Eclipse Light Falloff Table

     f/      Time (m:s)
    ----     ----------
      0        75:00    First Contact
    -1/3       50:06
    -2/3       39:28
     -1        31:56
    -4/3       26:10
    -5/3       21:37
     -2        17:57
    -7/3       14:57
    -8/3       12:29
     -3        10:28
   -10/3        8:46
   -11/3        7:22
     -4         6:12
   -13/3        5:14
   -14/3        4:25
     -5         3:44
   -16/3        3:10
   -17/3        2:41
     -6         2:17
   -19/3        1:56
   -20/3        1:39
     -7         1:25
   -22/3        1:12
   -23/3        1:02
     -8         0:53
   (-10?)      ~0:35
 (-11 or -12?)  0:00    Second Contact

f/ is in photographic "stops", relative to the start at first contact. Each whole number is ½x as much light as the previous one.

The table thus covers a range in illumination levels of at least 28=256x, so the last solid entry at -8 is 0.39% of the first one. As the total brightness of the corona might be 0.02-0.04%, after this time its contribution to the remaining tiny sliver of sun at its limb (where limb darkening is greatest) will start to become significant, so total light levels after that becomes increasingly difficult to predict.

In principle, if the total brightness of the corona can be determined (during totality), so that it can be subtracted off, the total light level during about the last minute before second contact could provide information on the limb darkening right at the sun's limb, where it is most difficult to measure otherwise.

The 75 minute time from first to second contact is simply a convenient reference. In use, one would typically want to scale all the times for the particular eclipse under consideration. The table assumes a constant angular rate of motion of the moon across the sun, which at some level will be an inaccurate assumption. The moon's angular rate of motion will only be constant over several hours when it's near perihelion (which is also when it's largest and therefore more likely to be able cause a total eclipse), but in general it will be either side of perihelion and therefore increasing or decreasing in angular velocity on the sky.

Similarly, the eclipse is assumed to be near the local meridian, so variable atmospheric extinction, due to it rising or setting over the course of the event, can be (was) ignored.


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