Metric Time for Mars

Bruce A. Mackenzie

Copyright © 1988, 1995 by Bruce Mackenzie
Copyright © 1989 by American Astronautical Society
as published in "Case for Mars III" conference proceedings,
AAS 87-269, vol 75, page 539

current address as of 1/1/96:
Bruce Mackenzie
110 Van Norden Rd., Reading, MA, 01867-1246
(617)258-2828 (w), 944-7027
BMackenzie@draper.com

As people leave the Earth, we will no longer be bound to the exact length of the Earth's day. It is an ideal time to convert to the metric system instead of the hours-minutes-seconds system based on multiples of 12 and 60.

People on Mars could use decimal fractions of the Martian day: centidays, millidays, microdays. To aid its acceptance, units close to hours and seconds are also proposed. This "Martian Metric Time" is intended as an alternate to defining new hours, minutes and seconds stretched to fit the Martian day. It is only for convenience in everyday activities on the surface of Mars. Earth time units should continue to be used for scientific measurements.

If a significant number of people live throughout the solar system before Mars is populated, it would be better to use the second as the basic unit for compatibility with current scientific practice. For example, use kiloseconds instead of hours.


PROBLEM

The Martian day is 24 hours, 39 minutes, and 35.238 seconds long. It is impossible to divide it into an even number of hours, or any other units; and still have those units be the same as on Earth. Most Martian residents will want to be awake during daylight hours, and can easily adjust their circadian rhythm to be synchronized with the Martian day. They will want simple ways to measure time, such as being able to set their alarm clocks for the same time every day. Whatever habits the early Martian residents adopt will gain inertia and be hard to change later. Before choosing a system (or falling into the habit of one), we should consider its usefulness to Martian residents after several generations.

It may be best to use two time systems; use Earth time for interplanetary navigation and astronomical observations; and a new system for general use on Mars, such as scheduling daily activities. Using two different systems would not actually be any additional burden during communications between planets. Since the round-trip delay time for radio signals varies from 8 to 40 minutes, radio operators would want several clocks on their wall: local time, the time their voices will be heard, and the time when transmissions now being received were sent, and perhaps more clocks if multiple time zones on either planet are involved. Clocks showing Earth time would use hours, minutes and seconds; clocks showing Martian time could use whatever units are chosen.

Since the Martian day and year are not synchronized with the Earth, the Martian calendar could also be different. This is not considered here.


GOALS

There are several conflicting goals which a time system for Mars should try to meet:

  1. Be identical to Earth time (of course time zones and radio delay complicate this).
  2. Use units the same length as Earth units, or at least with a simple conversion factor to them.
  3. Similar to Earth time, to ease culture shock for new arrivals; but using clearly distinct names to avoid misunderstandings.
  4. Synchronized with Martian day, since people's daily schedules will also
  5. Units should be multiples of each other, especially divide the day into an integral number of hours; for ease of computing elapsed time.
  6. Simplicity; for example avoid arbitrary ratios between units such as 60, 12, 24; as well as 7, ../31, and 365.


OPTIONS

There are several possible systems Martian residents could use to measure time:

  1. Earth Time. Keep clocks synchronized with a local Earth time, such as Greenwich Mean Time. This certainly will be done on short missions where the crew is in frequent contact with the Earth. The problem is that clocks would have no relationship with the local day; for example, dawn and breakfast would be almost 40 minutes later each day.
  2. Synchronized by Radio. Astronauts (or ground controllers) could set their clocks based on the radio signals they receive, which are delayed by 5 to 20 minutes. This would simplify radio communication in one direction, but complicate navigation and astronomical observations.
  3. Add Additional Minutes to Each Day. The Martian clocks would have hours and minutes the same length as on Earth, but count up to 24:39:35 at midnight, and then reset to 0:00:00 . Every fourth day an additional "leap second" should be added to keep the clocks synchronized with the sun. Computing the elapsed time from one day to the next would be complicated. This may be the best solution in the short run; but try to imagine how archaic it would seem to third generation Martian school children who are raised with the metric system and have no first hand experience of Earth. (Ref. 2)
  4. Stretch All Units. Divide the Martian day into 24 hours; each of 60 minutes; each minute divided into 60 seconds. This is described by James Lovelock in The Greening of Mars (Ref 1):

