Astronomy 106

Mathematical Formulae

Wednesday, Jan. 13, 1999

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 Foundations Astronomy 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 Foundations Astronomy 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 602)
   
2. Significant figures
   
3. Units, dimensions and conversions(Page 602) (Problems 1-3,1-4,8-5,8-6)
   
4. Velocity, Distance and Time (Problems 1-2,12-3,14-3,16-3,16-9) 
   
5. Stellar Magnitudes(Page 13)(Problems 2-1,2-3,2-6,2-7,18-6)
   
6. Angular Measurements (Page 18)
   
7. Small-angle formula (Page 42)(Problems 4-3,4-4,8-2,8-3,11-1,13-5,14-2,14-8,15-6,16-7)
   
8. Kepler's Third Law (Page 72) (Problems 4-5,4-7)
   
9. Acceleration (Page 79) (Problem 5-2)
   
10. Orbital Velocity (Page 84) (Problems 5-3,5-4,15-8)
    
11. Escape velocity (Page 86) (Problems 5-7,15-5,17-6)
    
12. Wavelength-Frequency Relationship (Page 99)
    
13. Resolving power of a telescope(Page 108) (Problems 6-5,6-7)
    
14. Stefan-Boltzmann Law (Page 126) (Problem 7-5)
    
15. Wien's Law (Page 127) (Problems 7-1,7-3,11-2,12-10,15-7,19-3)
    
16. Doppler Effect(Page 140) (Problem 7-9)
    
17. Density and Volume (Page 143) (Problems 11-7,12-9,13-6,13-8)
    
18. Parallax (Page 170) (Problems 9-1,9-2)
    
19. Magnitude-Distance Formula (Page 173) (Problems 9-3,9-5,17-3)
    
20. Luminosity, Radius and Temperature(Page 175) (Problem 12-4)
    
21. Masses of Binary Stars(Page 189) (Problem 10-2)
    
22. Mass-Luminosity Relation((Page 200) (Problem 10-11)
    
23. Einstein's Mass-Energy Formula(Page 227) (Problems 12-6,12-8,18-1)
    
24. Life Expectancies of Stars(Page 247) (Problems 13-2,13-3,13-7,14-1)
    
25. The Hubble Law(Page 344) (Problem 17-7)
    
26. The Hubble Time(Page 395) (Problem 19-5)
    

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