Katie Paterson
—there lay the Days between—, 2021
A ‘ticker clock’ recording every Earthly sunrise since the beginning of our planet’s history,
edition 1 of 5 with 2 APs
edition 1 of 5 with 2 APs
130.3 x 42.8 x 15 cm
51 1/4 x 16 7/8 x 5 7/8 in
(not yet fabricated)
51 1/4 x 16 7/8 x 5 7/8 in
(not yet fabricated)
A ticker clock displaying the number of sunrises since Earth began Katie Paterson Sunrise and sunset are markers of time: daily reminders of the Earth’s rotation on its axis and...
A ticker clock
displaying the number of sunrises since Earth began
Katie Paterson
Sunrise and sunset are markers of time: daily reminders of the Earth’s rotation on its axis and our proximity to the Sun. To create this new artwork, we had to establish a number that accounts for each sunrise since Earth’s origin.
How many sunrises have passed since Earth began?
This may seem like a simple enough question. In fact, creating this artwork has involved exploring some of life's biggest questions including theories of the origin of Earth and Earth-Moon system. There have been some inconclusive answers. Yet, we have pushed the limits available to us to establish the number shown in the artwork. In doing so we have undertaken innovative research in the sciences and arts. This has involved investigating various field of research in geology and astronomy including: tidal friction; the Earth-Moon system; theories of the origin of the Moon; thermal evolution of the Earth’s core; paleotidal and paleorotational data; rhythmites; meteorites; rocks; solar eclipses; as well as the history of timekeeping. Our collaborators include Dr Steve Fossey, University College London; Professor Catherine Heymans, Astronomer Royal, Scotland; and Professor Carl Murray, Queen Mary University, London.
We know that the length of one day on Earth has changed through time. We also know that the length of one year has remained (pretty much) the same. From this we can determine that if we are able to generate a reasonable estimate for the length of day through Earth’s history then we can state the total number of sunrises since Earth began 4.54 billion years ago.
How has the length of day changed?
Our research has focused on the following:
1. Tidal Friction: the Earth - Moon System. The Moon’s orbit is getting gradually larger and therefore the rotational speed of the Earth is getting gradually slower.
2. Thermal evolution of Earth’s core.
On the whole we know that the Earth's rotation on its own axis is slowing down. We have found that this is largely due to tidal friction: the tidal effects that the Moon has on the Earth’s rotation. The law of conservation of angular momentum tells us that the Earth's rotation speeds up when the Moon is near the Earth and slows down when the Moon is away from the Earth. The length of day is also affected by the thermal evolution of Earth’s core. Currently this effect is minor.
Earth rotates once in about 24 hours with respect to the Sun, but once every 23 hours, 56 minutes, and 4 seconds with respect to other, distant, stars. Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth's rotation. Atomic clocks show that a modern-day is longer by about 1.7 milliseconds than a century
2
ago, slowly increasing the rate at which UTC is adjusted by leap seconds. Analysis of historical astronomical records shows a slowing trend; the length of a day increased about 2.3 milliseconds per century since the 8th century BCE. Scientists reported that in 2020 Earth has started spinning faster, after consistently slowing down in the decades before. Because of that, engineers worldwide are discussing a 'negative leap second' and other possible timekeeping measures.
Core
There is ongoing debate on whether core formation occurred quickly at the beginning of the Earth’s life through hot accretion (the most common theory); or if core formation occurred via cold accretion in the Archaen/Proterozoic era (2500 million years ago). The thermal radiation produced by the energetics of core formation have been found to have an impact on the length of day. This impact currently is very minor. Tidal friction is far more significant. However, in the early life of Earth this may have been the other way around. The paper Astron. Nachr / AN (2011) models quantitively different kinds of core formation scenarios to determine which scenarios would best agree with the empirical paleo-LOD data - i.e which scenario best matches the geological evidence we can find through meteorites and rocks.
