How to calculate Coordinated Mars Time (MTC)?

Question

I'm trying to figure out how to calculate Coordinated Mars Time (MTC). Can it be calculated directly from Earths current time/date, or calculated from the current Mars Sol Date (MSD)?

From this wiki page I can calculate the current Mars Sol Date using:

MSD = (Julian Date using International Atomic Time - 2451549.5 + k)/1.02749125 + 44796.0, where k is a small correction of approximately 0.00014 d (or 12 s)

but how would one calculate Coordinated Mars Time?

Answer 1

The fractional part of MTC corresponds to a period of 24 Martian hours.

So,

${HH \over 24} + {MM \over 60 \cdot 24} + {SS \over 60 \cdot 60 \cdot 24} = frac(MSD)$

Conversion in the opposite direction is a little more complicated: If $frac$ is the fractional part of a number, and $floor$ is the integer part (rounding by truncation), then,

$$ F_h = frac(MSD); \\ HH = floor(24 \cdot F_h) \\ F_m = frac(24 \cdot F_h) \\ MM = floor(60 \cdot F_m) \\ SS = 60 \cdot frac(60 \cdot F_m) \\ $$

Note:

1. This is according to the convention o using a 24-hour "Mars clock" on which the hours, minutes and seconds are 2.7% longer than their standard (Earth) durations. That means these aren't SI system seconds - these are arbitrary periods of time corresponding to 1/(24*60*60)th of Sol.
2. HH and MM are integers. SS are given as a Real, including the fractional part of the "second".

_{we should really find some better names for these time units}

Answer 2

On the page you refer: 

https://en.wikipedia.org/wiki/Timekeeping_on_Mars#Formulas_to_compute_MSD_and_MTC

MTC is simply the fractional part of MSD, in hours, minutes and seconds:

MTC = (MSD mod 1) × 24 h