Kurzgesagt – In a Nutshell
Sources – Moon Crash
We thank the following experts for their help with this script:
Dr. Matthew Caplan
Illinois State University
Dr. Tenley Banik
Illinois State University
Dr. Michael Sussman
Dr. Lucas Kreuzer
Deutsches Zentrum für Luft- und Raumfahrt
Sources – What if the moon fell?
– We know that earth’s gravity pulls everything towards it, including the Moon, but somehow, it stays up, as if suspended by some opposite force. But there is no other force countering gravity - instead, the trick to staying up is a ‘sideways’ motion that we call an orbit. You see orbits every day: when you throw a ball it makes a tiny little orbit. The only difference between that ball’s orbit and the moon’s is that the ball eventually hits the ground. Basically, the reason is speed.
#NASA, What Is an Orbit?, 2017
https://www.nasa.gov/audience/forstudents/k-4/stories/nasa-knows/what-is-orbit-k4.html
Quote: “An orbit is a path. It's the way something goes around an object in space. The moon goes in orbit around Earth. You're in orbit right now! That's because Earth is following an orbit all the way around the sun. The International Space Station orbits Earth. An object in orbit is called a satellite. A satellite can be natural, like the moon. It can be human-made, like the space station. Earth is a natural satellite of the sun.
[...]
An orbit is a curved path, like a circle or an oval. (The technical word is "ellipse.") A comet's orbit is very long and thin. Sometimes the comet is close to the sun and moves quickly. Most of the time it is far from the sun and moves slowly. The moon's orbit is almost circular.”
– If you could throw your ball fast enough, it would bend around the world and come back to you. If there was no air slowing it down, it could orbit forever. And this is what the moon does: Falling sideways around earth, very fast, with no air slowing it down. Orbiting earth every 27 days, at 3600 km/h.
Staying in orbit means moving around the Earth at a certain velocity. Small orbits need higher velocities. Large orbits need lower velocities. There are simplified explanations for why this happens. You could imagine a satellite as a ball at the end of a piece of string, being spun around. A centrifugal force appears to lift the ball outwards, and it is countered by the pull of the string, just like an orbiting satellite seems to be able to counter gravity. The reality is that ‘centrifugal force’ is a fictitious thing and gravity is an illusion caused by the curvature of space-time in general relativity. Or maybe, according to quantum mechanics, gravity is a force carried by a massless particle called the graviton just like light is carried by the photon… scientists aren’t sure. No-one has a complete explanation. But we do have simple methods that can describe what happens to an orbit even if we don’t really know why.
A satellite orbiting just outside the Earth’s atmosphere, at an altitude of 160 kilometers, travels around the Earth at 7800 m/s or 28,080 km/h.
In our hypothetical baseball scenario, we would need a velocity of 7905 m/s or 28,458 km/h to perform a circular orbit around the Earth.
The Moon orbits at an average altitude of 384,400 kilometers, so its orbit is a much slower 1022 m/s or 3680 km/h.
#ESA, Low Earth orbit?, 2020
https://www.esa.int/ESA_Multimedia/Images/2020/03/Low_Earth_orbit
Quote: “A low Earth orbit (LEO) is, as the name suggests, an orbit that is relatively close to Earth’s surface. It is normally at an altitude of less than 1000 km but could be as low as 160 km above Earth – which is low compared to other orbits, but still very far above Earth’s surface.
[...]
LEO’s close proximity to Earth makes it useful for several reasons. It is the orbit most commonly used for satellite imaging, as being near the surface allows it to take images of higher resolution. It is also the orbit used for the International Space Station (ISS), as it is easier for astronauts to travel to and from it at a shorter distance. Satellites in this orbit travel at a speed of around 7.8 km per second; at this speed, a satellite takes approximately 90 minutes to circle Earth, meaning the ISS travels around Earth about 16 times a day.”
#NASA, Moon Fact Sheet, retrieved 2021
https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
You can calculate the orbital velocity at each altitude around the Earth using this calculator:
#Keisan, Orbit of a satellite Calculator, retrieved 2021
https://keisan.casio.com/exec/system/1224665242?lang=en&charset=utf-8&var_h=24000&ketasu=14
Set the orbit to 160 km for a satellite in Low Earth Orbit, or to 0 km for a baseball at ground level.
– In a nutshell, to change an object’s orbit, you need to change its speed, which changes where gravity takes it.
The Moon wants to travel in a straight line. Gravity bends its trajectory. If the gravitational pull and the Moon’s speed are balanced exactly right, the Moon goes in a circle around the Earth.
#NASA/University of Waikato, Earth-Moon system and gravity, 2013
https://www.sciencelearn.org.nz/images/260-earth-moon-system-and-gravity
We know that there is a relationship between gravity, mass, velocity and the orbit of a satellite, as described in the following equation:
#San Francisco State University, Some Useful Relations Governing Satellite Motion, retrieved 2021
http://www.geosci.sfsu.edu/geosciences/classes/m415_715/Monteverdi/Satellite/Geosynchronous.html
G is a universal constant. Mcentral in this case is the mass of the Earth. R is the radius of the satellite’s orbit, measured from the center of the Earth. We cannot change the gravitational constant G, nor the mass of the Earth. With these aspects fixed, the only factor affecting a (circular) orbit is velocity. Therefore, to change the orbital radius R, we must change the satellite’s velocity v.
– But even small changes require enormous forces, which is why all the large objects in the solar system are so stable nowadays.