Tides
Kant first hypothesized that the motion of ocean tides raised mainly by the Moon and by the Sun exerts a force “on continental margins and the sea floor that slowly retards the Earth”. This was in 1754, at that point Kant could not find any historical evidence to back this up. Delauney picked it up in 1865. Since then it has been widely recognised as true.
Essentially the gravitational pull of the Moon upon Earth’s oceans (‘tidal bulge’) affects the speed of Earth’s axial rotation. This is because the Moon’s elliptical orbit is increasing in size; the Earth and the Moon are getting farther away from one another. Therefore the length of day is slowing down over time. This has played a significant role in the length of day since the formation of the Earth-Moon system.
The leading theory of the Moon's origin is that a Mars-sized body (Theia) collided with the Earth approximately 4.51 billion years ago, and the resulting debris from both Earth and the impactor accumulated to form our natural satellite. The newly formed Moon was in a molten state. We have looked into the paper “Geological Constraints on the Precambrian History of Earth’s Rotation and the Moon’s Orbit”, which examines the evidence in sedimentary rocks to track the distance of the Earth from the Moon. It tells us that there is not enough evidence in the geological record to determine what this distance is - from 4.5 billion years ago. The paper explores how sedimentology provides a way to trace the history of ‘Earth’s tidal deceleration and the evolving lunar orbit through analysis of sedimentary tidal rhythmites’. A rhythmite consists of layers of sediment or
3
sedimentary rock which are laid down with an obvious periodicity and regularity. They may be created by annual processes such as seasonally varying deposits reflecting variations in the runoff cycle, by shorter term processes such as tides, or by longer term processes such as periodic floods. Rhythmites serve a significant role in unraveling prehistoric events.
Certain marine deposits that were modulated by tidal cycles show us ‘paleotidal’ and ‘paleorotational’ data for the late Neoproterozoic (1BYA – 541MYA). From here we know that the length of day at this time (about 620mya) was 21.9hrs +/- 0.4hrs. The average rate of lunar recession since then is 2.17 +/-0.31 cm per year. We also know that now the rate of lunar recession is 3.82 +/-0.07 cm / year (this is measured via lunar laser ranging).
A closer look at the science
To determine the number of sunrises since Earth began, we have looked to these scientific papers as our primary references:
• “Geological Constraints On The Precambrian History Of Earth's Rotation And The Moon's Orbit” (Williams, 2000). This paper deals with the geo-physics, analysing sedimentary tidal rhythmites to gain understanding of the Earth-Moon system, particularly looking at its beginnings and tidal friction.
• “Milankovitch Period Uncertainties And Their Impact On Cyclostratigraphy” (Waltham, 2015). This paper is focussed on geology and analysing sedimentary tidal rhythmites to gain understanding of the Earth-Moon system and tidal friction.
• “Measurement Of The Earth’s Rotation: 720 BC to AD 2015” (Stephenson, Morrison, Hohenkerk, 2016). This observational astronomy paper looks to records of ancient eclipses and lunar occultations to investigate variations in the Earth's rotational rate.
• “Proterozoic Milankovitch Cycles And The History Of The Solar System” (Meyers, Malinverno, 2017). The geologic record of Milankovitch climate cycles provides a conceptual and temporal framework for evaluating Earth system evolution.
The paper “Measurement of the Earth’s rotation: 720BC to AD 2015” compiles ancient, medieval eclipses from the period 720 BC to 1600, and lunar occultations of stars from 1600 – 2015 to investigate the rate of the Earth’s rotation. These records show that the rate of change in the length of day is on average +1.8 milliseconds per century. This is significantly less than the rate predicted on the basis of tidal friction which is 2.3 milliseconds per century. The difference can probably be attributed in part to the rate of change in Earth’s oblateness due to the changing load of the polar caps following the last deglaciation.
4
Over a period of several centuries—from the eighth century BC until perhaps well into the first century AD—Babylonian astronomers systematically measured the times of the beginning, end and often maximum of eclipses (in addition to observing other lunar and planetary events). The Babylonian scribes wrote on clay tablets, using a cuneiform script, which is now well understood. It just so happens that, because there are so many broken texts, we often have only the time of first contact. One of their motives for observation was to improve prediction of future eclipses, and many predictions (usually of the time of onset of an eclipse) are cited in the astronomical texts.
