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TEMPERATURE SCALE ON HR DIAGRAM
Name: michael w antrim
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: 1993 - 1999
Question:
What is the mathematical scale for the X AXIS (Temperature) on the HR
DIAGRAM? In successive increments, the temp range is cut in half: first
increment= 10000 K, second increment = 5000 k, third = 2500K. Isw this a log
scale? What is the base?
Replies:
Hi-
I have no idea what you're looking at. Give us a break. What's
the book, what's the page, and what does HR stand for. Are you looking
at a Hertzsprung-Russell diagram? or is it a Harvard-Rutgers joint
preprint? What is plotted on the x-axis, what is plotted on the
y-axis?
J Lu
Yes, it's a log scale. Here's what that means. The axis actually
starts, out looking like this:
------|----------|----------|-------->
log(10000) log(5000) log(2500)
The base of the log doesn't matter, and in fact, to draw this axis you don't 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 abov e 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 ~
.737, of the way from the log(5000) mark to the log(2500) mark (the .737 value i s 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 interes ting stuff would
get scrunched into a small area.
RC Winther
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Update: June 2012
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