If Today's Phoboday, this must be Mars.

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Janus
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Forget the currency exchange rate; if you are planning to spend your next vacation traveling the solar system, you'd better bring your calendar converter.

Of course, we all realize that the days and years will be different due to the various orbits and rotation rates but what about months and weeks?

Below is a guided tour through the calendar systems of the solar system.

Mercury:

Mercury has a orbital period of 88 days (Earth time) and a sidereal 'day' period of 59 days. For a calendar we use solar days, and adjusting for that, a Mercury day is 176 Earth days long. (For the rest of this post I'll use solar days for every planet without the conversion to Earth days.)

This brings up an interesting situation in that a day on Mercury is twice as long as a year!
The month is based on the phases of the moon, and since Mercury has no moon, it would have no month.

Which brings up the week. On Earth, the week originated from the fact that there were seven known "planets"(including the Sun and Moon), or objects that moved with respect to the stars. Using the same reasoning, Mercury would have a 6-day week, (Sun, Venus, Earth, Mars, Jupiter, Saturn)

Thus you would have a calendar of
0.5 days to a year.
6 days to a week (making a week 12 yrs long)

Venus:

Similar to Mercury; no month.
Six days to the week.
The days and years are reversed however, as there are just about 2 days to a Year. (Not exactly so once in a while you would have a leap year of only one day.)

Mars:
666 days to a year.

You have two moons added, and thus the week expands to 8 days (adding Phoboday and Deimoday).

Only Phobos is large enough in the sky to show phases so the month will be based on it. Phobos whips around Mars pretty quickly so its synodic month (full moon to full moon) is about 0.31 days long.
This gives us just a little more than 3 months to a day and 2142 months to a year!

Jupiter:
10566 days to a year.

From Jupiter, Mercury and Venus will lost in the Sun's glare, so we'll won't be able use them for days of the week, but Jupiter makes up for it by having a large number of moons, 8 of which are naked-eye visible from Jupiter, giving you a 12 day week.

For the basis of a month we run into a quandary. There are four moons that have a large enough apparent size to show visible phases from Earth. The one with the largest apparent size is IO with a synodic month of 4 1/3 days. The one with the longest month is Callisto, with a month of about 40 days. So which one do we use? Actually, Jupiter helps us out a little here because approximately every 120 days all four moons are full at the same time. So we’ll base our month on this period. This gives us 10 weeks to a month and 88 months to the year.

Saturn:
23909 days to a year

For the week, we lose Earth, but pick up Uranus (which finally becomes naked eye visible for at least a part of the year). We also have 17 visible moons. This gives us a week of 21 days.

With Saturn we have 7 moons that show visible phases. Unfortunately, it is not as easy to find a period where all of them show full. In this case, the moon with the largest apparent diameter also has the longest synodic month. This is Titan with a synodic period of about 36 days. If we use this as our basis for our month, we get 664 months to a year.


Uranus:
42619 day per year.

Mars drops out of the picture and we have 14 moons, giving us a 17-day week

Four moons show phases. Three of them are full together about 53 days apart. This would give us three weeks per month and 804 months per year.

Neptune
89835 days/yr
We lose no planets, and have 7 visible moons, for a 10-day week.

Triton with a synodic period of 9 days is the only moon to show visible phases. Our month will be 1 day shorter than the week. We will have 9982 months in a year, for a record.

Pluto

142111 days/yr
We have only one moon, so we are down to a 5-day week.

Charon is tidally locked with Pluto so a month will be 1 day long.

Of course, as with any calendar the lengths of the months will vary in order to make the months and years come out right, and there will be various leap year schemes to keep things in sync.
 

Answers and Replies

  • #2
Phobos
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Phoboday...I like it.
Good post, Janus. It would make a good Physics Post article too!
 
  • #3
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I must say this is the best post I've ever read on the Physics Forums. Or at least close.
 

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