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  • 1
    UID:
    gbv_1772251267
    Format: 1 Online-Ressource (XIII, 316 Seiten)
    ISBN: 9783030782672
    Content: This book shows readers how to calculate the orbit of Mars, based on their own observations and using observations made by the author. The historical, observational, and analytical aspects of the project to measure the orbit of Mars are all combined in this one book! Determining the orbit of Mars is particularly important, as originally solving this problem required the founding of modern science. Clark discusses how people came to believe in the Newtonian model of the Solar System, works through the mathematical basis for the theory of gravity, and shows how Newton ruled out the possibility of alternative theories. Readers also learn how it became possible to accurately measure the positions of Mars from a moving, spinning platform—the Earth. This mid-level observational challenge is well within reach of most serious amateur astronomers. For the observations, only a telescope with auto-guiding capability and the ability to mount a digital single lens reflex (DSLR) camera is required. For the calculations, it is assumed that the reader has a science, engineering, or mathematics background and is familiar with calculus, vectors, and trigonometry.
    Note: Chapter 1: Introduction -- Chapter 2. From Eve to Newton: Doubtful Legends about Knowledge from an Apple -- Chapter 3: Weighing the earth with a pendulum -- Chapter 4: Solving an Equation without Moving your Ellipse -- Chapter 5: Where’d the Earth Go? -- Chapter 6: You Don’t Take a Photograph: You Make It -- Chapter 7: Do you see what I see? A Planet, a Planet, Dancing in the Night -- Chapter 8: Without Data, You’re Just another Person with an Opinion -- Chapter 9: Finally we get around to the Answer. .
    Additional Edition: ISBN 9783030782665
    Additional Edition: ISBN 9783030782689
    Language: English
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Online Resource
    Online Resource
    Cham :Springer International Publishing :
    UID:
    almahu_9949176745702882
    Format: XIII, 316 p. 153 illus., 93 illus. in color. , online resource.
    Edition: 1st ed. 2021.
    ISBN: 9783030782672
    Content: This book shows readers how to calculate the orbit of Mars, based on their own observations and using observations made by the author. The historical, observational, and analytical aspects of the project to measure the orbit of Mars are all combined in this one book! Determining the orbit of Mars is particularly important, as originally solving this problem required the founding of modern science. Clark discusses how people came to believe in the Newtonian model of the Solar System, works through the mathematical basis for the theory of gravity, and shows how Newton ruled out the possibility of alternative theories. Readers also learn how it became possible to accurately measure the positions of Mars from a moving, spinning platform-the Earth. This mid-level observational challenge is well within reach of most serious amateur astronomers. For the observations, only a telescope with auto-guiding capability and the ability to mount a digital single lens reflex (DSLR) camera is required. For the calculations, it is assumed that the reader has a science, engineering, or mathematics background and is familiar with calculus, vectors, and trigonometry.
    Note: Chapter 1: Introduction -- Chapter 2. From Eve to Newton: Doubtful Legends about Knowledge from an Apple -- Chapter 3: Weighing the earth with a pendulum -- Chapter 4: Solving an Equation without Moving your Ellipse -- Chapter 5: Where'd the Earth Go? -- Chapter 6: You Don't Take a Photograph: You Make It -- Chapter 7: Do you see what I see? A Planet, a Planet, Dancing in the Night -- Chapter 8: Without Data, You're Just another Person with an Opinion -- Chapter 9: Finally we get around to the Answer. .
