By Jean Meeus

Acknowledged in book," almost each prior instruction manual on celestial calcuations used to be compelled to depend upon formaulae for solar Moon and planets that have been constructed within the final century or earlier than 1920. along with his specific knack for computations of every kind, the writer has made the fundamental of those glossy suggestions to be had to us all.

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**Example text**

Writing this relationship as an equation with the proportionality constant “s,” and comparing two different spheres (say, sphere 1 and 2) by dividing equations gives 3 s R23 V2 ✁s R2 = = = 3 V1 s R13 ✁s R1 R2 R1 3 . Since you know that one of the spheres (say, sphere 2) has a radius five times the other, you can use the mathematical substitution R2 = 5R1 . Plugging 5R1 in for R2 in the expression above and simplifying gives V2 = V1 5✚ R✚ 1 R✚ 1 ✚ 3 = 5 1 3 = 53 = 125. That is, a sphere with five times larger radius has 125 times larger volume.

This will minimize the build-up of rounding errors during multi-step calculations. 5 × 1017 seconds (the remaining lifetime of our Sun) in years. 8 m/s2 . Convert this number to ft/s2 and miles/hr2 . 3 It takes you 40 minutes to walk 2 miles to work. What is your average speed in miles per hour? Explain how you know your answer makes sense. 4 We communicate with spacecraft using radio wavelengths of light, which travel at speed c = 3 × 108 m/s. The distance between Earth and Mars varies between 56 million and 400 million kilometers.

2 × 100 . 3 Numbers as words If you were to read in an astronomy book that there are three hundred billion stars in our Milky Way galaxy, how can you make sense of that number? Certainly, if you need to do any calculations with numbers given in this format, you must be able to translate between words, decimal notation, and scientific 34 Fundamentals notation. Here’s a table of some of the words describing large numbers that come up in astronomy: Words Decimal notation Scientific notation Thousand Million Billion Trillion Quadrillion 1,000 1,000,000 1,000,000,000 1,000,000,000,000 1,000,000,000,000,000 103 106 109 1012 1015 Example: Write three hundred billion in scientific and decimal notation.