A Student's Guide to the Mathematics of Astronomy by Daniel Fleisch, Julia Kregenow

By Daniel Fleisch, Julia Kregenow

The learn of astronomy deals an enormous chance for us to realize a deeper realizing of our planet, the sunlight procedure, the Milky means Galaxy and the recognized Universe. utilizing the plain-language procedure that has confirmed hugely renowned in Fleisch's different Student's courses, this ebook is perfect for non-science majors taking introductory astronomy classes. The authors deal with themes that scholars locate so much difficult, on matters starting from stars and light-weight to gravity and black holes. Dozens of absolutely labored examples and over a hundred and fifty workouts and homework difficulties support readers familiarize yourself with the recommendations in every one bankruptcy. An accompanying web site encompasses a host of helping fabrics, together with interactive options for each workout and challenge within the textual content and a chain of video podcasts within which the authors clarify the real thoughts of each component to the publication.

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But if it’s been a few years since you’ve encountered scientific notation, or if you have any doubt at all about the difference between 6 × 10−3 and −6 × 103 , or how to calculate (8 × 107 )/(2 × 1012 ) in your head, this section may be helpful for you. 67 × 10−11 . 3, each of these expressions consists of three numbers called the coefficient, the base, and the exponent. The standard base for scientific notation is 10. Exponents are usually integers and can be positive or negative. The coefficient can be any number at all.

Ultraviolet light has a frequency that is about one hundred times that of infrared light. Which has a larger wavelength, and by how many times? 13. If one moon orbits at a certain distance from its planet, and another moon orbits three times farther from the same planet, compare the planet’s force of gravity on the closer moon to the planet’s force of gravity on the farther moon. 3 Rate problems In many science classes, you may be asked to calculate things such as how long it takes to travel a certain distance at a fixed speed, or how long a star will live if it burns its fuel at a certain rate.

So if you want to multiply 2 × 104 by 4 × 103 , you can just multiply the coefficients (2 × 4 = 8) and add the exponents (4 + 3 = 7) to get the correct result of 8 × 107 . To see why this works, you can write the numbers out in decimal notation: (2 × 104 ) × (4 × 103 ) = (20,000) × (4,000) = 80,000,000 = 8 × 107 . Notice that when you multiplied 20,000 by 4,000, the result had to have all the zeroes of each factor – that is, the sum of the number of zeroes, which is the sum of the exponents. That is why you add exponents when you multiply quantities in scientific notation.

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