Like many others, my family and I traveled for the holidays. Let’s see if you can figure out where we are. I’ll give you a few hints.

This morning (I’m writing early Friday morning, hoping to make my deadline), I’m expecting a beautiful sunrise at 7:16 am, which I’ll be sure to get out to see. In the Grand Haven area, the sun will rise an hour later, at 8:16 am. Probably it will be cold and cloudy in Grand Haven (I’ve not looked up your weather forecast), so I don’t know if you’ll get out to catch the sunrise.

Later today, at precisely 12:29 pm my time, halfway between sunrise and sunset, the sun will reach it’s highest altitude. This is called solar noon. At solar noon here, the sun will be 40 degrees above the horizon.

Solar noon in the Grand Haven area today is a bit later, at 12:46 pm, and then the sun will be just 23 degrees above the horizon.

Tonight I’ll be sure to get out to see a nice sunset at 5:45 pm. In the Grand Haven area today, sunset is at 5:18 pm.

Today I’ll see the sun for most of the 10 hours and 29 minutes it will be above the horizon; you’ll have sunlight for just 9 hours and 2 minutes.

Have you figured out where my family and I are spending the holidays this year? Here is another hint: we’ve not seen a snowflake since the plane that flew us here was on its takeoff roll last Saturday. We got out in the nick of time.

Here’s how the numbers add up. Recall that our round earth is mapped out by lines of latitude and longitude. Pardon me if this is a review, but so we’re all on the same page, it goes like this. Lines of latitude run east-west parallel to the equator and map how far north (or south) of the equator a place is. Lines of longitude run north-south, wraping around earth, all passing through the north and south poles. Longitude maps how far west (or east) from Greenwich, England a place is. (Why Greenwich, England? I don’t know, off hand).

Notice that at solar noon where I am the sun is 17 degrees higher in the sky than it is at solar noon in the Grand Haven area. This betrays the fact that my family and I have travelled to a location that is 17 degrees of latitude south of Grand Haven. Grand Haven’s latitude is about 43 degrees (N).

Notice that solar noon occurs where I am about 15 minutes before it does in Grand Haven. The east-rising/west-setting of the sun is a consequence of earth’s daily west-to-east rotation. Earth spins 360 degrees in 24 hours, so at a rate of 15 degrees per hour. The quarter hour difference between my solar noon and yours betrays the fact that my family and I have travelled to a place that is about 4 degrees lof longitude east of Grand Haven. Grand Haven’s longitude is about 86 degrees (W).

Where are we? Latitude 26 degrees (N), longitude 82 degreees (W) – Punta Gorda, Florida.

It’s warm and sunny here. Warm and sunny because the sun is higher above the horizon all day long here compared to West MI. Very nice.

I hope you are enjoying the holidays. And as nice as it is here in Florida, our return to the land of snow and ice is surely going to be harsh.

This column originally appeared in the Grand Haven Tribune on 26 December 2008.

True or false: every fourth year – each year divisible by four – is a leap year.

While you think about this, here is something else to consider. Suppose you really like the 2008 calendar that is now hanging on your fridge. After 2008 slides into the past, will you ever be able to use this favorite calendar again? In what future year will the days and dates of 2008 again line up properly?

You might start toward an answer by considering that a “common year,” as opposed to a “leap year,” is 365 days long, or 52 weeks plus 1 day. So, for example, if your birthday is on a Tuesday, let’s say, one year it will be on a Wednesday the next. That is, if neither year is a leap year.

If it weren’t for leap years, you could use your favorite calendar every seven years. But leap years mix up the way days and dates align year after year.

For example, you might continue toward an answer to the favorite-calendar question by reasoning that since a leap year has 366 days – 52 weeks plus 2 days – you would celebrate your Tuesday birthday on a Thursday the next year if either year were a leap year. But here you need to be careful because the extra day in a leap year is inconveniently added at the end of the second month of the year.

This recreation gets complicated pretty quickly, but for the fun of it you can use a most interesting on-line tool. This calendar calculator computes “identical years” – years in the past or future in which the days and dates line up the same as they do during any given year. You can use this tool to recycle a favorite old calendar you might have tucked away at the bottom of your kitchen junk drawer.

But for leap years like 2008 you don’t need a calendar calculator. Exactly 4 x 366 = 1464 days separate any given date in a leap year and the same date the next leap year. This is 209 weeks plus 1 day. Therefore, a leap-year calendar like 2008 will be good again after 7 leap years, or 28 calendar years.

So if you take good care of your 2008 calendar you can use it again in 2036, and again in 2064, and in 2092. Or, if you have a nice calendar from 1980, or 1952, or 1924, you can use it again this year.

But don’t get carried away until you answer the true-false question above.

Here’s the answer: false.

The set of rules and conventions that define our calendar include a rule for skipping leap years from time to time. Most of the time, every year that is cleanly divisible by 4 – like 2008 – is a leap year.

This would keep our calendar synchronized with the seasons if there were exactly 365 days plus 6 hours in a year. But actually, 1 year is 365 days 5 hours and 49 minutes long. If we added a leap day to our calendar every four years our calendar would slowly drift out of sync with the seasons.

So we skip leap years periodically; we skip three leap years every 400 years. The official rule is that century years are not leap years (even though they would be by the divisible-by-4 rule) unless the year is cleanly divisible by 400. With the leap-year-exception rule, year 2100 will not be a leap year, and our calendar will remain in sync with the seasons well into the predictable future.

Look for a new post on or about 9 March 2008.