The Solar System is filled with very large objects. You can sometimes look at the numbers for their mass and orbital velocity and fail to comprehend just how large they are. Hundreds to thousands of billion-billion tons, traveling at tens of kilometers per second around the Sun. Multiply the mass by the velocity to get the momentum. That monumental number you get is what you have to face if you want to modify the orbits of these objects.
Still, gravity can manage to disrupt these orbits. Its influence can extend over large distances and it can chip away at this momentum over the course of many years. Planets pull on each other, moons align with the Sun and comets passing at high velocity can all add up to modify an orbit.
Because of these factors, we consider the planets in the Solar System to be stable over extremely long periods. We can accurately predict their positions millions of years into the future. This is because the time period over which the Solar System remains ordered and predictable, also called the Lyapunov time, is estimated to be 5-10 million years.
The planet Uranus would take a billion billion years to be ejected from the Solar System due to interactions with the other gas giants - longer than the lifetime of our Sun.
#Renu Malhotra, Matthew Holman, and Takashi Ito. Chaos and stability of the solar system, 2001.
https://www.pnas.org/content/98/22/12342
Quote: “The orbital evolution of planetary orbits on giga-year time scales has been investigated recently via several numerical simulations. These have led to a most interesting conclusion that the orbits of the planets themselves evolve chaotically. The characteristic Lyapunov time is 5–10 million years.[...] The theory also confirms the numerical estimate of the Lyapunov time associated with this chaos and shows that the escape time of Uranus is long (10^18 years), substantially longer than the lifetime of our sun.”
– According to science, the moon is big and very massive. Even igniting billions of rocket engines all over its surface would barely move the Moon.
Let’s perform a rough estimate for how hard it is to move the Moon.
A big rocket engine, like the SpaceX Merlin, produces 981,000 Newtons of thrust. A billion of them would produce roughly 10^15 Newtons.
#SpaceX, Falcon 9, retrieved 2021
The Moon’s mass is 7.34x10^22 kg.
If we divide thrust by mass, we get acceleration. In this case, we obtain 1.36x10^-8 m/s^2 or about 1.17 mm/s every day. That’s a billion times less than the acceleration of a typical rocket from a launchpad.
#Moon Fact Sheet, NASA, retrieved 2021
https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
The Electron Rocket from Rocket Lab starts on the launchpad with a mass of 13,000 kg. Its nine engines give it an initial thrust of 224,190 Newtons. Its initial acceleration is therefore 17.2 m/s^2.
#RocketLab, Payload user’s guide, 2020
https://www.rocketlabusa.com/assets/Uploads/Rocket-Lab-Launch-Payload-Users-Guide-6.5.pdf
Quote: “VEHICLE MASS (LIFTOFF)
13,000KG”
Quote: “STAGE 1
PROPULSION
9X RUTHERFORD SEA LEVEL ENGINES
THRUST
5600 LBF SEA LEVEL (PER ENGINE)”
– For the first few days, nothing really changes. The moon gets a tiny bit brighter and scientists get confused, but the rest of us don’t notice anything different.
The Moon’s brightness naturally varies as it gets closer or further from the Sun during its orbit around the Earth.
#Cathay Jordan, Why do the size and brightness of the full moon change?, retrieved 2021
Quote: “There are several other factors that affect the brightness of the full moon. When the Earth (and therefore the Moon) is at its perihelion, the closest point in its orbit to the Sun, the sunlight that reflects off the Moon is slightly more intense, causing the full moon's brightness to increase by about 4%, which is imperceptible by the human eye.”
The Moon’s orbit is not perfectly circular either. 384,000 km is only the average; its distance from the Earth actually varies between 357,000 and 407,000 km. It appears 407,000/357,000 = 1.14 or 14% larger at its closest point than at its further point.
In our falling Moon scenario, the Moon’s average size will increase slowly, only appearing 384,000/200,000 = 1.92 or 92% larger after month 2 when the distance to the Earth has been reduced to 200,000 km.
#NASA, Moon Fact Sheet, retrieved 2021
https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
Quote: “The orbit changes over the course of the year so the distance
from the Moon to Earth roughly ranges from 357,000 km to 407,000 km”
Professor Matt Caplan simulated the position of the Moon as it comes closer to the Earth in our scenario (the units are hundreds thousand kilometers):
And according to that simulation, here is the decreasing distance of the Earth to the Moon. The orange line is an altitude of 35,800 km:
One thing you might notice is the changing face of the Moon.
Currently, the Moon's orbit around the Earth's and the Moon's rotation around itself are in sync. Both take 30 days. So we always see one face pointed towards the Earth. As the Moon gets closer, its orbits will get shorter but its rotation rate will stay the same. So we will see the other faces of the Moon and even the ‘far side’ we never see today.
The NASA link below contains images generated from the Lunar Reconnaissance Orbiter and shows us all the faces we will end up seeing.
#NASA, The Far Side of the Moon -- And All the Way Around, 2011
https://www.nasa.gov/mission_pages/LRO/news/lro-farside.html
– The only noticeable real effect of the moon on the earth are the tides. Tides exist because while earth pulls on the moon, the moon’s gravity pulls back on the earth. Since the strength of gravity gets weaker with distance, different parts of the earth feel a slightly different pull. Which causes the earth, especially the oceans, to bulge when the moon is above them, and contract a little on the sides when it’s not.
Tides are changes in the gravitational forces on the Earth causing the oceans to shift. The major sources of these forces are the Sun and Moon. The Moon has a much weaker gravitational pull than the Sun but it is much closer to us, so lunar tides are much stronger than solar tides.
