What Causes Time Dilation on Mars?

[goodabouthood]

Is this as simple as the Earth making one complete revolution around the Sun in one year?

Would you say Mars makes the revolution around the Sun in x year(s) and that is its time?

I take it we are using time relative to the Sun in these questions.

 

[Ryan_m_b]

Are you asking what time of the year it is on Mars? Obviously the time depends on where on Mars you are talking about.

 

[goodabouthood]

I just want to know how one figures out the time on Mars or even on Earth for that matter.

Or for instance is time slower or faster on Mars than Earth and what does that imply?

 

[Drakkith]

I just want to know how one figures out the time on Mars or even on Earth for that matter.

Or for instance is time slower or faster on Mars than Earth and what does that imply?

The way we determine the amount of time that has passed is based on clocks which initially used the sun to base our day on. One can use the same 24 hour time on mars, however this would not match with Mars rotational period. We could easily use that rotational period to base the Martian day on however. Whichever one you use is simply based on preference and circumstances.

Our year is simply how long it takes the Earth to make one full orbit around the sun. Mars takes a longer period of time to orbit once due to its increased distance and slower orbital speed.

 

[TMEubanks]

Time is slippery, and this question has at least 3 (really 4!) answers.

First, there is "what day is it?" Mars has a different length of day than the Earth's - close, but not the same. A Mars day is called a "sol;" lander activities being measured in sols. For some reason I cannot fathom, each lander has started with "sol = 0" when it landed, even the lander / rovers than have come down in pairs close together in time (i.e., Viking 1 and 2 and MER A and B). So, something that happened on Sol 500 for MER-A ("Spirit") happened on a different Sol on MER-B (Opportunity). (I have suggested that Sols for Viking Lander 1 should be the Martian equivalent of Julian Days on the Earth (an uninterrupted count from a particular early date), but so far no one has adopted this.)

Second, there is "what season is it?" Mars has seasons (at this epoch) much like the Earth's, of course with a longer year, and there have been several proposals forMartian Calendars. There is not even uniformity as to the number of months - the calendar I linked to above has 12 months of up to 70 sols, while the Darian Calendar has 24 months, of 27 or 28 sols each. As far as I know, no astronomer or space mission has made use of these calendars, although they certainly worry about the seasons.

Third, there is "what is the time of day," or, "what solar time is it?" Just as on Earth, the amount of sunlight varies with the season, and there is also a (larger) "equation of time" (i.e., the local solar noon can http://www.giss.nasa.gov/research/briefs/allison_02/.) The Martian orbital eccentricity is large enough that it cannot be ignored in local solar time, even at a crude level. Since missions need to know the times of sunrise, noon and sunset, this has been calculated and used right from the start of Martian exploration.

Fourth, there is "what second is it" or (really) "is there a Martian coordinated time?" Time keeping on Mars has to date almost entirely been done on Earth, and transferred to Mars, as a good clock has never been sent to Mars. Actual spacecraft time is typically only good at the second level or so, and the only need for independent timing on Mars has been during superior conjunctions, the one or two week period when Mars is almost behind the Sun, and communications are difficult or impossible. For that, again, relatively crude clocks and roughly a second accuracy as sufficient.

With the Deep Space Atomic Clock (DSAC), where a very good clock will be included on missions to use for navigation. In addition, Phobos Grunt also has a good clock, the "Ultra-Stable Oscillator," that willl hopefully go to Phobos. Once two such clocks are sent to Mars, there will be a need for coordination of Martian timekeeping (i.e., for Mars Coordinated Time, or MTC). Because neither the Earth nor Mars is in a circular orbit, MTC will drift back and forth with respect to UTC. That can be calculated, but whether MTC will be allowed to free run (i.e., to be a true time scale) or kept synced to UTC, is way too soon to tell.

 

[goodabouthood]

Do clocks tick slower on Mars than on Earth? I would imagine this is due to gravity but I'm not sure.

 

[TMEubanks]

Clocks tick faster on Mars. Its gravity is less, and (more importantly) it is further out in the solar gravitational well. Just as GPS clocks are made to run fast to match UTC, MTC clocks could be made to run fast and not drift off from UTC, but (unlike GPS) the eccentricity of the two orbits means that there will be periodic offsets that cannot be removed by just a rate change

 

[Janus]

I just want to know how one figures out the time on Mars or even on Earth for that matter.

