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MATH CALCULATIONS IN MASTERINGASTRONOMY
Generally, every weekly homework assignment will have one or two problems, each of which
involves a calculation or a series of calculations. Since there are 20 questions per assignment and
each question is weighted the same, problems involving calculations may represent as much as
10% of the maximum points possible for a given assignment. Obviously, one could skip the
math-based problems and still pass the course. However, every semester we have a significant
number of students who finish the course just short of a higher grade by a few points. The
difference could be those skipped math problems! So if you would like to increase your chances
for receiving a higher grade or simply like solving problems that involve math, here are some
tips for finding those correct answers.
You Can Do Math – When it comes to problems involving math, many students will state “I am
no good at math” or something of a similar tone. For this astronomy course, we very rarely find
this statement to be true. The reason is simple. The math in this course involves no more than
basic skills in arithmetic and elementary algebra – skills that the vast majority of people use in
their everyday lives without realizing it. So the first thing you need to do (if you have not done
so already) is to stop saying, “I can’t do math”.
Formulas – The real issue with doing assignment questions involving calculations (where
student frustration is at its highest) is with determining which formula to use (if it is not given in
the actual question). There is no magic cure for deciding which formula to use for a given
situation. It basically takes listening to your instructor during lecture, reading your text, and
comprehending the situation at hand. However, we can still offer you a few hints: 1) Look
through the chapter that corresponds to your homework and see if the “Cosmic Calculation”
parallels your assignment question; 2) A significant number of calculations involve a “rate
equation” (e.g., distance = speed x time, where speed is the rate in this case); 3) Look for
common themes to previous assignments (e.g., the inverse square law implicitly, if not explicitly,
appears throughout the text); and 4) Take a look at Appendix B – “Useful Formulas”.
Data – Once you have a formula, usually you will have one unknown (which is what you will be
solving for) and you will need to plug in numbers for the other variables. Often the problem itself
will tell you what these numbers are. However, you will not necessarily be given everything up
front; you will be expected to look for “standard” data in a table or similar arrangement. DO
NOT use the Internet or similar sources to obtain these numbers. Use either the appendices in the
back of your book (or any other location within your text) or the “Constants” table found on the
MasteringAstronomy web site.
Powers of 10 and Units – Once you have your formula and your numbers, you cannot simply
plug in and calculate. You need to be sure that you have everything in compatible units and if
not, you will need to convert accordingly. Also, you can save yourself a lot of grief if (under
certain circumstances) you work with numbers expressed in powers of ten (or scientific
notation). You are expected to know how to do all this. However, if your skills in these topics are
a bit rusty, consult Appendix C, “A Few Mathematical Skills”, for an excellent review.