#NOAA, Tides and Water Levels, retrieved 2021
https://oceanservice.noaa.gov/education/tutorial_tides/tides06_variations.html
Quote: “The moon is a major influence on the Earth’s tides, but the sun also generates considerable tidal forces. Solar tides are about half as large as lunar tides and are expressed as a variation of lunar tidal patterns, not as a separate set of tides. When the sun, moon, and Earth are in alignment (at the time of the new or full moon), the solar tide has an additive effect on the lunar tide, creating extra-high high tides, and very low, low tides—both commonly called spring tides. One week later, when the sun and moon are at right angles to each other, the solar tide partially cancels out the lunar tide and produces moderate tides known as neap tides. During each lunar month, two sets of spring tides and two sets of neap tides occur”
The exact reason why there are tides is because the pull of these gravitational forces is not uniform across the surface of the Earth. The Moon’s pull is stronger on the part of the Earth that is closest to it; the equator facing the Moon, and weakest at the parts furthest from it; the equator facing away from the Moon.
The forces are not all oriented in the same direction either. The pull is parallel to the Moon at the equator but at an angle at the poles. The result is that water is pushed outwards at the equator and pulled inwards at the poles.
Here is a graphic showing the direction and scale of all these forces:
#Dale E. Gary. Physics 320 Lecture Notes, Differential (Tidal) Forces, Precession and Nutation, retrieved 2021
For a version with the moon included in the picture, it looks like the following:
#Todd Thompson, Astronomy 161, Fall 2011, The Ohio State University
http://www.astronomy.ohio-state.edu/~thompson/161/tidalbulge.gif
#University of Rochester, Lunar Tides, retrieved 2021
http://www.pas.rochester.edu/~blackman/ast104/tides.html
Quote. “Consider a water molecule in the ocean. It is attracted gravitationally by the Earth, but it also experiences a much smaller gravitational attraction from the Moon (much smaller because the Moon is much further away and much less massive than the Earth). But this gravitational attraction of the Moon is not limited to the water molecules; in fact, the Moon exerts a gravitational force on every object on and in the Earth. Tides occur because the Earth is a body of finite extent and these forces are not uniform: some parts of the Earth are closer to the Moon than other parts, and since the gravitational force is weaker with increasing distance those parts experience a larger gravitational tug from the Moon than parts that are further away.
[...]
The effect of differential forces on a body is to distort the body. The body of the Earth is rather rigid, so such distortion effects are small (but finite). However, the fluid in the Earth's oceans is much more easily deformed and this leads to significant tidal effects.”
– As earth rotates every day underneath the moon, the moon’s influence fluctuates, causing the water-level of the oceans to rise and fall by about half a meter twice a day.
#Sunil Yeshwant Kelkar and Mohan Rajaram Vaishampayan. Coastal Geomorphology, page 43, 2019
https://books.google.co.uk/books?id=oQ6nDwAAQBAJ&pg=PA43&lpg=PA43#v=onepage&q&f=false
Quote: “The typical tidal range in the open ocean is about 0.6 meters (2 feet) closer to the coast, this range is much greater”
#NOAA, Tides and Water Levels, retrieved 2021
https://oceanservice.noaa.gov/education/tutorial_tides/tides05_lunarday.html
Quote: “Because the Earth rotates through two tidal “bulges” every lunar day, coastal areas experience two high and two low tides every 24 hours and 50 minutes. High tides occur 12 hours and 25 minutes apart. It takes six hours and 12.5 minutes for the water at the shore to go from high to low, or from low to high.”
–But with the moon drawing ever closer, high tide gets higher every day. At first barely noticeable, within a month the moon has covered half the distance to the earth and ocean tides have grown to 4 meters.
In our falling Moon scenario, the forces pulling on the Earth are magnified as the Moon gets closer. The tidal force increases with the inverse cube of distance. It means that the force pulling on the tides, and therefore their height, increases dramatically as the Moon gets closer.
#Chris Mihos, ASTR 221 - Fall 2005 Lecture Notes, Gravitational Tides, retrieved 2021
http://burro.astr.cwru.edu/Academics/Astr221/Gravity/tides.html
We can use that relationship between tidal force and distance to estimate how high the tides get as the Moon gets closer.
In our scenario, the Moon travels from a distance of 384,000 km to 200,000 km in 1 month, so the distance has decreased by a factor 200,000/384,000 = 0.52.
We can estimate that the Moons gravitational pull has increased by 1/(0.52^3) = 7.1, making it about seven times greater than before.
Because the tide height is influenced by the increasing gravity, we can expect them to rise from half a meter to 0.5x7.1=3.55 or about 3.6 meters.
Professor Matt Caplan has a graph showing the increasing height of the tides caused by the Moon’s approach in our scenario:
– Everyday high tide comes and waves flood coastal cities. And there is no end in sight. With the moon drawing ever closer, tides rise ever higher, inundating another city and more inhabited land with salty water every day.
Multiple studies are being conducted on how vulnerable global populations are to sea level rise caused by climate change. The average sea level can increase by 2 meters by the end of the century if we do not manage our emissions. This rise is mostly driven by the melting of the Antarctic ice sheet. It would expose hundreds of millions of people to regular flooding while putting major cities like Calcutta, Miami and Tokyo at risk of destruction.
#Scott A. Kulp and Benjamin H. Strauss, New elevation data triple estimates of global vulnerability to sea-level rise and coastal flooding, 2019
https://www.nature.com/articles/s41467-019-12808-z
Quote: “Most estimates of global mean sea-level rise this century fall below 2 m. [...] Under high emissions, CoastalDEM indicates up to 630 M people live on land below projected annual flood levels for 2100, and up to 340 M for mid-century, versus roughly 250 M at present. We estimate one billion people now occupy land less than 10 m above current high tide lines, including 230 M below 1 m.”
