Physics & Astronomy Modules

# Time in Astrophysics

## The nature of time

We perceive time as a passage of events, a marker of change. The daily cycles of Sun rise and set, the monthly phases of the Moon, and the annual repeating seasons are natural "clocks", standards that are references for other changes. We see in how we currently measure distance that time and distance are entwined, that our distance scale of the meter derives from our time scale based on an oscillating atom and the remarkable constancy of the speed of light. Einstein found it very helpful to treat time as another dimension, like space in some ways, and connected to it so that space and time mix. Moving clocks run slow to outside observers. Moving lengths shorten.

Classical physics regards time as uniformly passing and continuous, that is it is not discrete, evenly divided into the smallest measurable increments in modern experiments that can see events in atoms and molecules lasting less than 10-15 second. While Newton thought of time as absolute, as if there is one cosmic time that is the same everywhere, we know now that is not the case. Time is altered not only by motion, but also by gravity. A clock close to the Earth runs a little slower than one out in orbit.

In astrophysics applied to nearby events, we think of time in the way that Newton did, while realizing under some circumstances that will fail. Of course this then begs the question, why does time go only one way? In classical physics we can run the theoretical clock backward. In either direction, the universe is predictable, and seemingly reversible. The universe is symmetric with respect to time in the details, but the real world has a past, and a future. At least a part of the answer to this puzzling state lies in the idea of entropy, insuring more disorder as time goes by.

## The Measurement of Time

The standard unit of time is set in terms of Earth's rotation on its axis, that is how long on average it takes for the Sun to return to the same position east-west in the sky. We divide that day by 24 to get an hour, and the hour by 60 to get a minute, and the minute by 60 to get a second. Time synchronized in that way is called solar time, and is the reason we have a time keeping system that has 12's and 6's instead of 10's. and 1000's.

The problem with solar time is that the Earth's rotation is not constant, and the appearance of the Sun as it crosses the mid-day sky also depends on the speed of Earth in its non-circular orbit around the Sun. The result is that from day-to-day as measured by a steady clock the local noon is not at exactly the same clock time. For example, on January 16, 2017, in Richmond, Virginia, local solar noon is at 12:20 US Eastern Standard Time. A month later, on February 16, noon is at 12:24. The Earth is not a good clock.

Nevertheless, we used Earth for centuries as we grew to understand the astronomical reasons for these variations. We defined a standard place on Earth to measure from, the meridian that runs through Greenwich, England that we call the Prime Meridian. Averaged over the year then our clocks were set to Greenwich Mean Time, or GMT, and we kept them synchronized by observing distant stars as our reference, rather than the Sun, because we could make even more precise and frequent measurements that way. GMT is also affected by Earth's crustal motion, and we correct for that to have a time system called Universal Time, or UT1.

We established this system in which the Earth was found to complete an orbit with referenced to stars outside our solar system with a period of

1 sidereal year = 365.256363 days

and to rotate once on its axis with an average period with respect to stars of

1 sidereal day = 86 164.1005 seconds

Averaged over a year, measured from noon to noon

1 mean solar day = 86,400.0016 s

while the day is defined to be exactly

1 day = 86,400 s

That is, the real day is just slightly longer than our convention, but you would not notice it from day to day. You would notice it after a few years, when the discrepancy amounts to a second. Consequently, every few years we have been dropping a second from the clock so it stays in step with reality.

Fundamentally, the problem with keeping time based on the Earth is that its motions are not constant, so using it is like using a rubber ruler. A solution is to use the natural oscillations of the electronic structure of a cesium atom, and to compare clocks in many different countries so as to have an average that is not subject to local environmental effects. This system is International Atomic Time, or TAI. The TAI time scale was set to match UT1 on January 1, 1958. Of course the problem does not end there, since atomic clocks have random errors and are located on a moving Earth and subject to Earth's gravitational effects (which alter time!).

The international (SI for systeme international) agreed unit of time is the second as defined by the atomic clocks. TAI is a uniformly running time, and it is used to set UTC, "coordinated universal time", which also flows uniformly. As of January 2017, UTC was 37 seconds behind the TAI clock so that it is within 1 second of the non-uniform UT1 that is synchronized to Earth's rotation.

