Design a clock and a calendar that will work on Mars.
Introduction
Use the Mars information provided here to design a martian calendar and a martian clock. Doing this will help you understand how the earth calendar works.
The Clock
To Do and Notice
In designing your clock you'll have to decide how to handle a division like an hour, and like a minute. Along the way you'll need to decide what to do about the second too. How many hours will there be in a mars day? How many minutes in a mars hour? Do you keep the second the same or change it?
The Calendar
To Do and Notice
In designing the calendar you'll need to decide what to do about weeks, and months and leap year days. How many days will there be in a mars week, a mars month? How many months will there be in a year? What will be the names of the days and the months?
Background Information:
The solar day on Mars has been given a name, it is called a Sol.
There are approximately 668.6 Sols per Martian
Year.
(Actually there are 668.5991 sols per sidereal year, how does this
affect your calendar?)
The Sol is 24 earth hours 39 earthminutes 35.25 earthseconds long. This is the length of the martian mean solar day measured in earth time units. The mean solar day is the average time between noon and noon, averaged over an entire year, on earth it is 24 hours.
Mars orbits the sun in 686.98 earth days
Its axis is inclined from a perpendicular to the ecliptic by 25.19° , similar to earth's 23.5 degree inclination.
Mars rotates once in 1.026 earth days or 24 earthhours 37 earth minutes 22.663 seconds with respect to the distant stars. This is the sidereal day. On earth the sidereal day is 23 hours 56 minutes 4.0905 seconds. See the earth rotation activity for further explorations of solar and sidereal days. (A sidereal day is the time it takes a star to go from meridian crossing to meridian crossing, when the sun crosses the meridian we say it is noon, AM means antemeridian, before the meridian crossing, while PM is postmeridian.)\
Mars has two moons:
Phobos with a sidereal period of revolution (orbit) of 0.319 earth days or 7 h 39 m 26.6s (earth times)
and Deimos with a sidereal period of 1.262 earthdays, 30 h 18 m. (earth times)
These sidereal periods are not the periods for the moon to return overhead, they are the times to orbit the planet and then return to the same place relative to the stars, while the moon orbits, the planet rotates.
What's Going On?
There is no agreed upon right answer to this assignment. Each group of students should be able to present a usable clock and calendar proposal and to defend this proposal in front of questions from other groups.
At the end have the class adopt one proposal. In this way they will be behaving like standards organizations that must adopt a standard for compact disk recordings, or CDROMS, or even when daylight savings time starts and stops.
Examples of proposals:
A calendar can abandon week and month and include 16 day intervals since 668 is evenly divisible by 16.
Many groups decide to keep the second the same because it is the basis of the SI system of units.
Some groups change the length of the second to make the day have 24 Mars hours.
Other groups keep earth minutes, and hours and treat the extra half hour at the end of the day by introducing the time 0 hours plus minutes after midnight until the clock reaches 0 h 39 m 35.25 s and then reset the clock to midnight. That is 11 PM, is followed by 0 AM until about 0 :39 AM at which time the clock resets to 12 AM and continues through the next day.
Some groups of students define these extra 39 minutes as daily party time! Perhaps partry time should be midday?
Students will have to develop a program of leap years to take care of the 0.6 day per year. They will need three leap years every 5 years. Since 0.6 = 3/5. On earth the number of days per year is approximately 365.25 the extra 0.25 day per year or 1/4 day means 1 day of leapyear every 4years.
Historical notes on the earth Calendar
The year is the cycle of the seasons, and the time for the earth to make one revolution, orbit, around the sun. The Egyptians divided the year into 12 months of 30 days, or 360 days total. Since the year is about 365.25 days long this meant they had five days left over each year. They used these days for feasting and celebration. Julius Ceasar dealt with that pesky 0.25 day by adding a leap year day to February every 4'th year. This was the Julian calendar. But this still wasn't right so the Gregorian Calendar dropped the leapyear on all years divisible by 100 but not 400. Thus 1900 had no leapyear even though it is divisible by 4, while 2000 did have a leap year.
The month is a period derived from the orbit of the moon. The moon takes about 29.5 days to go through one complete cycle of phases. Todays months of 28,30 and 31 days are convenient bill paying intervals.
The week is a convenient market interval. African tribes have weeks that range from 4 to 10 days, oddly enough the seldom have 7 day weeks. The Greeks had 10 day weeks, and the Romans 8 day weeks that included a day of rest. The week of seven days comes from the Christian tradition where the earth was created in seven days including one day of rest. The French revolution introduced a 10 day week which worked until Napoleon took over and restored the 7 day week.
The Egyptians divided the night into 12 hours based on the rise of constellations of stars. They divided the day into 10 hrs with a shadow clock, then addd a twilight hour morning and evening. This gave rise to a 24 hour day.
When clocks became accurate enough hours were divided into 60 minute pieces called of course, minutes.
Later minutes were divided into 60 smaller pieces called second minutes, which we know today as seconds.
The divisions by 12 and 60 came from Babylonian mathematics.
Scientific Explorations with Paul Doherty 

10 October 2003 