The following paper lists the cities most vulnerable to flooding, but the figures are from 2007; they would be even higher today as global population has increased and more people have moved to coastal cities.
#OECD, Ranking of the world’s cities most exposed to coastal flooding today and in the future, 2007
Quote: “Table 1: Top 20 cities ranked in terms of population exposed to coastal flooding in the 2070s (including both climate change and socioeconomic change) and showing present-day exposure (Source: Nicholls et al (2007), OECD, Paris)”
A falling moon would cause sea levels to rise to far greater heights than just two meters. The amplitude of destruction and flooding would be much greater as a result, with humanity watching the seas advance and retract twice a day with the tides.
– By the end of month 2 the moon has covered two-thirds of the distance to earth, and global infrastructure is crumbling as tides rise above ten meters – displacing up to a billion people who happen to live near the coastlines.
We know that the tidal force increases with the inverse cube of distance as the distance decreases. We can use that relationship to estimate how high the tides get as the Moon approaches.
#John Taylor, Classical Mechanics, page 335, 2005
http://www.pacificcrn.com/Upload/file/201702/22/20170222175913_71935.pdf
By now, the Moon has travelled from a distance of 384,000 km to a distance of 133,000 km, so the distance has decreased by a factor 133,000/384,000 = 0.346
We can estimate that its gravitational pull has increased to 1/(0.346^3) = 24.1 times greater than before. We can therefore expect the tides to rise from half a meter to 0.5x24.1 = 12.05 or about 12 meters.
This is what the US east coastline would look like under such conditions, and you can create your own maps with more or less flooding to see what happens:
#Flood Map, 2020
– As ports become inoperable shipping grinds to a halt. Not only will it slow down the delivery of Kurzgesagt products but also less exciting things like food. Global communications fall into disarray – 95% of the internet is carried by ocean-crossing cables, and while these largely don’t mind the water, their terminals on land do. Living inland doesn’t guarantee safety either, tidal bores cause rivers to flow backwards, carrying saltwater to contaminate surface and groundwater supplies.
Ports today are already considered vulnerable to a sea level rise of less than 2 meters; they would be completely overwhelmed by regular sea level rises of 12 meters.
#Austin Becker and Michele Acciaro. A Note on Climate Change Adaptation for Seaports: A Challenge for Global Ports, a Challenge for Global Society, 2013
https://www.nature.com/articles/s41467-019-12808-z
Quote: “Sea level rise of up to 1.9 meters by 2100 indicates that many existing ports will face frequent inundation, even in moderate storm events.”
International Internet infrastructure relies almost entirely on undersea cables and it will be greatly damaged by even moderate sea level rise as the spots where cables come out of the sea and connect to colocation centers (rented data centers) become vulnerable.
#Ramakrishnan Durairajan et al., Lights Out: Climate Change Risk to Internet Infrastructure, 2018
https://ix.cs.uoregon.edu/~ram/papers/ANRW-2018.pdf
Quote: “Our analysis recognizes the vulnerability of buried fiber conduit and colocation centers in coastal areas. The results of our overlap analysis show that ∼4.1k miles of fiber conduit will be under water and over 1.1k colocation centers will be surrounded by water in
the next 15 years.”
#UNEP, Submarine cables and the oceans: connecting the world, 2009
Quote: “There is a common misconception that nowadays most international communications are routed via satellites, when in fact well over 95 per cent of this traffic is actually routed via submarine fibre-optic cables. Data and voice transfer via these cables is not only cheaper, but also much quicker than via satellite.”
Tidal bores can cause seawater to rush up the length of rivers, and seawater intrusion can contaminate fresh water sources.
#Britannica, Tidal bore, retrieved 2021
https://www.britannica.com/science/tidal-bore
Quote: “Tidal bore, also called bore, body of water that, during exceptionally high sea tides, rushes up some rivers and estuaries near a coast where there is a large tidal range and the incoming tide is confined to a narrow channel.”
#MJ Thomas, Sea-level change on the Severn Estuary, 2013
https://orca.cardiff.ac.uk/59443/4/2014thomasphdpt3.pdf
Quote: “Large spring tides commonly lead to the formation of a tidal bore that propagates up the Severn at a height of up to 2m. The wave is formed as the water is funnelled into the narrowing and shallowing channel as the tide rises. Flooding can result when the bore causes overtopping where soils are already saturated, as it did in February 2009”
Quote: “Groundwater and surface water resources may be impacted by salt water intrusion and/or by increased tidal influence within coastal areas, increasing the salinity within estuaries. ”
– Three months in and the moon is close enough to disrupt communication and navigation satellites. While it is normally far too distant for its gravity to cause any major problems for our satellites, the closer it gets the more warped their orbits become. As their fuel for orbital corrections runs out, satellites careen out of control.
As the Moon gets closer to the earth, the higher satellites will get disrupted first and as time passes, progressively lower satellites will get disrupted. The highest regular orbit for a satellite is Geostationary Orbit, at an altitude of about 35,800 km, so those get affected first.
Professor Matt Caplan explains that in chaotic 3-body systems (the Earth, the Moon, the Satellite), it might take hundreds of orbits over the course of weeks to months before the satellite is either ejected into interplanetary space or crashes into one of the bodies. He simulated the trajectories for a few Geostationary Satellites to find out how they would behave as the Moon gets closer. As predicted by theoretical estimates, major disruptions to their orbits occur after the 3rd month of our scenario, resulting in ejections or crashes by the 4th-6th months.