Or for instance is time slower or faster on Mars than Earth and what does that imply?

The base unit of time, the second wouldn't be any different ( too many scientific constants rely on the second as a unit of time), but the mean Solar day( call a "Sol", and is the average time from noon to noon.) would be about 40 min longer than Earth's,(88775.24409 sec vs. 86400 sec) and a year would be ~668.6 Sols long.

Developing a clock for Mars would be interesting. How do you solve for the problem of those additional 2375.24409 secs if you don't change the length of the sec? I guess you could create a new unit, (a Marsec?) as the Martian civil version of the sec equal to 1.027491251 standard seconds. This would allow you to keep 86400 marsec per Sol, 60 Marsec per Mars minute (Mminute?) and 60 Mminutes per Martian Hr(Mhour) and 24 Mhours per Sol.

Another option would be to keep the standard 24 hr clock and let it drift with respect to the Martian Sol. With this system local dawn would jump ~40 mins per day.

A possible third option would be to keep the standard 24 hr clock and readjust it by ~40 min every Sol. For instance at, 12:40 AM the clocks adjust back to 12 midnight. Easy for digital clocks, a bit of hassle for mechanical ones. A disadvantage would be that each Sol would have two period of times that covered 12 midnight to 12:40 AM. Thus you would have to indicate which time period you were considering (did you mean first 12:30 AM or second 12:30 AM?)

Developing a calendar for Mars that keeps in step with the local seasons would have to take this into account. For instance, you could still have 12 months split between 4 of 55 sols in length and 8 of 56 sols(8 weeks if we keep the 7 "day" week), or if you want to keep the month about the same length, you could go with 24 months, split between 20 of 28 sols( exactly four weeks in length) and 4 of 27 sols.

You will still have to account for the ~.6 Sols left over. You would have to institute some type of leap year system, that would add 3 leap Sols every 5 Martian yrs. You could add a day every 20th month for the 12 mo calendar or every 40th month for the 24 mo calendar. If we space our short months throughout the year (every 3rd, or every 6th mo), we can add our leap day to the closest short month to the end of each 20 or 40 mo cycle (when it doesn't already fall on a short month).

Such a calendar would only drift off by a 1 day approximately every 1600 years. And this can be accounted for by dropping a normally scheduled leap day every 16 centuries (much like we do with our calendar every 400 yrs.) This should keep our calendar synced to the seasons to a fairly high accuracy over an extended period.

 

[russ_watters]

What did the rover teams do, D_H?

 

[D H]

What did the rover teams do, D_H?

They used sols and seconds, just as described by Janus. Sols are important because many of the sensors on the rovers are passive. Seconds are important because there are just too many physical constants that are based on the second. Besides, the second is no longer tied to an Earth day. It is just "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom (at zero K)"

 

[goodabouthood]

Let's say I had two clocks that were synchronized on Earth. Ignoring the effects of traveling to Mars I take one clock and put it on Mars.

Now what happens to the clock on Mars? And why?

 

[TMEubanks]

Let's say I had two clocks that were synchronized on Earth. Ignoring the effects of traveling to Mars I take one clock and put it on Mars.

Now what happens to the clock on Mars? And why?

The Martian clock will tick faster, and thus gain on the terrestrial clock, and so they will get out of sync. The Martian clock is further out in the solar potential well (more gravitational potential means slower time), so it is faster. It is moving slower than the Earth in orbital velocity, so it is faster again. (The first effect is predicted by General Relativity, the second by both General and Special Relativity.)

The above is true for a clock on anybody in the outer solar system. Now, it happens that Mars is less smaller and massive than the Earth, and so the Martian clock will also tick faster because is is on a smaller body, with less rotational velocity (assuming that neither clock is on its planet's poles). That effect is smaller, but should be observable.

And, that is really it (at least in general relativity), except that to actually predict the clock sync offset you need to worry about the actual orbits of the two planets, including their orbital eccentricity and at least the major perturbations from the other planets. Also, in practice you will measure sync by passing photons back and forth between the two clocks, and so you in practice will need to accurately determine the orbits and rotation of the Earth and Mars, and also account for the Shapiro delay of the photons in the solar and planetary potentials.