A Taxonomy of Martian Historical Periods

INTRODUCTION

There is a lot of misinformation about Martian time on the World Wide Web, and unfortunately, some of this erroneous material is associated with otherwise reputable sources. Inspired by the "Bad Science" and "Bad Astronomy" websites, "Martian Time" points out errors by people (including journalists) and institutions that ought to know better. (Notice that we don't pick on hapless students and laypersons. Not only would that be mean-spirited, it would also be extremely time-consuming, as there are many examples. So if you're looking for Martian mean time, get lost pal, you're in the wrong place.) When such errors are pointed out to these august entities, they ought to correct them, since less-knowledgable people will take the information at face value. But, for some reason, they don't acknowledge or correct their errors, so instead we honor them with the "Bad Time on Mars" award.

But before we look at bad time on Mars, what is good time on Mars?

Just about any astronomy book will tell you that the rotational period of Mars is 24.6229 hours, or 24 hours, 37 minutes. However, note that the same table also gives Earth’s rotational period as 23 hours 56 minutes. But isn’t Earth’s day 24 hours long? What happened to the missing four minutes? The difference is that the 23 hours 56 minute figure is a sidereal day, i.e., Earth’s rotation is measured from the point of view of a fixed star. The fixed star is at a distance that approaches infinity in relation to the size of Earth's orbit around the sun, so the direction from Earth to the fixed star can be assumed to be constant. As Earth completes one rotation, it also travels a little less than one degree in its orbit around the sun, and the direction from Earth to the sun changes by the same angle. Thus, "from sun to sun" takes Earth a bit more time to rotate through this additional one degree of arc, 1/365 of a day, or about four minutes. This is the solar day of 24 hours. In the course of a year, the diverging angle between the direction from Earth to the fixed star and the direction from Earth to the sun accumulates to 360 degrees, or one entire rotation, and those daily four-minute increments sum to one full day. So there is exactly one less solar day than there are sidereal days in a year. There are 366.2564 sidereal days in a sidereal year. The number of solar days in a sidereal year is exactly one less than this, or 365.2564.

Since the Martian year is nearly twice as long as Earth's, but the Martian day is only a trifle longer than a terrestrial day, the difference between the sidereal day and the solar day is only about half: a bit more than half a degree of arc, or about two minutes. Again, there is one less solar day in the year than there are sidereal days, because the daily half-degree increments sum to 360 degrees in the course of a Martian year.

The math is easy, but people do need to understand the concepts behind the numbers and think through all of the necessary steps in logic. Just about any astronomy book will tell you that the orbital period of Mars is 686.98 (Earth) days. A Martian sidereal day is 24:37:22.4 / 24 = 1.02595 Earth days. The number of Martian sidereal days in a Martian year is therefore 686.98 / 1.02595 = 669.6. The number of Martian solar days, or sols, is one less that this, or 668.6. The length of the sol is then 686.98 / 668.6 = 1.0275 Earth days. To be exact, the sol is 24 hours, 39 minutes, 35.244 seconds. The exact length of the Martian year depends on the type of Martian year being referenced: sidereal, tropical, anomalistic, et cetera. For a detailed explanation, see "What is a 'Year' (on Earth or Mars)?"

And now, let's have some bad times on Mars!

DUNCE CORNER

Megan Smith

Bad Time on Mars:

http://www.fromquarkstoquasars.com/curiosity-celebrates-one-martian-year-on-the-red-planet/

After one Martian year or 687 Earth days (sols), everyone’s favorite rover–Curiosity–has successfully completed her main objective.

Good Time on Mars:

If a sol were the same as an Earth day, we wouldn't have had to come up with a new name for it.

Amy Thompson

Bad Time on Mars:

http://www.spaceflightinsider.com/missions/curiosity-celebrates-one-martian-year-science/

Here on earth it takes 365 days (sols) to complete one Earth year, while it takes 687 days (sols) to complete one Martian year.

Good Time on Mars:

This is the same mistake as Megan Smith's. Again, if a sol were the same as an Earth day, we wouldn't have had to come up with a new name for it.

Cornell University

Bad Time on Mars:

http://athena.cornell.edu/educators/lp_14.html

Mars has a rotation rate such that one day or sol (Martian day) equals 24.6 hours, or 24 hours, 37 minutes. The Earth rotates once every 24 hours.