We can see the results of these simulations in the charts below. The blue line is the trajectory of a geostationary satellite. The orange circle is the Earth’s radius. When the lines intersect, it means the satellite has crashed into the Earth.
Here are those same simulations in graph format. The blue line is the satellite’s position and the orange line is the Earth’s radius.
#ESA, Types of orbits, 2020
https://www.esa.int/Enabling_Support/Space_Transportation/Types_of_orbits#GEO
Quote: “Satellites in geostationary orbit (GEO) circle Earth above the equator from west to east following Earth’s rotation – taking 23 hours 56 minutes and 4 seconds – by travelling at exactly the same rate as Earth [...] at an altitude of 35 786 km. This is much farther from Earth’s surface compared to many satellites.”
– On earth, the tides are rapidly growing to about 30 meters and will be reaching 100 m in height in a few short weeks. At low tide, the ocean recedes hundreds of kilometers, exposing the continental shelf like vast deserts, while at high tide walls of water drown agriculture, houses and skyscrapers.
If the Moon orbits at an altitude of 60,000 km, it will create huge tides.
We estimate their height based on the inverse cube relationship the tidal force has with distance.
#John Taylor, Classical Mechanics, page 335, 2005
http://www.pacificcrn.com/Upload/file/201702/22/20170222175913_71935.pdf
The distance of the Moon to Earth after 5 months is 60,000/384,000 = 0.15625 times the original distance.
The tidal force becomes 1/(0.15625^3) = 262.1 times stronger, causing the original half-meter tides to surge from 0.5 meters to about 0.5x262.1 = 131.07 or about 131 meters. This is more than the height of a 30 story building.
The coastlines are often surrounded by continental sea shelves that are very wide and relatively shallow. Huge areas would be exposed when the sea level falls in between these incredible lunar tides.
In the map below, the light blue areas are 5 to 210 meters deep.
#Ocean Basemap, 2021
https://www.arcgis.com/apps/mapviewer/index.html?webmap=5ae9e138a17842688b0b79283a4353f6
– And now, almost five months in, the apocalypse has finished its warm-up act. Since the oceans are on average only 3 kilometers deep, the tides have reached their maximum. Up until now, the water in the oceans could flow, absorbing most of the moon's gravitational squeezing, but now the earth itself is really feeling the squeeze of the ever approaching moon. These aren’t so much tides of ‘water’, but tides of ‘rock.’ The squeezing of the planet, combined with the weight of quintillions of tons of water sloshing on and off the tectonic plates, creates enormous stresses below and begins to cause earthquakes of increasing magnitude and intensity. It’s impossible to say how serious these earthquakes might be or where they occur, but like a child jumping on their bed until it breaks, no good can come of it.
Tidal forces affect everything on the Earth’s surface. Sea tides are most noticeable because water flows easily, but even the rock underneath our feet can bend and flex.
#ESA, Solid Tides, retrieved 2021
https://gssc.esa.int/navipedia/index.php/Solid_Tides
Quote: “Solid tides comprise the Earth's crust movement (and thus the receiver location coordinates variation) due to gravitational attracting forces produced by external bodies, mainly the sun and the moon. The Solid Tides produce vertical and horizontal displacements”
These tides of rock already exist right now, they're just small. They'd be increasing at the same rate that the water tide has been the past few months. According to Dr. Michael Sussman this might lead to progressively increasing earthquake frequency that would've been happening until this point.
– Strong tidal forces lead to volcanism on other planets and moons. On earth, squeezing the planet disrupts the magma reservoirs inside the crust, triggering sizable, climate-altering eruptions in Chile, New Zealand, Yellowstone, and elsewhere.
We have observed moons like Io, the most active satellite of Jupiter, get squeezed by tidal forces so much that its interior melts and volcanoes erupt from its surface.
#Katherine de Kleer et al., Variability in Io's Volcanism on Timescales of Periodic Orbital Changes, 2019
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2019GL082691
Quote: “Tidal heating is one of the central processes that generates heat in the interiors of planets and moons and is in part responsible for the existence of subsurface oceans and geological activity on moons in the outer solar system. Under this process, the amount of heating that occurs, and the stresses in the crust, vary periodically with the periodic tidal flexing.”
It is not certain, but there is some data suggesting that the earthquakes and volcanoes are affected by tidal stresses and are much more likely to erupt at the peak of the lunar cycle, when the Moon and Sun are pulling in the same direction.
#Társilo Girona et al., Sensitivity to lunar cycles prior to the 2007 eruption of Ruapehu volcano, 2018
https://www.nature.com/articles/s41598-018-19307-z
Quote: “A long-standing question in Earth Science is the extent to which seismic and volcanic activity can be regulated by tidal stresses, a repeatable and predictable external excitation induced by the Moon-Sun gravitational force. Fortnightly tides, a ~14-day amplitude modulation of the daily tidal stresses that is associated to lunar cycles, have been suggested to affect volcano dynamics. However, previous studies found contradictory results and remain mostly inconclusive. Here we study how fortnightly tides have affected Ruapehu volcano (New Zealand) from 2004 to 2016 by analysing the rolling correlation between lunar cycles and seismic amplitude recorded close to the crater. The long-term (~1-year) correlation is found to increase significantly (up to confidence level of 5-sigma) during the ~3 months preceding the 2007 phreatic eruption of Ruapehu, thus revealing that the volcano is sensitive to fortnightly tides when it is prone to explode. ”
– Meanwhile, watching patiently above is the moon. Still no bigger in the sky than a small cloud.
