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I am trying the make (not super accurate, just for fun really) simulations of light curves, as just circles with various sizes and temperatures, then computing the RegionDifference.

As just a note, luminosity $L$, which is what a light curve measures, is proportional to both radius $R$ and temperature $T$ as $L\propto R^2T^4$

Currently, I can get things partially working with 

lights = Table[Area[Region[RegionDifference[Disk[{0, 0}, 1], Disk[{-3 + t, 0}, r]]]], {t, 0, 6, .1}];
ListPlot[lights]

This works for objects of the same temperature, since the $R^2$ factor really is just about the area, but I now want to weight the disks by their temperature. How might I go about this?

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  • $\begingroup$ So there is one light source and one body that passes by on top of it, blocking the light from the source? Why does the temperature of the object blocking the source matter? $\endgroup$
    – C. E.
    Feb 15, 2019 at 18:22
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    $\begingroup$ What is a "light curve"? $\endgroup$
    – David G. Stork
    Feb 16, 2019 at 4:38
  • $\begingroup$ Both bodies can be luminous, as in the case of binary star systems. If both objects are the same temp, they have the same brightness per unit area, and so the current code, which only measures eclipsed area of the stationary object, is fine, sans the fact that the area drops to 0 for the same size objects, which would correspond to a nonluminous object, but as this would just add a constant bit, it wouldn't be hard to change. I just cant figure out how to weight regionss, take their difference, and then measure the area. $\endgroup$
    – Brandon Myers
    Feb 16, 2019 at 20:11
  • $\begingroup$ But why does the luminosity decrease when one of the objects moves in front of the other if they are both luminous? Maybe it's not necessary for me to know this to provide an answer, but I don't really understand the question at this point so I am trying to get an intuition for the problem. Your formula says that $L\propto R^2T^4$. To me, it seems that $L$ should be the computed on the union of the disks, not the difference. $\endgroup$
    – C. E.
    Feb 16, 2019 at 23:53
  • $\begingroup$ While luminous, they aren't transparent. So moving a dimmer object in front of a brighter one causes an overall decrease in the brightness. Perhaps a better explanation could come from imagine.gsfc.nasa.gov/science/toolbox/timing1.html $\endgroup$
    – Brandon Myers
    Feb 20, 2019 at 21:10

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