Good Time on Mars:

There are several errors here. The first mistake is the imprecise use of the terms "rotation rate" and "day." A planet's rotation rate is usually expressed in a sidereal inertial reference frame, and in that context Mars does indeed rotate in approximately 24 hours, 37 minutes. But, this is not a sol, which is a Martian solar day of about 24 hours, 39.6 minutes. The statement that "The Earth rotates once every 24 hours" is also misleading. In the sense that Mars rotates in 24 hours, 37 minutes, Earth rotates in 23 hours, 56 minutes. In the sense that the Martian solar day is 24 hours, 39.6 minutes, Earth's solar day is 24 hours.

Cornell has mixed apples and oranges here. Worse still, this site is intended to be a resource for educators to use in developing lessons for their students. But, Cornell is mis-educating the educators!

It also happens that the principal investigator for the NASA/JPL Mars Exploration Rover missions is from Cornell. Scary, isn't it? Scarier still is that the wording of this misinformation is nearly identical to the wording found at several locations on the NASA/JPL website (see below), indicating that it may have a common source. Bad information propagates like bad rabbits!

Harvard University

Bad Time on Mars:

http://balancedassessment.gse.harvard.edu/docs/he005.doc

It takes 669.3 "days" (rotations of Mars) for Mars to orbit the Sun. Design a Martian calendar in which certain "years" are 669 days long, and others are 670 days long. Carefully explain which years are designated as leap years.

Good Time on Mars:

Well, first of all, why not carefully explain how you came up with the number 669.3? The correct value is 668.6 Martian solar days (called "sols"). More precise values depend on the type of Martian year being referenced. The purpose of this Harvard site is to develop innovative mathematics assessment tasks and help teachers to use them in their classrooms. The Martian calendar problem is a wonderful opportunity for students to exercise their creativity and problem-solving skills, but of course they need to start out with the correct information.

NASA/Ames Research Center

Bad Time on Mars:

http://quest.arc.nasa.gov/mars/ask/misc/Martian_calendar_and_leap_years.txt

From various sources we find that the Martian year is 686.98 Earth days. The Mars solar day (sol) is considered to have a length of 24 hours, 39 minutes, and 35.25 seconds (24,65979 days); it is usually abbreviated as sol. So the Martian year has (686.98 * 24) / 24,65979 = 668.59937 Martian days.

Of course, we should not use the siderial Martian year, but a synodial but I do not have data about that.

Good Time on Mars:

The mathematical competence of the writer has to be questioned from the fact that he begins with a figure for the Martian year in Earth days that has 5-digit precision, and ends up with a figure for the Martian year in Martian sols that has 8-digit precision. In fact, the Martian year is currently not known to that precision. His calculation comes closest to the figure for the Martian sidereal (which he misspells) year, which is 668.5991 sols.

He also misspells "synodic," and even if he spelled it correctly, why would he propose that it should be the basis of a Martian calendar when he does "not have data about that?" And why doesn't he have data about that? Any but the most basic-level astronomy texts give the synodic period of the planets.

What is a synodic period? The synodic period of any two planets is the time it takes for a given alignment to recur. For instance, Mars was in solar opposition to Earth in late August 2003. When will the next opposition occur? This is a very easy thing to calculate:

   1           1        1
-------  =   ----- +  -----
Synodic        Y1       Y2

where Y1 is the annual period of Planet 1 and Y2 is the annual period of Planet 2.

The mean synodic period for Earth and Mars with respect to each other is 779.94 days, or 759.07 sols. The time from one alignment to the next varies by a few days due to the eccentricity of Mars' orbit, for Mars moves more quickly in its orbit when it is closer to the Sun.

But there's something wrong with the idea of basing the Martian calendar on the synodic period. Mars undergoes seasonal climate changes due both to the inclination of its rotational axis to its orbital plane, and due to the eccentricity of its orbit. Thus, one could make an argument in favor of basing the Martian calendar on the tropical year, one of the equinox or solstice years, or even on the anomalistic year, but what is the argument in favor of using the synodic period? Yet Mr. Wennmacker says "of course" we should use it. This is not science, it's unsubstantiated opinion.

DISHONORABLE MENTION

NASA/Jet Propulsion Laboratory

JPL gives us a double shot of bad time.

Bad Time on Mars:

http://mars.jpl.nasa.gov/classroom/pdfs/marscalendarproject.pdf

Mars has a rotation rate such that one day or sol (Martian day) equals 24.6 hours or 24 hours, 37 minutes.

Good Time on Mars:

This is the value for the Martian sidereal day, and it cannot be used as the basis for a Martian calendar. The length of the the Martian solar day is 24 hours, 39 minutes, 35.244 seconds. This NASA/JPL site is meant to help teachers develop astronomy as part of their classroom curricula. Once again, the Martian calendar problem is a wonderful opportunity for students to exercise their creativity and problem-solving skills, but of course they need to start out with the correct information.