As the Moon gets closer, it appears bigger. At 75,000 km, it looks to be 385,000/75,000 = 5.133 or about 5 times larger than its original size.
– Within 75,000 km of earth, it is bright enough to illuminate the night sky like twilight.
We can simplify the Moon as a light source that emits light in all directions. Light is subject to the inverse square law: as we get closer to a light source, its intensity increases by an inverse square factor.
#Hyperphysics, Inverse Square Law Light, retrieved 2021
In the above representation, S is the strength of the light source, r is the distance to the source. Plugging in the corresponding values into the equation, one can calculate the intensity I on a given surface. In our scenario, S is constant, we only change the r since the Moon is approaching Earth. Therefore, when the Moon is at 75,000 which is 0.195 times its original distance, from the inverse square relationship, we can estimate that the light we receive from it becomes 1/(0.195^2) = 26.2 times more intense, assuming nothing else about the Moon changes.
Professor Matt Caplan calculated the brightness of the Moon during its fall to the Earth. Here is a graph of that change:
Reading from the chart above, we find that the lux levels from the Moon on months 6 to 7 are about 10. This is similar to the 10.8 lux of Twilight according to the table below.
#Engineering Toolbox, Illuminance - Recommended Light Level, retrieved 2021
https://www.engineeringtoolbox.com/light-level-rooms-d_708.html
– After half a year, the moon is entering the space once occupied by geosynchronous satellites where it orbits earth every 24 hours. It appears to float at one spot in the sky, unmoving, cycling through a full set of phases every day, but only visible to half the planet. With the moon ‘stationary’ above the earth, the tides seem to freeze in place – half the world flooded, half with its water seemingly returned to the sea, as if Earth is holding its breath to prepare for the worst.
A geostationary orbit has the feature that a satellite placed there would seem to sit above a single spot on the ground, without moving. It is useful for communications as an antenna only needs to point in a single direction to transmit and receive from a satellite rather than tracking it across the sky.
Our Moon in this orbit would also seem to be frozen in place.
# ESA, Types of orbits, 2020
https://www.esa.int/Enabling_Support/Space_Transportation/Types_of_orbits#GEO
Quote: “Satellites in geostationary orbit (GEO) circle Earth above the equator from west to east following Earth’s rotation – taking 23 hours 56 minutes and 4 seconds – by travelling at exactly the same rate as Earth. This makes satellites in GEO appear to be ‘stationary’ over a fixed position. In order to perfectly match Earth’s rotation, the speed of GEO satellites should be about 3 km per second at an altitude of 35 786 km. This is much farther from Earth’s surface compared to many satellites.
GEO is used by satellites that need to stay constantly above one particular place over Earth, such as telecommunication satellites. This way, an antenna on Earth can be fixed to always stay pointed towards that satellite without moving. It can also be used by weather monitoring satellites, because they can continually observe specific areas to see how weather trends emerge there.”
– As the moon sinks further, you might wonder if its gravity would overpower Earth’s, pulling you up and ending your misery? Fortunately not. The earth’s surface gravity is about 6 times stronger than the moon’s, so even if the moon were hovering right on top of you, you would still stay on the ground.
The gravity on the Moon is 1.62 m/s^2, which is 6.05 times weaker than the gravity on Earth of 9.81 m/s^2. If a 70 kg person were standing on the Moon, they would feel as if they weighed just 11.5 kg on the Moon. If this person was caught between the Earth and the Moon, Earth’s gravity would win out and keep the person on its surface.
#NASA, Moon Fact Sheet, retrieved 2021
https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
– On the moon things are different though: the near side of the moon is more strongly affected by earth’s gravity, so during the next few months, it starts to stretch forward towards the earth, into something of an egg, triggering deep moonquakes as the lunar rock flexes and changes shape. Though barely noticeable now, this ‘squish’ will grow to hundreds of kilometers in a matter of months.
The pull of Earth’s gravity depends on how far away something is from it. Newton's law of universal gravitation states that gravitational force has an inverse square relationship with distance.
#Britannica, Newton's law of gravitation, retrieved 2021
https://www.britannica.com/science/Newtons-law-of-gravitation
Quote: “Newton’s law of gravitation, statement that any particle of matter in the universe attracts any other with a force varying directly as the product of the masses and inversely as the square of the distance between them.”
The Moon has a diameter of 3,475 km. If it is orbiting at an altitude of 50,000 km, its near side would be at a 50,000-3475 = 46,525 km distance from the Earth, and its far side would be at a 50,000+3475 = 53,475 km distance from the Earth.
That means that the near side is 46,525/53,475 = 0.87 times the distance of the far side. It experiences 1/(0.87^2) = 1.32 times the gravitational pull from Earth. This difference in force acting on the near and far sides of the Moon is very likely enough to distort its shape into something more elongated, and this effect only worsens as it falls closer to Earth.
A small body like an asteroid does not experience much difference in the gravitational pull it experiences across its length, but the Moon is far too large.
#NASA, The Roche limit, 2010
https://ase.tufts.edu/cosmos/view_picture.asp?id=1204
Quote: “A large satellite (top) that moves well within a planet’s Roche limit (dashed curve) will be torn apart by the tidal force of the planet’s gravity. The side of the satellite closer to the planet feels a stronger gravitational pull than the side farther away, and this difference works against the self-gravitation that holds the body together. A small solid satellite (bottom) can resist tidal disruption because it has significant internal cohesion in addition to self-gravitation.”
