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Home , Day, Equation of time, Hour, Sidereal year, Solar time, Timekeeping on Mars

What is it on ? (Some features of the physics of time) Dr Vincent Smith, School of Physics, University of Bristol (1)What -is- time ? (2) How we measure time on (3) Time on Mars What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know. (St Augustine)

What is time ? It produces change, rhythm, … It decides the order of events

A great philosopher once said: “Time is what stops everything happening at once !” (in fact, without time, nothing happens)

Is time an illusion ? Is the already decided ? Does time flow, or do we just move through a fixed landscape ? Do we have free will ?

If time flows, can we swim against the current ?

Is time a straight line, or a circle ? (a succession of universes ?)

“Time is what measure…” → We can measure the passage of time in two ways:

(1) Repetition (‘15 ’) /, the , your pulse, the ticking of a , …

(2) Evolution (or decay) Growth, maturity, old , , …

It’s important to distinguish two meanings of the English word ‘time’:

(1) time interval, , elapsed time between two events;

(2) absolute time, time coordinate or label, ‘’, age, …

For this, we need a ‘time zero’ or origin: often a matter of convention, for example BC/AD, Julian , Chinese, Jewish, Muslim New , AVC, 68EII, etc…also time, Central European time, etc… Choice of a clock: count regular events (what is regular ? agreement between different devices) Advances in physics have produced more and more accurate clocks: Drips of water, , and balance wheel, quartz crystal, …

The Earth as a clock on its axis: day →

NB Earth rotates once every 23hr 56 min wrt (a ‘sidereal’ day) (so there are 366 sidereal days per year), but each day it moves forward in its and the is in a slightly different position, so is 4 min later each day (365 solar days per year.)

Revolution of the round Earth: (29.531…solar days) Revolution of Earth round Sun: year (365.2422…solar days) (Similar to choice of day, there are different definitions of , different … see later) If we choose the day, how to subdivide it ? 24 (Babylonians) By day: a : shadow of a ‘’ which points to the North Celestial Pole → By night (or when it’s cloudy!): the clepsydra () →

When to start the day ? , , , ? 12hr day, 12hr night, all year round ? (In middle ages, work all day, sleep all night!) Solar time changes with place ():

Bristol time is 11 later than Greenwich →

Solution: times zones round the Earth. → But solar time also changes through the year! There are two contributions:

(1) The path of the Earth round the Sun is not a circle, but an ellipse. Its speed is faster at perihelion (January) than at aphelion (July.)

(2) The Earth turns at a steady rate relative to the stars (once every 23hr56min, or 366 times in a year), but once every 24hr relative to the Sun, or 365 times in a year. If the Sun made its annual journey at the level of the , its speed would be constant, but it travels 23½º North and South. →

Thus its speed changes with the seasons, and so solar (sundial) time is ahead or behind the average time (‘mean time’.) The two effects together produce the ‘’: the difference between actual solar time and mean solar time: originally used to correct clocks to show sundial time, but now used to correct to show mean time. → (NB unequal sunrise/sunset times: shortest day is on 21 December, but earliest sunset comes a before, latest sunrise a week after.) NB Two sorts of year:

(1) Sun returns to same place wrt stars (same place in ) – . (2) Sun returns to same place wrt equator, eg crosses it going N (spring in N hemisphere): same seasons – .

But the Earth wobbles as it spins, the north pole points to different places in the , and the equator crosses the Earth’s orbit at different places. So these definitions are not the same: about 20 min difference per year ( = one whole year in 25,000 years.)

This is called the ‘ of the ’: the equinoxes move round the zodiac once every 25,000 years.

The ‘First Point of ’ is now in Pisces (or is it the ‘age of Aquarius’ ?) Length of the year (or synchronisation of the with the seasons…)

1 year = 365.2422 days (not exactly 365.25)

Julius Caesar’s calendar had one in every four. The result was too long: the seasons crept later and later in the year. Pope Gregory decided to suppress these extra days (10 days cut out in 1582) and to avoid leap years in 1700, 1800, etc (but 2000, 2400, etc remain as leap years.) 1 Gregorian year = 365.2425 days. Britain waited until 1752 to join this scheme ! (11 days by then…)

The is good until at least 5000 AD. (But search for the Revised , identical to Gregorian until 2600 AD.)

Aside: why 31, 28, 31, … days per month ? And 365 = 52 x 7 + 1. ‘’: (31,30,30) x 4 + 1 extra day (or 2 in a leap year.) Formally used by Bulgarian Orthodox . But using the rotation of the Earth is not a very accurate way to measure time: the Earth’s rotation is not constant: it is gradually slowing down, by century.

