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Name: Michael W Antrim
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Question:
What is the mathematical scale for the X-axis (Temperature) on the H-R Diagram? In successive increments, the temp range is cut in half: first increment = 10000 K, second increment = 5000 k, third = 2500 K. Is this a log scale? What is the base?



Replies:
Yes, it is a log scale. Here is what that means. The axis actually starts out looking like this:


------|----------|----------|--------> 
 log(10000) log(5000) log(2500)
 
 
The base of the log does not matter, and in fact, to draw this axis you do not need logs at all; note that for these equally-spaced hash marks, if the value at a given mark is log(N), then the value at the next mark to the right is log(N/2). Since log(N/2)=log(N)-log(2), this means that values at adjacent marks differ by a constant; that is, the above is a "regular" axis, just with unusual values marked. You do need logs if you want to locate, say, log(3000), on this axis: it is [log(5000)-log(3000)]/[log(5000)-log(2500)], or ~ 0.737, of the way from the log(5000) mark to the log(2500) mark (the 0.737 value is independent of the log base used; check it!). Finally, for the H-R diagram (and other such graphs) the "log"s are dropped. Try to imagine how the H-R diagram would look if a "regular" (i.e., linear) scale were used for temperature. A lot of the interesting stuff would get scrunched into a small area.

RC Winther


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