    Of course, we have a "24-hour day" just as people on Earth, but each of our hours, minutes and seconds lasts a little longer than their (Earth) equivalents. To be precise, a Martian second would equal 1.0275 Earth seconds. This has minimal psychological impact on those arriving from Earth. Unfortunately, all technical measurements must account for this 1.0275 conversion factor. For example, specifications for machinery and electronics are in units of meters/second, cycles/second, microseconds, megahertz, etc. If the units are stretched, it is critical to give them different names so that a person knows if the conversion factor has been factored in.
  5. Metric Time based on Earth Seconds. We already use the metric system for measuring milliseconds and microseconds; extend its use to kiloseconds (about 15 minutes) and larger units. An Earth day would be 86.4 kiloseconds, a Martian day would be 88.775 kiloseconds. This is the system I would recommend when a significant number of people are no longer tied to the length of any planets day. The residents of a space colony or Lunar base might choose a 85, 88 or 90 kilosecond day-night cycle, whatever is comfortable for them. Vacation resorts with late night casinos might use a 95 kilosecond day. To avoid favoritism toward any one planet or space colony, we could use gigaseconds and megaseconds since the year 1 A.D. for astronomy, communication, legal agreements, and recording history.
  6. Metric Time Based on Martian Day. Divide the Martian day by powers of 10 to produce "centidays", "millidays", and "microdays". This is proposed as a better alternative than stretching the units (option 4). It has the same disadvantage of requiring conversion factors to compute the equivalent Earth time; but if we are going to use conversion factors, we might as well go metric and avoid the factors of 60 and 24. This would be the most convenient system for day to day living on the Martian surface. For a comparison: on Earth we must sometimes convert velocities from meters/second to km/hour or km/day (factors of 3.600 and 86.400); a Martian could easily convert from meters/milliday to km/day or km/centiday (factors of 1 and 100). This system is described below, with some modification to ease its introduction.


MODIFIED MARTIAN METRIC TIME

To applying the metric system to the Martian day we divide by 100, 1000, and 1,000,000 to create the units: "centidays", "millidays", and "microdays".

However, the current system of hours-minutes-seconds is ingrained in our thoughts and language, any changes will meet much resistance. Indeed, the French tried to divide the day into 10 hours when the metric system was introduced, but it was not accepted. To ease the transition, also divide the Martian day into 25 "Martian hours". (It is closer to 25 hours than to 24.) The use of hours is not incompatible with the metric system: 1 Martian hour equals 4 centidays or 40 millidays. These Martian hours are only 2% shorter than earth hours. A (Martian) centiday is equally close to 15 minutes, which is a useful unit. 10 microdays is just slightly faster than a second, actually very close to a resting person's heartbeat. Therefore, I propose the following nicknames for these units:

"Hora"(from Greek for hour) = 4 centidays
"Quarter"(from quarter hour) = centiday
"Mil"(similar to minute) = milliday
"Beat"(from heart beat) = 10 microdays

Visitors to Mars who are accustomed to hours-minutes-seconds, or anyone uncomfortable with the metric system, could think of dividing the Mars day into 25 "hours" (hora), divide each hour into 40 "minutes" (mil), and each minute into 100 "seconds" (beat).

Using units as close as possible to the Earth units would simplify casual radio conversations between the planets, as well as easing the culture shock of new arrivals. As examples: Researchers on Earth may ask astronauts to continue an experiment "after an hour for lunch". A student on Mars may watch a video tape of a one hour lecture from an Earth university. A new immigrant could understand the phase; "We'll be ready in a 'quarter' (quarter-hour)."


