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Fermi's Piano Tuner Problem

How Old is Old?

If the Terrestrial Poles were to Melt...

Sunlight Exerts Pressure

Falling Eastward

What if an Asteroid Hit the Earth

Using a Jeep to Estimate the Energy in Gasoline

How do Police Radars really work?

How "Fast" is the Speed of Light?

How Long is a Light Year?

How Big is a Trillion?

"Seeing" the Earth, Moon, and Sun to Scale

Of Stars and Drops of Water

If I Were to Build a Model of the Cosmos...

A Number Trick

Designing a High Altitude Balloon

Pressure in the Vicinity of a Lunar Astronaut Space Suit due to Outgassing of Coolant Water

Calendar Calculations

Telling Time by the Stars - Sidereal Time

Fields, an Heuristic Approach

The Irrationality of

The Irrationality of

The Number (i)i

Estimating the Temperature of a Flat Plate in Low Earth Orbit

Proving that (p)1/n is Irrational when p is a Prime and n>1

The Transcendentality of

Ideal Gases under Constant Volume, Constant Pressure, Constant Temperature and Adiabatic Conditions

Maxwell's Equations: The Vector and Scalar Potentials

A Possible Scalar Term Describing Energy Density in the Gravitational Field

A Proposed Relativistic, Thermodynamic Four-Vector

Motivational Argument for the Expression-eix=cosx+isinx

Another Motivational Argument for the Expression-eix=cosx+isinx
Calculating the Energy from Sunlight over a 12 hour period
Calculating the Energy from Sunlight over actual full day
Perfect Numbers-A Case Study
Gravitation Inside a Uniform Hollow Sphere
Further note on Gravitation Inside a Uniform Hollow Sphere
Pythagorean Triples
Black Holes and Point Set Topology
Additional Notes on Black Holes and Point Set Topology
Field Equations and Equations of Motion (General Relativity)
The observer in modern physics
A Note on the Centrifugal and Coriolis Accelerations as Pseudo Accelerations - PDF File
On Expansion of the Universe - PDF File

Calendar Calculations 

The tropical year is the period of time required by the sun to pass from vernal equinox to vernal equinox. It is equal to 365 days, 5 hours, 48 minutes, and 46 seconds, or 365.2422 days. The tropical year is used to keep track of seasons, planting, and harvesting. Let's try to develop a calendar with an integral number of days per calendar year that will keep track of the tropical year and not get out of step with the seasons over time.

We begin with a calendar of 365 days per year. Our calendar year is shorter than the tropical year by 0.2422 days. So to correct (approximately), we add 1 day every four years (leap year). Thus, three calendar years are 365 days long; the fourth calendar year is 366 days long. The average length of the calendar year in days now becomes: (3 x 365 + 366)/4 = 365.25 days.

This calendar system was actually instituted for use in the Roman Empire by Julius Caesar around 46 BC. But since the Julian calendar was 0.0078 days (11 minutes and 14 seconds) longer than the tropical year, errors in timekeeping gradually accumulated. Between 46 BC and 1582 AD, this accumulated error amounted to a total of: 0.0078 x (1582 + 46) = 12.7 days. In 1582, Pope Gregory XIII reformed the calendar by specifying that all years divisible by 4 are to be leap years except for century years, which must be divisible by 400 to be leap years. Now, in 1200 years:

  1. A total of 300 years (including all century years {since any century year = N x 100, where N = an integer}) are divisible by 4, and are therefore candidate leap years.
  2. A total of 900 years are not divisible by 4, and are therefore regular years.
  3. Twelve century years are possible leap years.
  4. But only 3 century years (out of the 12) are divisible by 400 (i.e., {400, 800, 1200}, {1600, 2000, 2400}, etc.), so only 3 century years are actually leap years9 .

Since 12 - 3 = 9, Gregory's rule eliminates 9 leap years out of 1,200. Thus: 300 - 9 = 291 years are actual leap years, and 900 + 9 = 909 years are regular years. The average length of the year becomes (291 x 366 + 909 x 365)/1,200 = 365.2425 days, with an error of 365.2425 - 365.2422 = 0.0003 days per year, or one day every 3,333.3 years.

The Gregorian calendar came into use in Roman Catholic countries in October 1582 when the seasons were brought back into step by eliminating 10 days from the calendar then in use. Thursday, October 4, was followed by Friday, October 15 (which caused some consternation among the populace, especially those with birthdays on the eliminated dates!). Britain and its colonies did not introduce the Gregorian calendar until September 1752 by which time an additional one day correction was required (actually, {1752 - 1582} x 0.0078 = 1.33 day). Some British documents from the period before the British reform actually contain two dates, an old and a new.

9 Line up the years as follows


1 ... 100
100 ... 200
200 ... 300
300 ... 400
400 ... 500
500 ... 600
600 ... 700
700 ... 800
800 ... 900
900 ... 1000
1000 ... 1100
1100 ... 1200

In each century, one out of every four years is divisible by 4. Of the century years, only 400, 800, and 1200 are divisible by 400, leaving 100, 200, 300, 500, 600, 700, 900, 1000, and 1100 that are not.

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Responsible NASA Official: Theresa.M.Scott (Acting)