Category: Super fact

This post is about a super-fact. The goal of this blog is to create a list of facts or insights that are important and not trivia, known to be true, and yet highly surprising, shocking, amazing, or widely disputed amongst the public but not disputed among the scientists or experts in the relevant fields. However, not all of my posts are super-facts. This category distinguishes posts that are super-facts.

Early Homo Sapiens lived at the same time as many other human species

Super fact 86 : Early humans, early homo sapiens, lived at the same time as many other human species including Neanderthals, Denisovans, Homo floresiensis, Homo naledi, Homo luzonensis. Homo heidelbergensis, Homo erectus, and maybe other species as well.

Photo of a reconstruction of a Neanderthal man. | Early Homo Sapiens lived at the same time as many other human species
Reconstruction of a Neanderthal by Natural History Museum. Werner Ustorf, CC BY-SA 2.0 https://creativecommons.org/licenses/by-sa/2.0, via Wikimedia Commons.

Homo sapiens co-existed with several other Homo species. Homo erectus and Homo heidelbergensis are direct ancestors to Homo sapiens that survived long enough to exist at the same time as Homo sapiens.

Homo sapiens emerged around 300,000 years ago in Africa and Homo erectus died out around 100,000 years ago and Homo heidelbergensis died out around 200,000 years ago. Homo floresiensis died out 50,000 years ago, the most recent Homo luzonensis is 50,000 years old but they may have survived longer, Homo naledi existed approximately 335,000 to 236,000 years ago, Neanderthals interbred with homo sapiens and died out around 40,000 years ago, the Denisovans also interbred with homo sapiens and died out around 30,000 to 50,000 years ago. You can read more here and here.

You may wonder how different species can interbreed with each other. More on that later in this post.

I consider this a super fact because it is true, surprising to those who did not know this, and ancient human history is kind of important. Even if you knew that homo sapiens lived along other homo species the fact that the world used to be so crowded with different homo species may come as a surprise. Where did they all go?

Direct Ancestors of Homo Sapiens

Homo heidelbergensis is widely considered a pivotal common ancestor to Homo sapiens, Neanderthals, and Denisovans. Since Homo Erectus is a direct ancestor to Homo heidelbergensis it is also a direct ancestor to Homo sapiens, Neanderthals, and Denisovans. Homo Erectus is also a direct ancestor to Homo floresiensis but Homo heidelbergensis is not considered an ancestor to Homo floresiensis. The picture below shows the direct ancestors to Homo Sapiens.

The skulls are from left to right Australopithecus africanus 3.3 - 2 million years ago, Homo habilis 2.4 to 1.5 million years ago, Homo erectus 1.6 to 600 thousand years ago, Homo heidelbergensis 700 thousand to 200 thousand years ago, early homo sapiens 300 thousand to 45 thousand years ago, anatomically modern human 130 thousand years ago until now.
Skulls of successive (or near-successive, depending on the source) human evolutionary ancestors, up until ‘modern’ Homo sapiens. Mya – million years ago, kya – thousand years ago. SimplisticReps, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0&gt;, via Wikimedia Commons.

Geographic spread of Homo Sapiens and other Homo Species

Homo heidelbergensis is an ancestor to Neanderthals, Denisovans and Homo sapiens (and Homo erectus is an ancestor to Homo heidelbergensis). However, whilst Neanderthals emerged in Europe and Asia, Denisovans evolved in Asia, and Homo sapiens emerged in Africa.

The map shows the movement of Homo heidelbergensis originating in Africa and moving into Europe and Asia with Neanderthals (in yellow) emerging in Europe and moving into Asia. The Denisovans emerged in Asia and spread further east. | Early Homo Sapiens lived at the same time as many other human species
The evolution and geographic spread of Denisovans as compared with Neanderthals, Homo heidelbergensis and Homo erectus. John D. Croft at English Wikipedia, CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0, via Wikimedia Commons.

The map below indicates where skeleton remains of Neanderthals had been found as of 2017.

This map of Europe and West Asia shows the region where Neanderthals have been found.
Known Neanderthal range in Europe (blue), Southwest Asia (orange), Uzbekistan (green), and the Altai mountains (violet), as inferred by their skeletal remains (not stone tools). There were 165 such places by 2017. Nilenbert, N. Perrault, auteur du guide complet du canotageI, CC BY-SA 3.0 <http://creativecommons.org/licenses/by-sa/3.0/&gt;, via Wikimedia Commons.

