Liam Nolan, M. Mechtley, R. Windhorst, K. Knierman, T. Ashcraft, S. Cohen, S. Tompkins, L. Will
{"title":"Interactive cosmology visualization using the Hubble UltraDeep Field data in the classroom","authors":"Liam Nolan, M. Mechtley, R. Windhorst, K. Knierman, T. Ashcraft, S. Cohen, S. Tompkins, L. Will","doi":"10.32374/aej.2021.1.1.003","DOIUrl":"https://doi.org/10.32374/aej.2021.1.1.003","url":null,"abstract":"We have developed a Java-based teaching tool, \"Appreciating Hubble at Hyper-speed\" (\"AHaH\"), intended for use by students and instructors in beginning astronomy and cosmology courses, which we have made available online. This tool lets the user hypothetically traverse the Hubble Ultra Deep Field (HUDF) in three dimensions at over 500x10^12 times the speed of light, from redshifts z=0 today to z=6, about 1 Gyr after the Big Bang. Users may also view the Universe in various cosmology configurations and two different geometry modes - standard geometry that includes expansion of the Universe, and a static pseudo-Euclidean geometry for comparison. In this paper we detail the mathematical formulae underlying the functions of this Java application, and provide justification for the use of these particular formulae. These include the manner in which the angular sizes of objects are calculated in various cosmologies, as well as how the application's coordinate system is defined in relativistically expanding cosmologies. We also briefly discuss the methods used to select and prepare the images in the application, the data used to measure the redshifts of the galaxies, and the qualitative implications of the visualization - that is, what exactly users see when they \"move\" the virtual telescope through the simulation. Finally, we conduct a study of the effectiveness in this teaching tool in the classroom, the results of which show the efficacy of the tool, with over 90% approval by students, and provide justification for its further use in a classroom setting.","PeriodicalId":424141,"journal":{"name":"Astronomy Education Journal","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127559420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Historical Method Approach to Teaching Kepler’s 2nd law","authors":"W. Lyra","doi":"10.35542/osf.io/a5bqn","DOIUrl":"https://doi.org/10.35542/osf.io/a5bqn","url":null,"abstract":"Kepler’s 2nd law, the law of the areas, is usually taught in passing, between the 1st and the 3rd laws, to be explained “later on” as a consequence of angular momentum conservation. The 1st and 3rd laws receive the bulk of attention; the 1st law because of the paradigm-shift significance in overhauling the previous circular models with epicycles of both Ptolemy and Copernicus, the 3rd because of its convenience to the standard curriculum in having a simple mathematical statement that allows for quantitative homework assignments and exams. In this work I advance a method for teaching the 2nd law that combines the paradigm-shift significance of the 1st and the mathematical proclivity of the 3rd. The approach is rooted in the historical method, indeed, placed in its historical context, Kepler’s 2nd is as revolutionary as the 1st: as the 1st law does away with the epicycle, the 2nd law does away with the equant. This way of teaching the 2nd law also formulates the “time=area” statement quantitatively, in the way of Kepler’s equation, M = E – e sin E, (relating mean anomaly M, eccentric anomaly E, and eccentricity e), where the left-hand side is time and the right-hand side is area. In doing so, it naturally paves the way to finishing the module with an active learning computational exercise, for instance, to calculate the timing and location of Mars’ next opposition. This method is partially based on Kepler’s original thought, and should thus best be applied to research-oriented students, such as junior and senior physics/astronomy undergraduates, or graduate students.","PeriodicalId":424141,"journal":{"name":"Astronomy Education Journal","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127697964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}