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Astronomy 105

Mathematical Formulae

Wednesday, Aug. 27, 1997

Mathematics is an essential part of astronomy. Many relationships between properties of stars, distances, sizes, temperatures, etc. can be expressed accurately and concisely in terms of a mathematical formula. Although the material covered in this course is primarily descriptive and non-mathematical, problem solving and the use of appropriate mathematical formulae is a very important part of the course. It is expected that each student will become adept at solving problems and will demonstrate his ability both in the homework assignments listed in the syllabus and on the examinations.

The mathematics in Astronomy Today is usually explained well in the text, but the formulae are scattered throughout the book. On these pages, I have attempted to consolidate the mathematics you will need in the course and to give a brief explanation about how each formula is used and if appropriate, derived. I have also listed the page in Astronomy Today on which each formula initially appears as well as the homework problems which depend on each of the equations.

We will be referring to this handout throughout the class. By the end of the course, you will all be familiar with each of the equations listed here.

  1. Scientific notation (Page 8) (Problem 1-3)
  2. Significant figures
  3. Units, dimensions and conversions
  4. Speed of light (Page 58) (Problems 1-1,2-1,6-2,8-1,13-4)
  5. Velocity, Distance and Time (Problems 1-1,1-2,2-1,6-2,7-3,7-4,8-1,9-3,12-1,13-4,16-2) 
  6. Angular Measurements (Page 14)(Problems 1-2, Additional Problem Set 9)
  7. Basic Trigonometry (Page 22)(Problem 1-4)
  8. Parallax (Page 24) (Problems 1-5,10-4)
  9. Small-angle formula (Problems 1-6,5-4,8-5,9-2,11-4,13-2,Additional Problem Set 10)
  10. Kepler's Third Law (Pages 42,48) (Problem 2-3)
  11. Newton's Law of Gravitation (Page 45) (Problems 2-4,8-4,10-1,11-1,12-4, 14-1)
  12. Wavelength-Frequency Relationship (Page 56) (Problem 3-1,4-1)
  13. Inverse Square Law (Page 67) (Additional Problem, Set 2, Problems 10-3, 13-1)
  14. Photon Energy and Wavelength (page 79) (Problem 4-2)
  15. Light Gathering Power (Page 101) (Problem 5-1)
  16. Resolving power of a telescope (102) (Problem 5-2)
  17. Density and Volume (Page 131) (Problems 6-1,7-1,9-1,12-2, Additional Problem Set 10)
  18. Escape velocity (Page 136) (Problem 6-3, Additional Problem Set 8)
  19. Orbital Angular Momentum (Problem 15-1)




Hans Krimm
Tue Aug 19 14:55:05 EDT 1997