Interbreeding and Defining a Species

Homo Neanderthalensis and Homo Sapiens (or Homo Sapiens Sapiens) interbred, and so did Homo Denisova and Homo Sapiens, and Homo Neanderthalensis interbred with Homo Denisova. What a mess! Homo Neanderthalensis and Homo Sapiens were different species, so it may seem strange that they could interbreed. However, species is a complex concept.

Speciation is considered relative. It is often said that two animals belong to the same species if they can interbreed in nature and produce viable, fertile offspring. However, it is not that simple. An animal A may be able to successfully interbreed with an animal B, and that animal B may be able to successfully interbreed with an animal C, but animal A and C cannot interbreed. Animal A could be said to be a different species relative to animal C but animal B could be said to be the same species as both animal A & C. A great geography related example of this is ring species. In a ring species, gene flow occurs between neighboring populations of a species, but at the ends of the ring the populations don’t interbreed.

The picture depicts different subspecies as little colored circles centered around a big lake. The color changes a little bit at the time. All the circles next to each other can interbreed.
Illustration of ring species, an example of how speciation can be relative. All the circles next to each other can interbreed but at the end it no longer works. Andrew Z. Colvin, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0&gt;, via Wikimedia Commons.

For the case of Neanderthals and Homo sapiens (and Denisovans); at certain points in history, you could consider Homo Neanderthalensis and Homo Sapiens to be different subspecies rather than different species. That is why you sometimes hear the terms Homo Sapiens Neanderthalensis and Homo Sapiens Sapiens. I can add that Homo sapiens certainly got around, as you can see on the map below.

A world map showing portions of Africa being yellow and red, and portions of Asia being yellow and dark yellow with red arrows representing migrating Homo Sapiens. The map features several time markers representing the arrival of Homo Sapiens. | Early Homo Sapiens lived at the same time as many other human species
The spread of Homo Erectus (yellow), Homo Sapiens (red) and Homo Neanderthalensis (dark yellow). NordNordWest, Public domain, via Wikimedia Commons.

Is Thomas Wikman a Neanderthal ?

I can add that genetic testing can reveal how much Neanderthal DNA you have. I took a test with 23AndMe to find out about my ancestry (it was 98% Scandinavian and Finnish) and to find out about my risk for genetic illnesses. 23AndMe also told me that I was in the 99 percentiles with respect to carrying Neanderthal genes, meaning that I had unusually many Neanderthal genes. I joined the 23AndMe Neanderthal club (you had to be in the 98 percentile).

However, I quit after people in the club started saying that we should demand reparations from those with less Neanderthal genes because they exterminated us. It might have been a bizarre joke, but I decided not to stay around to find out. Later, after 23AndMe went bankrupt, I deleted mine and my wife’s data and quit. I was afraid 23AndMe might sell the DNA data to health insurance companies.

Man geneticist. Doctor sits at table in genetic laboratory. Chains of DNA or RNA. Sequencing human genome. Doctor studies DNA. Geneticist conducts scientific experiments Geneticist looks at test tubes
Geneticist sequencing human genome Asset id: 2479929725 by FOTOGRIN
This is some other evolution and natural history related posts
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Birds are Avian Dinosaurs

Super fact 84 : Modern birds are classified as part of the clade Dinosauria. They are direct descendants of small, feathered maniraptoran dinosaurs that survived the Cretaceous-Paleogene extinction event 66 million years ago. Maniraptoran dinosaurs in turn are a major subgroup of coelurosaurian theropod dinosaurs. In other words, birds are avian dinosaurs.

3D illustration showing two carnivorous dinosaurs and two large herbivores looking up at a burning asteroid. | Birds are Avian Dinosaurs
Some dinosaurs survived the Cretaceous-Paleogene extinction event 66 million years ago. Shutterstock Asset id: 2196200279 by funstarts33

Birds are descendants of specialized maniraptoran theropod dinosaurs that survived the extinction event that killed most dinosaurs 66 million years ago. Maniraptoran dinosaurs in turn are a major subgroup of Tyrannoraptora, which include the well-known Tyrannosaurus Rex. Tyrannoraptora  in turn is a major subgroup of coelurosaurian theropod dinosaurs. Both the well-known dinosaur called velociraptor, and birds belong to the group Maniraptora. Even though the velociraptor was not a bird they shared many bird-like features, including feathers, wishbones, hollow bones, and similar wrist joints.