Why is this important? It is because physics depends on time, and to predict motion we must know the time. It is also because to determine position using the speed of light, we measure time as well. Your GPS depends on time measurements as accurate as 1/billionth of a second, a nanosecond. That is the time interval over which light travels 1 foot.

While we keep time relative to the Earth's position in space at some instant in the past, you can find a time here on Earth from the National Institute of Standards in the US that is set by the oscillations of an atomic master clock at

## Absolute and Relative Time

Is there an absolute time scale to the universe, and can we measure time in the same way everywhere? At first it may seem so. We know the universe had a beginning when it was infinitesimally small and the Big Bang launched the cosmic expansion that has been going on ever since. Our best current meassurement puts that zero point at

Age of Universe = 13.82 billion ($1.382 \times 10^{10}$) years

In terms of our local situation

Age of Earth = 4.54 billion ($4.54 \times 10^9$) years

which are known to remarkable precision from measurements based on physics.

Apart from the non-uniformity of the Earth's rotation rate, we have atomic clocks that are precise enough to run GPS and allow us to navigate the solar system. Nevertheless, though it seems that time is absolute in this context, the rate at which time passes, and therefore the perception of time, depends on relative motion. This is a stunning outcome of Special Relativity, and it means that all time is relative, and there is no absolute universal time measurement. Also, time passes differently in the presence of gravity, a discovery of General Relativity that has been verified even in the weak field of Earth's gravity (indeed, GPS would not work if General Relativity were not included in the calculations). This video from Veritassium shows how our brains affect the perception of time and causality.

While to us it seems that time is absolute, it is not. The measure of time will differ depending on what sources of gravity are nearby and the relative speeds of the clock being measured and the observer.

## Barycentric time

For determining properties of systems distant from Earth based on observations made here or on spacecraft, we must have a agreed upon system of time keeping, in effect a place on which to stand to make these measurements. The surface of Earth is a moving location following a very complex path set by the rotation of the planet and its interaction with the Sun, Moon, and other planets. Even apart from the relativistic effects of gravity and relative velocities, the transit time of signal across the solar system affects our perception of when events occur. Jupiter, nominally 5 astronomical units from the Sun, may be as far away as 48 light minutes, or as close as 32. The prediction of where its satellites will appear to be has to take into account the light travel time. For the purpose of modeling astronomical events, the standard reference is the barycenter of the solar system. This is the point in space which in our local frame of reference we can regard as stationary, the center of mass of the Sun and all the components of its system. Of course it is not stationary, but itself in motion around the Milky Way, which is also in motion with repect to other galaxies.

The Julian day or JD provides a continuous time system in which the base time interval is the solar day, referenced to noon UTC in our current time keeping system. That is, at midnight the JD will be an integer plus 0.5. On August 22, 2021, at 5 PM EDT the JD at the moment was 2459449.375 when UTC was 21.000 hours, since UTC is calculated from midnight when JD was 2459448.5. The large integer value of JD stems from the zero point of the scale, which is a date before any written history. That is, the JD at midnight is an integer plus 0.5, and at noon UTC it is exactly the next integer. In this example it has been 21 hours since midnight UTC, or $21/24 = 0.875$ of a day since then, and $2459448.5 + 0.875 = 2459449.375$ . At noon the JD was 2459449.0.

Because the large integer part can overflow computers with insufficient word size, a Modified Julian Day or MJD subtracts 2400000.5 and also sets the zero point midnight, thus simplifying calculations connected to UTC. However the barycentric JD or BJD keeps the full count and adjusts the time to the arrival of a signal at the solar system barycenter. Adding to the diversity, there is a topopcentric JD as well, which is when the signal would arrive at the local observatory, and a geocentric JD for the signal arriving at the reference position of Earth's center at that moment. Conversion of times from those observed to BJD is a complex process requiring knowledge of the location of the observer, Earth's reference surface, the Earth's position relative to the Sun, and the location of the solar system barycenter in this coordinate system.