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Among the following two methods what is the right way to get the Mars sol date?

  1. Using this equation from Timekpeeing on Mars Wikipedia page

    MSD = (Julian Date using International Atomic Time - 2451549.5 + 1/7200)/1.02749125 + 44796.0

Feb 18, 2022 as Julian Date is 2459628.88889. If we do the calculation with this value, MSD becomes 52658 and 52658%668 is 554. This means today is day 554 of 668 on Mars.

  1. New Year as Feb 7, 2021, and 1 sol as 24 hour 39 minutes 35 seconds

    MSD = (time difference between Feb 7, 2021, and today in seconds)/88775.24 (Mars' sol in seconds)

On this NASA website it states Mars' New Year is Feb 7, 2021, and one sol lasts 24 hours 39 minutes, and 35 seconds.

Time difference between Feb 18, 2022, 00:00:00 and Feb 7, 2021, 00:00:00 in seconds is 32486400.

And if we divided 32486400 by 88775.24 (Mars sol in seconds) it gives us 365.93

Like this, if we do calculations based on these two given facts today becomes day 365 of 668

These two methods yield two different results. Can someone help to figure out which one is right?

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    $\begingroup$ Welcome to the site. You need to edit and add your formulae and calculations if you expect an answer. $\endgroup$
    – GdD
    Feb 18 at 9:21
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    $\begingroup$ @GdD thanks for the feedback, just updated the post $\endgroup$
    – Seungjun
    Feb 18 at 10:03
  • $\begingroup$ upvoting because it's been a while since I actually dug through a paper to try to answer an SE question. that was fun, thanks for asking the question $\endgroup$
    – Erin Anne
    Jun 26 at 5:00

2 Answers 2

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Reading further down the Wikipedia page, it is clear that no general agreement exists on how the Martian calendar should be described. There are at least seven different proposed calendars, but none of them have been widely accepted as the right way, so there isn't one right calculation.

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The Mars Solar Date system is defined by Michael Allison and Megan McEwen in their paper "A post-Pathfinder evaluation of aerocentric solar coordinates with improved timing recipes for Mars seasonal/diurnal climate studies."

They note in the paragraph surrounding Equation 32 (which defines MSD in a way mathematically identical to your definition) that MSD 0 corresponds to a Mars $L_s$ of 277.13 degrees. The MSD scale isn't defined to start at 0 at the beginning of a Martian solar year ($L_s = 0$), and this likely accounts for the hundreds-of-sols discrepancy you're finding between your methods.

The paper's explanation for their Equation 22 (not a typo; the MSD equation 32 is derived from 22, which gives a Martian Mean Solar Time) includes all the magic constants in the equation you give for MSD apart from the 1/7200:

JD 2451549.5 (2000 January 06 00:00:00) corresponds to a near coincidence of the terrestrial Greenwich mean solar midnight and the Martian mean solar (prime meridian) midnight. The addition of the integer number 44796 assures a positive result for the indicated fractional part in (22) for any date since JD 2405522 (1873 December 29.5).

That 1873 date is MSD 0, apparently chosen to simplify solar time calculations.

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just to verify, the MSD for Feb 7 2021 (the beginning of Mars Year 36) is 52293, 364-and-change sols prior to Feb 18 2022. Given that Mars Year 36 needn't have started at 0 UTC, the fractional error between that result and the result of your second method is negligible. If you want to know the MSD, use the first method. If you want to know how many sols have passed since the beginning of the latest Mars year, use the second. The purposes don't really overlap.

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