In times, when the coal forests were growing, (360 million years ago) the day was only 22 hr long. So instead of the Earth, we use the most accurate clocks we have made so far: atomic clocks.

The Earth is still slowing down: to bring our clocks back in step, we add one most years! I don’t have time (!) to talk about the progress of timekeeping technology from , to springs, to quartz and to atomic clocks, or of the physics of each choice, but I’ll just quote our definition of the second in the SI:

“The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the -133 ” (1967) and what about the inverse (reciprocal) second ? … How to change the time at a distance:

We need two equations: (1) for a steady speed, distance = speed x time (I call this Pickering’s equation, after my school maths teacher, who taught it to me.)

(2) Arrival time = departure time + journey time (I like to call this Smith’s equation, since I discovered it independently.)

Suppose there is an happening now at the centre of the (that is, at a distance of x = 30,000 light-years.) A radio signal will reach here after x/c = 30,000 years.

But if I walk at 1 m/s towards the centre of the galaxy, and I continue for 30,000 years ( = 3.104.3.107 = 1012 s), I will have covered v.x/c = 1012 m, and I will be that much closer to the centre. Because of this, the signal will reach me vx/c2 = 1012/(3.108) = 3600 s = 1 before it reaches you. But from my point of view, I am at rest, and you are moving at 1 m/s to the rear. The centre of the galaxy is approaching me at 1 m/s, but the radio signal has to travel all the way from where the centre was when it left there. It travels the same distance at the same speed for me, as it does for you, so it has the same journey time. Of course, it reaches you an hour after it reaches me, but that is because you are 1012 m further away after those 30,000 years.

Thus we record arrival times for the signal which differ by one hour, even though the journey times are the same. The only explanation is that the departure times were also different by one hour ( vx/c2) !

We can translate from your time to my time using the equation: t′ = ( t – vx/c2 )

(For experts, there is also a factor of γ, but this is negligible at 1 m/s ) By the way, although what you call now at the centre of the galaxy is one hour ago for me, and what I call now will happen in one hour’s time by your clock, neither of us will know anything about it for 30,000 years, and we can’t influence it for another 30,000 years.

------What time is it on Mars ? →

(a) Relative to the Sun:

Mars turns on its axis once every 24h 39m 35.2 s = a ‘’ (=24.65 h)

And its year is 687 of our days, ie 668.59 of its ‘sols’.→ Its orbit is more eccentric than ours, but its inclination is much the same (25º)

The difference between the start of its actual solar day and its mean solar day (its ) can vary by up to ±50 minutes. → explorers, meteorologists (and farmers ?) will need to know the time of sunrise, noon, etc by reference to the real sun, so they will need to keep a clock with a varying length of the day.

Of course, the start of the day will also depend on longitude, so they may divide Mars into time zones like the Earth (24 or 24.7 of them ?), or perhaps they may just keep to local times, especially if there are only a few bases. How to subdivide year ? 668/669 Sols, but what about , months ?

Perhaps 24 months of 27/28 sols ? (compare the World Calendar ?) Or 20 months of 33/34 sols? (closest to Earth months…) Or 18 months of 37/38 sols (favoured by Patrick Moore) Or just count sol 1 to sol 668/669 (no weeks or months) Your chance to name the months!

How to subdivide the Sol ? 24 Mars hours, minutes, (each 2.7% longer than Earth hours, etc) 24 Earth hours, plus extra ~ 40 minutes before midnight ? Or just give decimal fraction of the Sol ?

There are many interesting ideas out there on the Web, (including many from various nutters.) Wikipedia “” is a good one. So is Nagin Cox: What time is it on Mars? | TED Talk (b) will also want to know Earth time…

Mars is between 75 million km and 325 million km from Earth, depending on our relative positions in our .

The signal delay between Mars and Earth will vary between 4 minutes and 20 minutes in each direction, which will make telephone conversations difficult !

The relative speed can be between 0 and ±50 km/s along our line of sight, so the differences due to Special Relativity are only ±50 ms. An astronaut on Mars who wishes to know the time to this accuracy will need to know this difference as it changes through the year, and add or subtract it from his clock to know the exact time on Earth. When there are atomic clocks on Mars, this effect will become important ! (There will also be a small correction (GR) for the lower gravity at the surface of Mars.)

If we get this far, it’s THE END.