Tag Archives: calendar

Leap Year Explained Simply

It’s Leap Day today, and that means people born on February 29th finally get to have a birthday. But why do we have Leap Years? What’s the purpose? Well, it ensures that our seasons don’t drift.

You see, it takes the Earth 365.256363004 days to orbit the sun (this is known as the sidereal year). The calendar year is 365 days. But every 4 years, we have an extra day. So, we add a day to the years that can be divided by 4. This year is 2016, and is divisible by 4.

Sounds simple, doesn’t it? But it gets a bit complicated.  This accounts for 365.25 days. But what about the extra 0.006363004 days? This accumulates, and after 400 years, it equals about 3 days extra. So, we have 3 too many Leap Days every 400 years. So what do we do? We just drop the Leap Days that happen on century years, but keep the ones that can be divided by 400. As a result, the year 2000 was a Leap Year, but 1900 and 2100 are not.

Leap years fall on years that can be divided by 4, except if they can be divided by 100 (not including the ones that can be divided by 400). This balances the calendar and seasons, and we don’t have any drift.

But why is it called Leap Year? Well, in normal years, let’s say that March  31st is a Monday, then the next year it’s a Tuesday, and then it’s a Wednesday the following year. But then, on a Leap Year, we leap over the next day (Thursday) so it’s on a Friday. And that is why we call it a Leap Year.

Any questions?

Creating a Fictional Planet’s Calendar

When humans finally manage to colonise another planet, there will be some significant differences between life on that planet and life on Earth.  One of them is the calendar.  Why would the Earth’s calendar be inadequate?

First, the orbital period of the new planet will be different than Earth’s 365.25 days.  Second, the length of the day is going to be different.  Third, with these two basic pieces of information, the year will start at different seasons, and midnight would happen at different times of day.  It would make no sense.

So, what we need to do is create a new calendar and timekeeping system.  I’m going to use my fictional world of Ariadne as an example.  I have yet to figure out the calendar, so I’m doing it on the fly as I write this post.

First of all, we need to determine the distance of the planet from the star, which is Beta Comae Berenices.  To do this, we need an equation.  We’ll start with the equation that is used to determine the temperature of a planet (and rearranged to solve for distance D).

D = (Ts^2Rs/2Tp^2)((1-a)/(1-τ/2))^1/2

D is the distance to the star, Ts is the temperature of the star, Tp is the temperature of the planet, Rs is the radius of the star, a is the albedo of the planet, and τ is the optical depth of the planet’s atmosphere.  Going through this, I want Tp to be equal to 288 Kelvin, which is similar to Earth’s.  The albedo should also be similar to Earth’s which is 0.39.  And the optical depth should be similar to Earth’s, considering the atmosphere is very similar.  Therefore, that should be 0.6.  The temperature of Beta Comae Berenices is 5,935 Kelvin, which is slightly hotter than the sun.  The star is also slightly larger than the sun, 1.106 times the size, and therefore has a radius of 770,154,252 metres.  Plug all these in the equation, and we get a distance of 152,657,589 km, which is slightly larger than the distance of the Earth from the sun.

Now, to determine the orbital period of the planet, we need the mass of the star, the orbital radius, and the mass of the planet.  We’ll use Kepler’s Third Law for this. To simplify this, I used this very handy tool to calculate the period.  The semimajor axis is set to 152,657,589 km, the mass of the planet is 1.028 Earth masses (as it’s 2.8% more massive than Earth), and the mass of Beta Comae Berenices, which is 1.15 times the mass of the sun.

We have a result of 0.961094 Earth years, or 351.046 days.

Now, as for the calendar, I’m going to be making up some numbers a bit here.  I’ll keep the numbers the same for the planet and star, but the year will be 351.1 days.  This means that the day on Ariadne is slightly shorter than Earth’s day by 13 seconds.  That’s all.  For the clock, a standard 24 hour clock with 60 minutes can continue to be used, though it’ll have to be adjusted a little.

As for the calendar, to get a nice round number of days per month is a bit difficult.  However, based on a 351 day year, a 12 month calendar with 29 day months is possible.  There are an extra 3 days, though.  They could be distributed around to 3 other months, but I’d like to do something special.  At the beginning of each year, there will be a 3 day month.  It’ll be a 3 day period for people to celebrate the colonisation of the world.

Now, to account for that extra 0.1 days, we can add leap years every 10 years.  Add an extra day on the decade to the holiday month, so on every 10th anniversary, there’s an extra long holiday.

As the year is slightly shorter, people’s ages will increase a bit faster.  So, a 50 year old person on Earth would have an age of 52 on Ariadne.  It won’t make a big difference, though.  However, colonists will have to figure out a new birthday based on this new calendar.  That can be calculated by regressing the calendar into negative years to find the birthdate.  The landing date will start with year 1, holiday month day 1.

Another matter is to name the months.  This will come at a later date, as the colonists haven’t arrived at the planet yet!  They’ll have time to name them.

I hope you found this post informative.  This is going to be Ariadne’s standard calendar, and it will be described with names in the future.