Crucially: we have adopted the definition of sunrise or sunset as the moment when the upper limb of the Sun is on the visible horizon, allowing for a mean refraction of 34′.
By assuming a form of Waltham’s (2015) simplified model of the tidal friction increasing smoothly and exponentially with time since Earth-Moon formation, and assuming the Elatina-Reynella tidal rhythmite point is correct, we were able to work back in time to the formation of the Earth-Moon system to make an estimate of the tidal friction and therefore the evolution of the Moon's orbital distance throughout time. From this, using Professor Carl Murray’s formula for converting the Moon’s orbit to day length, we used the assumed tidal-model friction and the lunar recession rate (adopting the solar eclipse research and rhythmite analysis) and generated the length of day throughout time. Allowing for uncertainties in the current lunar recession rate and the Elatina- Reynella point, we can say that within the simplifying assumptions of this model, the deep-time ‘base’ number we have calculated has an estimated precision of a few percent (to improve accuracy, a more comprehensive treatment applying the complex physics underlying the changing evolution of the Moon’s actual tidal friction is required).
Sundials
Babylonians and Egyptians built obelisks in which moving shadows formed a kind of sundial, enabling citizens to divide the day in two parts by indicating noon. The oldest known sundial was found in Egypt and dates from the time of Thutmose III: about 1,500 years BC. The duration of hour was constantly changing throughout the year and was equal to 1/12 of the time from sunrise to sunset or from sunset to sunrise. Hour duration hence varied depending on the latitude and time of year.
5
We have chosen to work into our total figure, the number of sunrises that have occurred since the time of this early sundial in 1500BC. This is 3520 years ago, which at Jan 1st 2021 is 1285680 days ago, and to bring the number up to today October 12th 2021 adds 283 days. This number increases by one each subsequent passing day. Total sunrises since 1500 BC = 1285963. Total sunrises = 2265200514262 (base)+1285963 (+1 daily). Beginning on 12th October 2021 the number of sunrises on Earth is:
2265201800225
2 trillion 265 billion 201 million 800 thousand 225
displaying the number of sunrises since Earth began
Katie Paterson
Sunrise and sunset are markers of time: daily reminders of the Earth’s rotation on its axis and our proximity to the Sun. To create this new artwork, we had to establish a number that accounts for each sunrise since Earth’s origin.
How many sunrises have passed since Earth began?
This may seem like a simple enough question. In fact, creating this artwork has involved exploring some of life's biggest questions including theories of the origin of Earth and Earth-Moon system. There have been some inconclusive answers. Yet, we have pushed the limits available to us to establish the number shown in the artwork. In doing so we have undertaken innovative research in the sciences and arts. This has involved investigating various field of research in geology and astronomy including: tidal friction; the Earth-Moon system; theories of the origin of the Moon; thermal evolution of the Earth’s core; paleotidal and paleorotational data; rhythmites; meteorites; rocks; solar eclipses; as well as the history of timekeeping. Our collaborators include Dr Steve Fossey, University College London; Professor Catherine Heymans, Astronomer Royal, Scotland; and Professor Carl Murray, Queen Mary University, London.
We know that the length of one day on Earth has changed through time. We also know that the length of one year has remained (pretty much) the same. From this we can determine that if we are able to generate a reasonable estimate for the length of day through Earth’s history then we can state the total number of sunrises since Earth began 4.54 billion years ago.
How has the length of day changed?
Our research has focused on the following:
1. Tidal Friction: the Earth - Moon System. The Moon’s orbit is getting gradually larger and therefore the rotational speed of the Earth is getting gradually slower.