    In: Springer Nature eBook
    Additional Edition: Printed edition: ISBN 9783030782665
    Additional Edition: Printed edition: ISBN 9783030782689
    Language: English
    Library Location Call Number Volume/Issue/Year Availability
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  • 3
    Online Resource
    Online Resource
    Cham, Switzerland :Springer International Publishing,
    UID:
    almafu_9960011502502883
    Format: 1 online resource (319 pages)
    ISBN: 3-030-78267-0
    Note: Intro -- Preface -- Acknowledgements -- Contents -- About the Author -- Chapter 1: In the Beginning -- Ptolemy's Model: Salient Features -- The Copernican Revolution: The Pun That Keeps oving -- Tycho Brahe, the Greatest Pre-telescope Observer -- Tycho and Mathematics -- Tycho's Instruments -- Galileo - Telescopes and Free Fall -- Free Fall and Motion -- The Telescope Bursts onto the Scene -- Encounter with the Inquisition -- Chapter 2: Read My Ellipses -- Kepler -- Ellipses -- Chapter 3: The Behaviour of Two Bodies in Orbit -- Christiaan Huyghens (1629-1695) -- Sir Isaac Newton (1642-1727): The Great Synthesizer -- Universal Gravitation -- Gravity Due to Point Masses and Spheres -- Angular Momentum and Its Implications -- The Bit Where Conic Sections Come In -- Time Evolution -- A Brief Aside: the Word Anomaly -- The Moon: A Challenge for Newtonian Physics -- Canonical Units -- Energy -- The Orbit Tells Us What the Force Law Is -- Chapter 4: Least Squares Fit to Sets of Equations -- Least Squares Fitting Subroutine -- Chapter 5: The Orbit of the Earth -- Sunny Side Down, Please -- From Solar Midday to Orbit -- Sorting Out Some Definitions -- Further Geometric Gymnastics with Ellipses -- Tilting My Lance at Obliquity -- Getting Around to Earth's Orbit -- Chapter 6: Here's Looking at You, Mars! -- Equipment -- Guiding -- Photographic Technique -- How I Made Measurements from Pictures Like Fig. 6.7 -- How to Obtain the Position of Mars from the Star Positios -- Main Program -- Angle Unit Changing Subroutines -- Least Squares Fitting Subroutine LSQFIT Has to Be Added -- Distance Unit Changing Subroutines -- Results -- The 2009-2010 Apparition of Mars -- Later Observing Campaigns -- Data from 2011 to 2012 (Table 6.5 and Fig. 6.31) -- Data from 2020 (Table 6.6 and Fig. 6.32) -- Chapter 7: First Shot at the Orbit of Mars. , Non-coplanar Orbits Facing in Random Directions -- Rotations -- What These Angles Are Used for -- Herget's Method -- Lagrange's f and g Functions -- The Sector-Triangle Ratio -- Introduction of Kepler's Equation -- Solution of Eqs. (7.89), (7.101) and (7.104) -- Solving Eq. (7.1) with Known Magnitude but Unknown Direction of Sun-Planet Distance -- Eureka! (Part One) -- Obtaining the Orbital Elements from Two Radius Vectors -- Software Listing -- Main Program -- Calculate Ascending Node -- Convert Observation Times to Canonical Units -- Use Escobal's Methods to Calculate Various Quantities -- Use Methods Given Above to Calculate the Longitude and Passage Time of Perihelion -- This Is Basically the Subroutine Described in Chap. 4 -- Eureka! (Part Two) -- Chapter 8: Refining the Preliminary Orbit -- Least-Squares Curve Fitting -- Gambling on Monte Carlo -- Monte Carlo Source Code -- Manual Adjustment of Orbits -- Using Knowledge of the 2020 Opposition -- Conclusions Drawn -- Da Capo al Fine: Can I Fit Tycho's Data? -- How Well Did I Do? -- Appendix 1: Parabolas and Hyperbolas -- Deriving the Equation of a Hyperbola in Polar Coordinates -- Deriving the Equation of a Parabola in Polar Coordinates -- Appendix 2: Multiplying Three Vectors -- Appendix 3: Proof of Trigonometric Addition Formulae for All Angles -- References -- Index.
    Additional Edition: ISBN 3-030-78266-2
    Language: English
    Library Location Call Number Volume/Issue/Year Availability
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