Leap Second and Leap Day

1) LEAP SECOND When mankind came to know that the sun rises in different  times in different countries, efforts were taken to fix  the country that watches  first the rising of the sun .  Japan was identified . It is the country of rising sun. If  in Japan the time is   6 am, in  India it  is 2:30 am ( 3:30; hrs difference )  Earth rotates towards east. If India goes to the position where Japan was at 6 am. Indian time becomes 6 am. US is  a vast country with different time zones. If it  is 6 am in NY It is 3 am in SFO ( 3  hrs difference ) In simple terms , NY is Japan and SFO is India ( such a huge distance ) Even US is divided into 6 times zones including Alaska and Hawaii. It is the earth's rotation that  causes the time difference.  The sun is in different points in the sky because of the rotation  of the earth.. The time changes from country to country. For easy identification  and comparison of timings of different countries, GMT came into use. GMT is replaced by UTC (Co ordinated Universal Time ) in 1972. Indian Standard Time ( IST ) =  GMT + 5:30. If it is 1 am in UK ( GMT ), in India it will be 1+ 5:30 = 6:30 am. ( India is 5:30 hrs ahead UK ) ( During summer UK time is advanced by one hour from GMT ) The Earth rotates once in 24 hours,  it is not exactly 24 hours, slightly less  in fraction of seconds . As a result, once in a few years, the rotation of the earth becomes one sec less than the clock time, which needs adjustment. How this adjustment is done ? I will explain with a simple example, as I  used to explain to my students.  A and B are two clocks running accurately , showing the  same clock time. At one stage,  A is running one sec more  than B. To make them to show the same clock  time , Clock 'A' which is running forward  by  1 sec ,should be stopped for one sec. Then A and  B will show the same clock time.  So,  for the adjustment, the object running forward should be stopped. Clock time is one sec forward than rotation time. So, the  clock time  should be stopped for one sec. ( Since the earth's rotation can not be made fast,  the clock should be stopped ) It is done on 31st Dec midnight,  just before the birth of New Year. Universal clock and all other clocks including the Big Ben of UK are stopped for one sec. It is called ' inserting  a leap second '.By this the rotation time and clock time are synchronized It is not done  every year, done whenever required. The last inserting of the  leap second was done in the year 2008, Dec 31st midnight. ( some times done at the end of June ) LEAP DAY The earth rotates once in 24 hrs. The earth revolves the sun in elliptical path, once in 365 days. Even this 365 is not accurate. During Julius Caesar period, it was calculated to be 365.25 days. The extra 0.25 day accumulates and becomes one day extra in 4 years. So,  once in 4 years a leap day  is added in the month of Feb. During  the time of Pope Gregory ( 1502 -1572 AD ) , it was calculated that  the earth takes 365.2425 days to orbit round the sun. Julius Caesar calculation 365.25 days. Gregory calculation        365.2425 days                                   --------------------- Difference                         0.0075 day ,  Excess every year. This excess ( 0.0075 day )  becomes 3 days in 400 years. 0.0075 x 400 =3.000 = 3 days  These 3 days which are excess in  every 400 years should be removed. Pope Gregory gave a formula. All century years ( ending with 00 ) should be exactly divided by 400 to consider as leap year. Explanation : Any year, exactly divisible by 4 is a leap year, year 2012/4 =503 ( no reminder, so 2012 is a leap year ) But century years like 2100,  2200, 2300, 2400 should exactly be divisible by 400 not by 4. 2100 is exactly divisible by 4 , 2100/4 =525 but it is not a leap year, being a century year, it should be divided  exactly by 400. 2100/400 = 21/4 , it is  not exactly divisible by 400 , so not a leap year. 2200/400 =22/4 , it is  not exactly divisible by 400, not a leap year. 2300/400 =  23/4 , it is  not exactly divisible by 400 , not a leap year. 2400/ 400 =6, it is exactly divisible by 400, so leap year. From the  year 2001 to 2400 there are 400 years. In these 400 years, 2100, 2200, 2300 are not leap years. By this 3 days are removed in 400 years. Like this, once in 400 years,  three days are removed from the calendar and adjusted. To consider leap years, ordinary years should exactly be divided by 4, Century years should exactly be divided by 400. Once in 400 years,  3 days are removed . Another interesting aspect, nowadays, by using highly sensitive atomic watches, it has been accurately calculated that the earth orbits  the sun in 365.24222 days.  Pope Gregory calculated   365.2425 days and ordered to reduce three days, once in 400 years. The accurate calculation is 365.24222 days , the difference is 365.2425                                                                                      - 365.24222                                                                                   -------------------------                                                                                            0.00028 day excess every year This difference, which is excess every year should be removed. This is very very meagre but can not be ignored, because it becomes one day excess in 4000 years. Calculation : 0.00028 x 4000 =1.12000=1.12=1 day. This one day excess should be removed once in 4000 years. Years 4000. 8000, 12000 will not be leap years even though these are divided exactly by 400.  In our present Gregorian Calendar,  1 day is added once in 4 years ( leap year ) 3 days are removed in every 400 years. One day is removed in every 4000 years.  =========================================                                     COMMENTS. Karuthedath wrote: "It is verymuch informative, Thanks"  Gurunathan Periyathiruvadi Thank you, interesting info. Pearly Reddy Very Informative. Thank You.