– At this point the apocalypse has arrived and we can summarize the months before the crash as “everybody left has a really bad time”. The tides sweeping over the Earth slow down and then reverse their direction because the moon now orbits earth faster than it rotates. The planet will experience an abundance of earthquakes and volcanism. Massive amounts of volcanic aerosols rise high into the stratosphere, shiny enough to reflect sunlight back into space. What little light gets through is rust-red and is periodically diminished by daily eclipses.
The tides follow the Moon. Currently, the Moon’s orbital period is about 30 days and is therefore much slower than the Earth’s rotational period of 1 day. This causes the tides to sweep from East to West. However, the Moon’s orbital period decreases as it gets closer to the Earth so it looks like the tides are slowing down. At geostationary altitude, the Moon’s orbital period is 1 day and the tides seem to freeze in place under it. Then, the Moon gets even closer, its orbital period becomes less than 1 day and the tides start to sweep backwards from West to East.
We know what happens when large volcanoes erupt because we have recorded history of their effects. A relatively recent example is the eruption of Mt Tambora in 1815, in today’s Indonesia. The material it ejected into the atmosphere triggered a massive global cooling event, called the Year without Summer.
#NCAR, Mount Tambora and the Year Without a Summer, 2012
https://scied.ucar.edu/learning-zone/how-climate-works/mount-tambora-and-year-without-summer
Quote: “On April 5, 1815, Mount Tambora, a volcano, started to rumble with activity. Over the following four months the volcano exploded - the largest volcanic explosion in recorded history. Many people close to the volcano lost their lives in the event. Mount Tambora ejected so much ash and aerosols into the atmosphere that the sky darkened and the Sun was blocked from view. The large particles spewed by the volcano fell to the ground nearby, covering towns with enough ash to collapse homes. There are reports that several feet of ash was floating on the ocean surface in the region. Ships had to plow through it to get from place to place.
But the smaller particles spewed by the volcano were light enough to spread through the atmosphere over the following months and had a worldwide effect on climate. They made their way into the stratosphere, where they could distribute around the world more easily. Earth’s average global temperature dropped three degrees Celsius. The effect was temporary. Eventually, even the smallest particles of ash and aerosols released by the volcano fell out of the atmosphere, letting in the sunshine.”
In our scenario, we would expect the combined output of many volcanoes from around the world to have an even greater effect on the climate. Between 40,000 km and 10,000 km, the Moon would orbit the earth from once every 27.6 hours to once every 5.76 hours, with an eclipse shadowing the Earth’s surface with each orbit.
We can determine the orbital period of an object circling the Earth using this calculator:
#Satellite Signals, Delta V calculator for LEO/MEO/GEO orbit injection, 2021
https://www.satsig.net/orbit-research/delta-v-geo-injection-calculator.htm
Here is Professor Matt Caplan’s graph showing the orbital period of the Moon as it gets closer to the Earth:
– The result is a rapid global cooling, with acid rains and summer snows killing even the hardiest plants.
We can also look at the effects hypothesized to follow a global nuclear war to guess what would happen in our Moon fall scenario. It could also be an indication of what a massive release of soot into the atmosphere over a short period could cause.
#NCAR, Mount Tambora and the Year Without a Summer, 2012
https://scied.ucar.edu/learning-zone/how-climate-works/mount-tambora-and-year-without-summer
Quote: ““Our research shows that in this U.S./Russia nuclear war scenario, nuclear winter would happen,” he said, adding that the models show an almost 10°C reduction in global mean surface temperature, extreme changes in precipitation, and a 90% reduction in the growing season across many parts of the midlatitudes.
To put things into perspective, Coupe said that the temperature change from preindustrial times to today was only 1°C. “But in nuclear winter, it approaches 10°C below the climatological mean after 2 or 3 years.”
Solar radiation, important not only for surface temperatures but also for photosynthesis, drops precipitously. Within the first couple of years of a nuclear winter, “there’s around a 75% decrease in surface radiation—which is substantial,” said Coupe.
Precipitation rates don’t fare any better, and global averages drop about 58% after soot injection into the stratosphere. Patterns of rainfall also shifted, including the weakening or disappearing of monsoons and new rainfall over desert regions.”
Volcanoes are large sources of sulfur dioxide. Multiple simultaneous eruptions around the world would release huge amounts of this gas, and cover everything with acid rains as a result.
#USGS, Volcanic gases can be harmful to health, vegetation and infrastructure, retrieved2021
https://www.usgs.gov/natural-hazards/volcano-hazards/volcanic-gases
Quote: “Magma contains dissolved gases, which provide the driving force that causes most volcanic eruptions. As magma rises towards the surface and pressure decreases, gases are released from the liquid portion of the magma (melt) and continue to travel upward and are eventually released into the atmosphere
[...]
By far the most abundant volcanic gas is water vapor, which is harmless. However, significant amounts of carbon dioxide, sulfur dioxide, hydrogen sulfide and hydrogen halides can also be emitted from volcanoes. Depending on their concentrations, these gases are all potentially hazardous to people, animals, agriculture, and property.”
Quote: “Sulfur dioxide is a colorless gas with a pungent odor that irritates skin and the tissues and mucous membranes of the eyes, nose, and throat. SO2 emissions can cause acid rain and air pollution downwind of a volcano—at Kīlauea volcano in Hawaii, high concentrations of sulfur dioxide produce volcanic smog (VOG) causing persistent health problems for downwind populations. During very large eruptions, SO2 can be injected to altitudes of greater than 10km into the stratosphere. Here, SO2is converted to sulfate aerosols which reflect sunlight and therefore have a cooling effect on the Earth's climate. They also have a role in ozone depletion, as many of the reactions that destroy ozone occur on the surface of such aerosols.”