2. Thermal evolution of Earth’s core.
On the whole we know that the Earth's rotation on its own axis is slowing down. We have found that this is largely due to tidal friction: the tidal effects that the Moon has on the Earth’s rotation. The law of conservation of angular momentum tells us that the Earth's rotation speeds up when the Moon is near the Earth and slows down when the Moon is away from the Earth. The length of day is also affected by the thermal evolution of Earth’s core. Currently this effect is minor.
Earth rotates once in about 24 hours with respect to the Sun, but once every 23 hours, 56 minutes, and 4 seconds with respect to other, distant, stars. Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth's rotation. Atomic clocks show that a modern-day is longer by about 1.7 milliseconds than a century
2
ago, slowly increasing the rate at which UTC is adjusted by leap seconds. Analysis of historical astronomical records shows a slowing trend; the length of a day increased about 2.3 milliseconds per century since the 8th century BCE. Scientists reported that in 2020 Earth has started spinning faster, after consistently slowing down in the decades before. Because of that, engineers worldwide are discussing a 'negative leap second' and other possible timekeeping measures.
Core
There is ongoing debate on whether core formation occurred quickly at the beginning of the Earth’s life through hot accretion (the most common theory); or if core formation occurred via cold accretion in the Archaen/Proterozoic era (2500 million years ago). The thermal radiation produced by the energetics of core formation have been found to have an impact on the length of day. This impact currently is very minor. Tidal friction is far more significant. However, in the early life of Earth this may have been the other way around. The paper Astron. Nachr / AN (2011) models quantitively different kinds of core formation scenarios to determine which scenarios would best agree with the empirical paleo-LOD data - i.e which scenario best matches the geological evidence we can find through meteorites and rocks.
Tides
Kant first hypothesized that the motion of ocean tides raised mainly by the Moon and by the Sun exerts a force “on continental margins and the sea floor that slowly retards the Earth”. This was in 1754, at that point Kant could not find any historical evidence to back this up. Delauney picked it up in 1865. Since then it has been widely recognised as true.
Essentially the gravitational pull of the Moon upon Earth’s oceans (‘tidal bulge’) affects the speed of Earth’s axial rotation. This is because the Moon’s elliptical orbit is increasing in size; the Earth and the Moon are getting farther away from one another. Therefore the length of day is slowing down over time. This has played a significant role in the length of day since the formation of the Earth-Moon system.
The leading theory of the Moon's origin is that a Mars-sized body (Theia) collided with the Earth approximately 4.51 billion years ago, and the resulting debris from both Earth and the impactor accumulated to form our natural satellite. The newly formed Moon was in a molten state. We have looked into the paper “Geological Constraints on the Precambrian History of Earth’s Rotation and the Moon’s Orbit”, which examines the evidence in sedimentary rocks to track the distance of the Earth from the Moon. It tells us that there is not enough evidence in the geological record to determine what this distance is - from 4.5 billion years ago. The paper explores how sedimentology provides a way to trace the history of ‘Earth’s tidal deceleration and the evolving lunar orbit through analysis of sedimentary tidal rhythmites’. A rhythmite consists of layers of sediment or
3
sedimentary rock which are laid down with an obvious periodicity and regularity. They may be created by annual processes such as seasonally varying deposits reflecting variations in the runoff cycle, by shorter term processes such as tides, or by longer term processes such as periodic floods. Rhythmites serve a significant role in unraveling prehistoric events.
Certain marine deposits that were modulated by tidal cycles show us ‘paleotidal’ and ‘paleorotational’ data for the late Neoproterozoic (1BYA – 541MYA). From here we know that the length of day at this time (about 620mya) was 21.9hrs +/- 0.4hrs. The average rate of lunar recession since then is 2.17 +/-0.31 cm per year. We also know that now the rate of lunar recession is 3.82 +/-0.07 cm / year (this is measured via lunar laser ranging).
A closer look at the science
To determine the number of sunrises since Earth began, we have looked to these scientific papers as our primary references:
• “Geological Constraints On The Precambrian History Of Earth's Rotation And The Moon's Orbit” (Williams, 2000). This paper deals with the geo-physics, analysing sedimentary tidal rhythmites to gain understanding of the Earth-Moon system, particularly looking at its beginnings and tidal friction.