PROPOSED MARS METRIC TIME UNITS

Unit & "nickname" Abbr Equivalent Mars times Equivalent Earth times Typical Uses
DAY
(Martian-day)
1 day = 25 hora
1 day = 1000 millidays
24 h 39 m 35.238 s
1.0275 Earth days
MARTIAN HOUR
"Hora"
4cd 25 hora = 1 day
1 hora = 4 centidays
1 hora = 40 millidays
.9864 hours
59.184 minutes
as an hour:
a meal, class, appointment
CENTIDAY
"Quarter"
cd 100 centidays = 1 day
4 centidays = 1 hora
14.796 minutes
(.9864 of 15 mins)
as in "quarter after the hour"
MILLIDAY
"Mil"
Md 1000 millidays = 1 day
40 millidays = 1 hora
10 millidays = 1 centiday
1.4796 minutes
88.775 seconds
(2 Md @ 3 minutes)
"just a minute"
BEAT 10µd 100 Beats = 1 milliday .88775 seconds as a second,
= 1 heartbeat (at 68 / min)
MICRODAY µd 106 microdays = 1 day .088775 seconds fast clicking

Writing Specific Times of Day

A day would officially start 10 horas (hours) before noon, and extend 15 horas after noon. This fixes noon at a convenient time: 10:00 . Times between 1:00 PM and 9:00 PM on Earth correspond to the Mars times 11:00 through 19:00, an easy adjustment for travelers from Earth. The day officially ends at 25:00. This is a couple of hours later than on Earth, so fewer people would be awake long enough to use the words "today" and "tomorrow" incorrectly after midnight.

The written form for a time on Mars would be:

horas : mils
or: horas : mils . beats
or: horas : mils . microdays

The corresponding way to write an Earth time is:

hours : minutes : seconds . fraction

Some common times of day are:

Martian Time Event (approximate Earth time)
0:00 official start of day (2:30 AM)
4:00 dawn (6 AM)
5:00 breakfast (7 AM)
10:00 noon (12 noon)
16:00 sunset (6 PM)
17:00 supper time (7 PM)
22:00 bed time (11 to 12 PM)
25:00 end of day, = 0:00 (2:30 AM)

Note that the first digit of millidays (mils) also represents centidays or quarter horas:

Martian Time Name (corresponding Earth time)
14:10 quarter after 14 (4:15 PM, quarter after 4 PM)
14:20 half past 14 (4:30 PM, half past 4 PM)
14:30 quarter of 15 (4:45 PM, quarter till 5 PM)

For more precision, simply add on "beats" with a decimal point; or add a decimal fraction of millidays using as many digits of precision as needed. This is not ambiguous, because beats are a decimal fraction of millidays:

Martian Time Name (corresponding Earth time)
14:39.99 1 beat before 15 (4:59:59 PM, 1 second till 5 PM)
15:00.01 1 beat after 15 (5:00:01 PM, 1 second after 5 PM)
15:01.00 one mil after 15 (5:01:00 PM, 1 minute after 5 PM)
15:00.003 3 microdays after 15 (5:00:00.3 PM, 0.3 sec after 5PM)

Computer programs and digital clocks could use millidays for internal computations. To convert a time to millidays, simply multiply the number of horas by 40 (mils/hora) and add. For example: 20:07.50 = (20 * 40) + 07.50 = 807.50 millidays, or 0.8075 days.

Initially, everyone on Mars should use the local time (mean solar time) of the first permanent base. As the population grows and spreads out; they can decide if they wish to keep one universal, planet wide time; or establish time zones.

Remarks

People often say they need more hours in the day, there would be on Mars. The cliché "I'll get back to you in a minute" might finally be accurate; no one on Earth "gets back to you" in 60 seconds; so we can replace the minute with the milliday, which is a minute and a half. Many people have a natural circadian rhythm of approximately 25 hours; this gives me the eerie feeling that we were destined to live on Mars instead of Earth.


REFERENCES

  1. James Lovelock and Michael Allaby, The Greening of Mars; André Deutsch Limited, Great Britain; also Warner Books, 666 Fifth Ave, NY, NY 10103; 1984, page 84.
    A fictional account by a second generation Martian colonist.
  2. James E. Oberg, Mission to Mars, Stackpole Books, 1982, page 93.