Measure Solar System Objects and Their Movements for Yourself! (eBook)

John Clark holds a Bachelor of Science, first class honors, in Physics, from London University, England, and a Ph. D. in Physics from Warwick University, England. He is a Fellow of the Institute of Physics, and spent two years as a post-doctoral researcher at Case Western Reserve University in the USA. Currently he is Managing Director of Fine R and D Limited. He has been an active amateur astronomer for many years.

Preface 5
Acknowledgments 9
Contents 11
About the Author 14
1: How Do We Know That Venus Orbits The Sun? 15
Circular Motion 18
Newton's Law of Gravity 23
Application to Circular Orbits 23
Back to Venus and the Earth 24
How to Predict the Greatest Western Elongation Date 25
Checking the Date of Greatest Western Elongation 28
Alternative Hypothesis: Venus Orbits Earth 30
When Can You Try This for Yourself? 33
Conclusion 33
2: How Big is the Earth? 35
Ways to Measure the Earth's Size 35
What Johnny Did Next 35
Conclusion 41
3: How Far Away and How Big is the Moon? 42
First Attempt 42
Calculations Using no more than High School Mathematics 44
Advanced Topic: A Sphere Attracts Like a Point Mass 50
Second Experiment 54
Extracting the Moon's Speed in Radii per Second Using only High School Mathematics 58
Extracting the Moon's Speed in Radii per Second Using Some College Mathematics 59
How to Create Axes Parallel to Lunar Motion Mathematically 62
Back to the Diameter Calculation: College Mathematics no Longer Required 64
Discussion of Quality of Results 64
Random Errors (Scatter) in Data of Figs. 3.14 and 3.15 64
The Moon's Orbit is Really Elliptical 65
The Telescope is not at Earth's Center 65
The Earth-Moon Center of Mass is not at the Center of the Earth 65
Whiteout due to Photographic Overexposure Makes Moon's Surface Uncertain 66
Variation of Earth's Radius and Gravitational Acceleration 68
Combination of Uncertainties 68
4: Jupiter's Moons: Where You Can Watch Gravity Do Its Thing 70
Why the Jovian System is a Good `Gravity Laboratory´ 70
My Equipment 71
Observing in the Rain (Well, Almost) 71
Measuring Angular Separations on Photos 74
Making Sense of the Moon's Positions 79
Other Jupiter Projects You Could Try 91
Conclusion 93
5: Sunrise, Sunset 94
A Mars Day for Work, Rest, and Play 95
The Celestial Sphere 100
Three-Dimensional Coordinates 103
Let Now the Sun Go Down Along Its Path 103
phiv Noon 104
On the theta Front 106
Conclusion 109
6: Getting Further from the Sun: How do you Ride an Epicycle? 110
Photography 111
Astrometry: Getting Data from Photographs 114
Actually Doing the Triangulation 121
Three-Dimensional Coordinates 122
Epicycles 133
Conclusion 138
7: Size Matters 139
AppendixA: Appendix A: Geometrical Appendix: Geometry for Those Who Have Forgotten 145
Basic Trigonometry 145
What Happens if A is bigger than 90? 147
Angular Units 147
Coordinate Systems 147
Proof of Coordinate Transform Formulae 147
Vectors: A Way of Simplifying Geometry 156
AppendixB: Appendix B: Statistical Appendix 162
Probability 163
A Measurement that Fluctuates 164
All Distributions Tend Toward a Normal Distribution 171
What Happens When I Can Only Make One Measurement per Observation of a Moving Body? 175