– Finally, at the end of the year,, the moon has reached the Roche limit. That’s the point where Earth’s gravitational pull on the Moon is stronger than the Moon’s own gravity. Things on the lunar surface start falling towards Earth and by the time it crosses 10,000 km the entire moon disintegrates into rubble, smearing itself into a massive ring system around the earth.
The Roche limit is the distance between the Earth and the Moon where the gravitational pull between them overcomes the internal gravity of the Moon and any other forces holding it together. Here is an equation which allows us to estimate this value:
#Michael C. LoPresto, A Simplified Theoretical Treatment and Simulated Experimental Calculation of the Roche Limit, 2006
Quote: “The Roche limit is generally accepted to be just under 2.5 times the planet’s radius.1 This numerical factor will vary depending on the density of the planet and the moon(s) being considered as well as the rigor of the derivation, which may include more factors than those mentioned above.”
In this case, ρM is the density of the Earth, equal to 5510 kg/m^3, ρm is the density of the Moon, equal to 3340 kg/m^3. RM is the radius of the Earth, equal to 6371 km. We obtain a value for d equal to 18,819 km.
However, that is the simplified treatment. The Roche limit is not just one number, but depends on the relative densities of the two bodies and how well the Moon can hold itself together against deformation. It is a range of values with a lower and upper limit. The lower limit assumes that the Moon is a perfectly rigid body that does not deform at all during the entire process, as if it was entirely made of strong metal. The following calculation gives the lower limit:
D = 1.26 x RM x (ρM / ρm) ^ (⅓) = 9,485 km
The upper limit assumes the Moon is perfectly deformable, as if it were made of gas. This stretching makes it more sensitive to gravitational stresses and therefore it breaks up further away from the Earth. The following calculation gives the upper limit:
D = 2.42 x RM x (ρM / ρm) ^ (⅓) = 18,217 km
We know that the Moon is not a rigid ball of metal and not a deformable sphere of gas. It is something in between, with different layers reacting more or less to the gravitational stresses. It will be severely affected starting at the upper limit of 18,217 km, and certainly destroyed by the time it reaches the lower limit of 9,485 km. The Moon has a metal core and rocky crust, which makes it fairly strong, so it is likely to reach these lower values.
Here is an explanation of the upper and lower Roche limit:
#William Lowrie and Andreas Fichtner, Fundamentals of Geophysics, page 60, 2020
#NASA, Moon Fact Sheet, retrieved 2021
https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html
– Any survivors are treated to a view of tremendous arches spanning the sky, glimmering in the sunlight, illuminating the night sky more brilliantly than any full moon ever could, while meteor showers of moondust fill the sky.
The Moon’s debris would not instantly spread into a shiny ring. It would be composed of chunks in slightly different orbits, bumping into each other and breaking down into smaller pieces with a more homogenous distribution. Eventually, they arrive at a steady state where particles clumping together is balanced by collisions breaking them down again.
#Nikolai Brilliantov et al., Size distribution of particles in Saturn’s rings from aggregation and fragmentation, 2015
https://www.pnas.org/content/112/31/9536
Quote: “We show that a power-law size distribution with large-size cutoff, as observed in Saturn’s rings, is universal for systems where a balance between aggregation and disruptive collisions is steadily sustained. Hence, the same size distribution is expected for any ring system where collisions play a role, like the Uranian rings, the recently discovered rings of Chariklo and Chiron, and possibly rings around extrasolar objects.”
It could be possible that some of those pieces get knocked around enough to fall into the Earth’s atmosphere, where they burn up as meteors. It is impossible to predict what this could lead to. In the best case, it is just a bit of dust that disappears harmlessly in the upper atmosphere. In the worst case, rocky blocks of thousands of tons crash into the ground to wipe out any life on the surface.
– It’s hard to say what happens next, but the tranquility may be short-lived. If too much moondust rains down, friction heats the atmosphere – possibly boiling the oceans. If not, the enormous shadows cast by the rings, combined with all the volcanic and meteoric aerosols, block even more sunlight, and a period of runaway cooling could begin that freezes much of earth’s surface solid.
The Earth did undergo a period 600 million years ago of global glaciation we call ‘Snowball Earth’. We don’t know what triggered it, but we know how the freezing progress to cover nearly the entire globe. It might be possible that the effects of our Moon falling to a lower orbit and disintegrating into rings would recreate the conditions necessary to trigger the runaway freezing that caused ‘Snowball Earth’.
#Indranil Banik, Snowball Earth, 2011
https://www.researchgate.net/publication/308037560_Snowball_Earth
Quote: “These glaciation events were so extreme that our entire planet would have been nearly as cold as the present Mars, and certainly colder than the Moon. In fact, it would have been cold enough to sustain the coldness, which is one key reason why it lasted so long. The mechanism responsible for this is called the ice-albedo feedback effect. Ice forms at low enough temperatures, and it reflects enough sunlight to reduce the temperature even further. Considering that almost every material is less reflective than ice (usually by a huge margin), the effect is considerable.
Under certain conditions, the ice will advance further and further until it reaches within 30° of the Equator. At this point, if a small perturbation to the climate system increased the amount of ice cover by one arbitrary ‘unit’, the temperature would decrease sufficiently to allow the formation of one more unit of ice (due to the reflection of more sunlight). This would be a self-sustaining geological version of a ‘chain reaction’. There could then be no stopping the ice from covering the entire planet, including the tropical oceans! As we will see later, however, small gaps in the ice cover sufficient to prevent a total extinction of surface life on Earth would likely have been left for a variety of reasons. ”