Bad Time on Mars:

http://marsprogram.jpl.nasa.gov/classroom/pdfs/Earth.Mars_Poster.back.pdf

Mars orbits the Sun in 687 Earth days or 670 Mars sols.

Good Time on Mars:

687 Earth days... yes. 670 Mars sols... not! If one divides the Martian year of 687 Earth days by the Martian sidereal day of 1.025954 Earth days, one arrives at the number of Martian sidereal days in a Martian year, which is approximately 670. The problem is that a Martian calendar must be based on the Martian solar day of 24 hours, 39.6 minutes, or sol, just as Earth calendars are based on the terrestrial solar day of 24 hours. The correct figure is 668.6 sols. If you can't trust NASA/JPL to supply good information on astronomy, who can you trust? But then, aren't these the same poeple who couldn't tell feet from meters, causing the Mars Climate Orbiter to smash into the planet in 1999?

Planetary Society

Bad Time on Mars:

http://www.planetary.org/explore/topics/mars/calendar.html

Time on Mars is easily divided into days based on its rotation rate and years based on its orbit. Sols, or Martian solar days, are only 37 minutes and 22 seconds longer than Earth days, and there are 668 sols (684 Earth days) in a Martian year.

Good Time on Mars:

One wonders how often the same error will propagate thoughout the Web without being checked. A Martian sideral day is 24 hours, 37 minutes, and 22 seconds; Martian solar day is 24 hours, 39 minutes, and 35.244 seconds. Also, the statement that there are 668 sols in a Martian year is a bit inaccurate; the correct figure is 668.59, which is closer to 669 sols if one wants to round off to the nearest integer. Finally, are there 684 Earth days in a Martian year? Nope! The correct figure is 687 days, which one can find in just about any astronomy book.

Robert Roy Britt

Bad Time on Mars:

http://www.space.com/scienceastronomy/101_earth_facts_030722-2.html

12. How long is a Martian year?

It's a year long, if you're from Mars. To an earthling, it's nearly twice as long. The red planet takes 687 Earth-days to go around the Sun -- compared to 365 days for Earth. Taking into account Mars' different rotational time (see #13 below) calendars on Mars would be about 670 days long with some leap days needed to keep things square. If you find one, please mail it to me. I'm curious how they worked out the months, given they have two moons. [The initial publication of this fact mistakenly said a Mars calendar would have 687 days.]

13. How long is the average Martian day?

A Martian can sleep (or work) and extra half-hour every day compared to you. Mars days are 24 hours and 37 minutes long, compared to 23 hours, 56 minutes on Earth. A day on any planet in our solar system is determined by how long it takes the world to spin once on its axis, making the Sun appear to rise in the morning and sending it down in the evening.

Good Time on Mars:

There is one true statement here, albeit tautological: a Martian year is a year long. Mr. Britt should have quit while he was ahead. Eventually he caught on to the fact that a Martian calendar would not have 687 days (actually, sols), but 670 sols isn't the right number either. How did he get it wrong again? If one divides the Martian year of 687 Earth days by the Martian sidereal day of 1.025954 Earth days, one arrives at the number of Martian sidereal days in a Martian year, which is approximately 670. The problem is that a Martian calendar must be based on the Martian solar day of 24 hours, 39.6 minutes, or sol, just as Earth calendars are based on the terrestrial solar day of 24 hours. But Mr. Britt might not have made these calculations... he might have gotten bad time from JPL instead.

In regard to a Martian calendar, Mr. Britt asks, "If you find one, please mail it to me. I'm curious how they worked out the months...." Apparently he wasn't curious enough to even do a Google search, which would have pointed him to dozens of examples.

THIRD PRIZE

Gary Barnhard, M.S., aerospace engineering

Bad Time on Mars:

http://www.marsnews.com/missions/science_lab/

In 2012, NASA's Mars Exploration Program landed a sophisticated new roving vehicle on the Red Planet. Dubbed the "Mars Science Laboratory" and also known as "Curiosity", it is much larger than the Mars Exploration Rovers Spirit and Opportunity, and is planned to operate on the surface for at least an entire Martian Year or 687 "sols", representing a dramatic increase over the planned lifespan of 90 "sols" that the current rovers are designed for.

Good Time on Mars:

You know the drill by now. A Martian year is 687 Earth days, but 668.6 sols.

From http://www.nss.org/about/bios/barnhard.html, we learn:

Gary Barnhard is the owner and president of Barnhard Associates, LLC, a systems engineering consulting firm and Internet Service Provider (Xisp.net) based in Cabin John, Maryland. He is a robotic space systems engineer whose professional work includes a wide range of robotic, space, and computer systems engineering projects.

