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Robert Tamayo

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The Most Expensive and Cheapest Months

February is the most expensive month. Sure, rent is the same price as any other month, but the month is more than 10% shorter than the longest month. A ten dollar subscription is comparatively cheaper per day in January than in February.

Consequently, the 31 day months are the cheapest months. But what is the absolute cheapest month? Despite all the 31 day months having the same number of days, there is actually a correct answer to this...sort of.

Due to daylight savings time, we can rule out March as being the cheapest month. March forces us to move the clocks forward one hour, making it one hour shorter than a true 31 day month. We get the hour back in November, but that's just a 30 day month.

We're left with January, May, July, August, October, and December as candidates for the cheapest month. It's still technically possible to narrow them down from here on technical terms, so I'll start on that path.

Each day is not exactly 24 hours. Sometimes the Earth spins faster than other days, but usually the difference is in the order of a few milliseconds. Even though the difference is extremely small, this might be why some days feel longer than other days - they are actually longer.

Using the fact that some days are longer than other days, it's possible to find the month with the greatest number of additional milliseconds added to it. To do this, I'll have to look up the exact length of time for each day in each of the 6 months above. Before doing that, however, there is something else to consider.

In addition to leap days, there are leap seconds. Leap seconds are added to either June 30 or December 31 on years when it's necessary to help sync up the time on the clocks with the actual rotation of the Earth. The last time a leap second was added was in December 2016.

Because December is a 31 day month, and it's also a candidate to receive a Leap Second, it's technically on average the longest month of the year. That makes December the cheapest month.

However, there is a caveat to that. Leap Seconds can be either positive or negative. If a negative leap second were added to December, then December could start to become on average shorter than the other 31 day months. If the Earth's rotation continues to speed up, then December leap seconds would start to become negative instead of positive, making the month shorter. During any year where a second would be subtracted from December, December would not be the cheapest month. However, on average, December would continue to be the cheapest month, at least until a minimum of 15 negative leap seconds were added to December.

Also, in any given December, if it did not have a leap second, then it's important to understand that the only way to figure out the cheapest month of the year is to do it the hard way and add up the total extra milliseconds for each day in each of the longest 6 months.

The Earth's rotation is currently speeding up, meaning that it is more likely that a negative leap second could be taken from December before a positive one is added to it. However, as things currently stand, December is still the longest on average month. There are only 31 days in each of the long months, and the longest days of each year are recorded in addition to the total sum of all days of the years. In the 70s, the entire year would be +1000 milliseconds, but the longest day would only be a couple milliseconds at most. Thus, no sum of a set of days with total excess milliseconds less than 32 could offset the length of time December gains by a leap second.

Since Earth's rotation is speeding up, it's likely that December will no longer be the cheapest month. If that happens, then the only way to find out the cheapest month of the year is to find out which of the 6 longest months had the longest total amount of time in them. And if Daylight Savings time ever goes away, then March would be back in the fight. Still, the current consensus is that the Earth's rotation will generally slow down over the long term, so maybe December will remain the cheapest month on average for hundreds of years even if it goes through a few decades of losing seconds.

Think of it like this: February is like paying 5 dollars and only getting 28 eggs instead of the normal 30 or 31. In December, you pay for 31 days and get one second free. (The one second free deal only comes every now and then, though.)

So there you have it. You get the least bang for your buck in February, and the most bang for your buck in December. 

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