varioustelescopes have been reported. Consequently, Herschel’s telescope can be considered tobe the modern equivalent of a good amateur telescope.**** Fig. 1 Simulated observation of Mars with Fig.2 Simulated observation of Mars with Herschel’s 20ft Newtonian Reflector from experimental parameters from Bath, England.Bath, England. Time: April 8, 1777 9:30 pm Time: April 8, 1777 9:30 pm. FOV= 0° 15’FOV= 1° 09’ The image of Mars portrayed in Fig. 1 would have been analogous to whatHershel had observed. It is evident that observing surface features with a FOV of 1° 09’ ismarkedly more difficult than one with a FOV of 0° 15’ (Fig.2). Nevertheless, the Martiansurface features appear too simplified, exhibiting no color gradient presumably becauseof pixelation limits within the program, to identify a good marker to signify a fullrevolution. These are also images of his preliminary observations done by Herschel tobecome familiar with the planet in search for permanent surface features to be