CALCULATING THE OCCULTATION OF STARS I'.Y THE MOON. yH^ 



We hnve now (i) an accurate method of telling whether an 

 occultation coni'-s off or not, together with its approxirmte central 

 tim3 (Greenwich conjunction + 2 hours + t). and (2) a rough 

 method of predicting the beginning and end of the phenomenon. 

 It remains to investigate more accurately the latter point, so 

 as to get a result which is reliable to a minute or two. There 

 are two cases, one easy, the other rather troublesome, the former 

 being that of i?k]y central occultation. 



Time 0/ ]airiy-cevtral occitUaiion. — If the diagram be 



exammed, it \\ill be seen that if the path be fairly central 



the points C and M ccme quite close together and the distance 



ACMB becomes greater and is approximately the moon's diameter. 



If OC, which in the dirgrrm represents the quantity a in the 



calculation, is less th?n | of the radius, the difference between 



AB and the diameter becomes insignificant. Hence, if a is less 



than ± o -10, no appreciable error is made in assuming that the 



occultation is exactly central, in which case the simple formula 



33 cos 6 . , . . 



T= — T~ gives the time m mmutes required for the star to 



cross behind the moon. Cos 0, by the way, is generally omissible : 

 it is equal to i when y' is smrll, and equals 0-98 w'hen y' is o -i 

 and goes down to -92 when y' is at its maximum, whether +or- . 

 It ma3^ be obtained sufficiently nearly by mental arithmetic from 

 the expression cos (9 = i - 1-5 [v'y. The term c is taken from 

 the table on page 784, and x' from the Almanac. We have there- 

 fore finally — 



Time of immersion in " central " occultation = G T 6 + 

 ^ hours + - - i T. 



Time of emersion in " central " occultation = G T 6 - 

 2 hours + T + ^T. 



For example, consider the case of ?; Piscium already mentioned, 

 in which a was found to be less than -o- 10. Taking cos B = 

 1-1-5 ( '^4) =^ 94> ^nd c to be -011 for 3 hours, we have T = 



^-^ = 80 minutes for the star to cross. Central occultation, 



•57--I8 



which is practically the same as conjunction since the point M 



which is the centre of occultation is very close to C, was at 3 hours 



47 minutes (Greenwich time of conjunction) + 2 hours + i hour 



5 minutes or 6.52 p.m., hence predicted immersion was at 6 hours 



52 minutes —40 minutes or 6.12 p.m., and predicted emersion 



at 6 hours 52 minutes 4- 40 minutes or 7.32 p.m. [Observed, 



6.16 and 7.33.] 



Non-central occultation. — When a is found to lie between 

 o 10 and 0-30 either plus or minus, the occultation is not central 

 and the calculation is more complicated. It amounts to finding 

 the lengths of CM and AB in terms of OC which is a, and is 

 therefore merely an exercise in the geometry of the circle. 



A. To consider CM first, the difference of time between 

 mid-occultation and conjunction : CM is OC sin 6, which irt terms 