Be afraid. Be very afraid.

SECOND PRIZE (tie)

James Lovelock, D.Sc., biophysics

Bad Time on Mars:

http://www.ops-alaska.com/time/authors/lovelock/lovelock.htm

Mars has a year of 687 days. To be more precise, it is 686.9804 days, which means we have 'leap years' every so often to keep the calendar straight. Our 'leap years' are not like those of Earth, though, which is why I use the expression in quotation marks. On Mars leap years come every fifty-one years, and we lose a day.

Good Time on Mars:

This is the most basic error in Martian timekeeping that anyone can make. Obviously, a Martian calendar must be based on the number of turns that Mars makes during the course of its year, not the number of turns that Earth makes in a Martian year. Since a sol is 24 hours, 39 minutes, 35.244 seconds, or 1.0275 Earth days, the number of sols in a Martian year is 686.98 / 1.0275 = 668.6 sols. Again, more precise values depend on the type of Martian year being referenced.

The Martian year is already long enough. Making it even longer is one of the worst possible times you can have on Mars!

Gunter Faure, Ph.D, geology
Professor Emeritus, School of Earth Science, Ohio State University

Teresa M. Mensing, Ph.D, geology
Professor Emeritus, School of Earth Science, Ohio State University

Bad Time on Mars:

https://books.google.com/VeryLongURL

One day on Mars (called a sol) is 37 minutes and 22 seconds longer than one day on Earth. Therefore, one sol is equal to 1.0259 Earth days and one year on Mars contains:

     686.98
     ------ = 669.63 sols
     1.0259

The sidereal periods of revolution and rotation on Mars in Table 12.3 may someday become the basis for a martian calendar to be used by humans living on Mars.

Good Time on Mars:

James Lovelock can be excused for not knowing the time of sol on Mars, as his field is biophysics, but it is unforgiveable for two planetary scientists not to know the correct number of sols in a Martian year. Where Faure and Mensing go wrong is in mistaking the length of the Martian sidereal day as the length of the Martian solar day (sol). As shown by the other examples in this article, this is a very common error, and here it produces the erroneous value for the number of sols in a Martian year. It is a really bad time on Mars when authors of a planetary science textbook get it wrong!

GRAND BOOBY PRIZE

Robert Zubrin, Ph.D., astronautical engineering

Bad Time on Mars:

http://www.ops-alaska.com/time/authors/zubrin/zubrin.htm

For those interested in calculating exact dates, the equation to use is:

Mars Year = 1 + 8/15 (Earth Year - 1961)

Good Time on Mars:

There is nothing "exact" about this. The fundamental flaw in Zubrin's approach is that it is based on approximations, whereas calculating a calendar must be as precise as possible, for any errors accumulate over time. In his equation, the Earth date is expressed as:

year + [(the numeric value of the Gregorian month - 1) x 30.4
        + (the numeric day of the month - 1)] / 365

The Martian date in year-month-day format must be extracted from the numeric value resulting from the basic equation.

Two approximations in Zubrin's algorithm accumulate to induce significant errors. First of all, he derives the length of the Martian year from the ratio of 15 Earth years to 8 Martian years. This is not terribly accurate. Earth’s year, measured from one vernal equinox to the next, is 365.2424 days. A Martian year, measured from one vernal equinox to the next, is 686.9710 Earth days. This means that in 15 Earth years, there are only 7.975062 Martian years. This doesn’t sound like much of a discrepancy, but it is, as you will see in a moment.

While less severe, the other error in Zubrin’s calculations is that he assumes there are 365 days per Earth year, whereas the actual value is 365.2424. Since the length of the Martian year is tied directly to the length of the Earth year via the 15:8 ratio, this short value for the Earth year has the effect of further shortening the duration of the Martian year in Zubrin’s algorithm. The combined error results in a Martian year of only 15/8 x 365 = 684.375 Earth days in Zubrin’s calendar.

When considering a Martian calendar, one needs to talk in terms of the Martian solar day (known as the "sol"), which is 2.75 percent longer than an Earth day. There are 668.6 sols in a Martian year. Because he uses the inaccurate 15:8 ratio and assumes 365 days in an Earth year, Zubrin’s calendar really has only 15/8 x 365/1.0275 = 666 sols in a Martian year. With this number in mind, you could say that Zubrin invented one "hell" of a Martian calendar!

For a detailed analysis of Zubrin's Martian calendar, see "A Critique of Robert Zubrin’s Martian Calendar."

We hope you have enjoyed your bad time on Mars. We think you won't find a more miserable time anywhere else in the solar system!