784 CALCULATING THE OCCULTATION OF STARS UY TIIK MOON. 



will be slightly further off when it gets to K which is the position 



\/ v'^~4- x'- 



of conjunction. Now OK /OS = s c ^ or v. - so if a star 



x' 



is to graze the moon at S its distance will be W unit, and at 



conjunction, since the angle is never very great, it can be assumed 



to be tW unit away. This is the condition for an occulta tion : 



the distance at conjunction of star and moon's centre in list not exceed 



o -30 unit. 



,It remains to calculate this distance (OC in the diagrcm) 



from the data given in the Almanac. The official complicated 



formula is: A=Y + y'T — p sin \ cosD + p cos \ sin D cos (HA) 



(wherein p is local radius and X local latitude, and D the star's 



dechnation and (HA) the corrected local hour-angle).*^ I propose 



to simplify this for amateurs' use. The expression cosD varies 



between i and o -88, and I shall assume it to be constant at about 



o -95. The third term in the above expression then simply becomes 



+ -42. The last term may be similarly simplified into the form 



r X D where D is in degrees + or — (from Almanac) and c is 



taken from the following small t^ble in which [HA] means 



(H-I-112+T). 



Table for r (always +). 



[HA] c 



A = Y 4- -42 + A'' T '" + c D ' and 

 A must be|less than''± 30 

 for an occultation. 



As an example, consider the occultation of ?/ Piscium of 

 15th February, igi8. From the Almanac Y= - -84, v' = + •20., 

 D= 4-15, H= — I .-. H = +111 and this with x' gives -r= +65m. 

 = 1-1 hours : hence y'T=4--22, and a=— •20 4-cD. To get 

 c find [H A] = IT + -r = nearlv 3 hours, hence c= -on and c D = + -16 

 .-. finalh' a = — o -04. This being nearly zero, a good occultation, 

 nearly central, is to be expected. Another example showing 

 the possibility of slight fallacies in the method is 115 B Sagittarii 

 of 24th June, iqi8, where a = — -37+ -42 — -lo — -24= — -29,, 

 and as a matter of fact the star just missed the moon : this was 

 probably because y' (and therefore the angle of slope 6') was small, 

 in which case a should not exceed ± o -28 or a quantity very 

 close to the moon's radius. 



It should be noted that if a is negative, the star passes t» 

 the south of the moon's centre {i.e., above in these latitudes). 

 This may also be ascertained from the " limits of latitude " given 

 in the Almanac : if the average of these limits is a greater minus 

 quantity than say —40 the star will pass below the moon's centre : 

 similarly, if the hmit-average is above —10, the star passes above 

 the moon's centre. 



r in hours, not minutes. 