• “Milankovitch Period Uncertainties And Their Impact On Cyclostratigraphy” (Waltham, 2015). This paper is focussed on geology and analysing sedimentary tidal rhythmites to gain understanding of the Earth-Moon system and tidal friction.
• “Measurement Of The Earth’s Rotation: 720 BC to AD 2015” (Stephenson, Morrison, Hohenkerk, 2016). This observational astronomy paper looks to records of ancient eclipses and lunar occultations to investigate variations in the Earth's rotational rate.
• “Proterozoic Milankovitch Cycles And The History Of The Solar System” (Meyers, Malinverno, 2017). The geologic record of Milankovitch climate cycles provides a conceptual and temporal framework for evaluating Earth system evolution.
The paper “Measurement of the Earth’s rotation: 720BC to AD 2015” compiles ancient, medieval eclipses from the period 720 BC to 1600, and lunar occultations of stars from 1600 – 2015 to investigate the rate of the Earth’s rotation. These records show that the rate of change in the length of day is on average +1.8 milliseconds per century. This is significantly less than the rate predicted on the basis of tidal friction which is 2.3 milliseconds per century. The difference can probably be attributed in part to the rate of change in Earth’s oblateness due to the changing load of the polar caps following the last deglaciation.
4
Over a period of several centuries—from the eighth century BC until perhaps well into the first century AD—Babylonian astronomers systematically measured the times of the beginning, end and often maximum of eclipses (in addition to observing other lunar and planetary events). The Babylonian scribes wrote on clay tablets, using a cuneiform script, which is now well understood. It just so happens that, because there are so many broken texts, we often have only the time of first contact. One of their motives for observation was to improve prediction of future eclipses, and many predictions (usually of the time of onset of an eclipse) are cited in the astronomical texts.
Crucially: we have adopted the definition of sunrise or sunset as the moment when the upper limb of the Sun is on the visible horizon, allowing for a mean refraction of 34′.
By assuming a form of Waltham’s (2015) simplified model of the tidal friction increasing smoothly and exponentially with time since Earth-Moon formation, and assuming the Elatina-Reynella tidal rhythmite point is correct, we were able to work back in time to the formation of the Earth-Moon system to make an estimate of the tidal friction and therefore the evolution of the Moon's orbital distance throughout time. From this, using Professor Carl Murray’s formula for converting the Moon’s orbit to day length, we used the assumed tidal-model friction and the lunar recession rate (adopting the solar eclipse research and rhythmite analysis) and generated the length of day throughout time. Allowing for uncertainties in the current lunar recession rate and the Elatina- Reynella point, we can say that within the simplifying assumptions of this model, the deep-time ‘base’ number we have calculated has an estimated precision of a few percent (to improve accuracy, a more comprehensive treatment applying the complex physics underlying the changing evolution of the Moon’s actual tidal friction is required).
Sundials
Babylonians and Egyptians built obelisks in which moving shadows formed a kind of sundial, enabling citizens to divide the day in two parts by indicating noon. The oldest known sundial was found in Egypt and dates from the time of Thutmose III: about 1,500 years BC. The duration of hour was constantly changing throughout the year and was equal to 1/12 of the time from sunrise to sunset or from sunset to sunrise. Hour duration hence varied depending on the latitude and time of year.
5
We have chosen to work into our total figure, the number of sunrises that have occurred since the time of this early sundial in 1500BC. This is 3520 years ago, which at Jan 1st 2021 is 1285680 days ago, and to bring the number up to today October 12th 2021 adds 283 days. This number increases by one each subsequent passing day. Total sunrises since 1500 BC = 1285963. Total sunrises = 2265200514262 (base)+1285963 (+1 daily). Beginning on 12th October 2021 the number of sunrises on Earth is:
2265201800225
2 trillion 265 billion 201 million 800 thousand 225