A colorful velociraptor covered in feather. It does not look like it could fly.
Velociraptor with feathers (well a little bit). Shutterstock Asset id: 2636534673 by Shutterstock AI Generator

Birds evolved during the Jurassic period from two-legged, carnivorous, and often feathered dinosaurs, and are the only surviving dinosaurs. They have been classified as avian dinosaurs since the 1980’s. In other words, they are dinosaurs. Initially feathers evolved among dinosaurs for insulation, sexual display, and camouflage rather than flight. One of the early birds was Eoconfuciusornis. It lived 131 million years ago, long before the Cretaceous-Paleogene extinction event 66 million years ago. Eoconfuciusornis could fly and it had colorful feathers.

A black bird with a long retrix / tail sitting on a tree. | Eoconfuciusornis 130 million years ago. | Birds are Avian Dinosaurs
Eoconfuciusornis 130 million years ago. Nobu Tamura, CC BY 3.0 https://creativecommons.org/licenses/by/3.0, via Wikimedia Commons

I brought up this fact in a recent post and I hinted that it was a super fact. It is true, surprising and kind of important. After all birds are all around us. In this post I am exploring the fact that birds are dinosaurs a little bit more than I did in my previous post. Below are a couple of modern birds.

A shoebill stork is a large gray-blue bird with a huge beak.
A shoebill stork standing at Ueno Zoo, Tokyo, five feet tall. Bob Owen, CC BY 2.0 https://creativecommons.org/licenses/by/2.0, via Wikimedia Commons
A taxidermy mount of a turkey standing on our dining room table. | Birds are Avian Dinosaurs
A wild turkey in our dining room.

Feathered Dinosaurs

A lot of dinosaurs had feathers, and some could fly. That included many types of dinosaurs other than birds. Dinosaurs with feathers include, for example, Velociraptor, Deinonychus, Archaeopteryx (could fly), Microraptor (could fly), Rahonavis (could fly), Gallimimus, Ornithomimus, Yutyrannus huali, Psittacosaurus, Psittacosaurus, Sinosauropteryx, Sinornithosaurus, Eoconfuciusornis, Wulong, Psittacosaurus, Sciurumimus, Kulindadromeus, Caudipteryx, Utahraptor, Deinonychus, and even young T-Rex and many others. We know that at least some dinosaurs had feathers as well as colors based on fossil finds. Below are some illustrations.

A Gallimimus dinosaur covered in hair and feathers.
Life restoration showing an adult with feathers, based on those known from the related Ornithomimus. Picture is from here. PaleoNeolitic, CC BY 4.0 https://creativecommons.org/licenses/by/4.0, via Wikimedia Commons
A bird like dinosaur with feathers. It has huge claws.
Life restoration of Pyroraptor olympius. Picture is from here. Mette Aumala, CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0, via Wikimedia Commons.
Birds are Avian Dinosaurs | Reconstruction of the 2014 microraptorine dromaeosaur dinosaur, Changyuraptor yangi. This is a dinosaur with four wings.
Reconstruction of the 2014 microraptorine dromaeosaur dinosaur, Changyuraptor yangi. This is a dinosaur with four wings. The picture is taken from here. Emily Willoughby (e.deinonychus@gmail.com, http://emilywilloughby.com), CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0&gt;, via Wikimedia Commons
Greyish bird like creature with a reptile like head.
Artistic restoration of D. albertensis Artistic restoration of D. albertensis. Picture from here. Fred Wierum, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0&gt;, via Wikimedia Commons
Six dromaeosaurs are shown, all covered with feathers. Microraptor gui (flying), Velociraptor mongoliensis, Austroraptor cabazai, Dromaeosaurus albertensis, Utahraptor ostrommaysorum, Deinonychus antirrhopus. A human is shown on the left. Most of the dinosaurs are bigger than the human.
Size of Utahraptor (5) compared with other dromaeosaurs and a human. It is the biggest one in the picture. The picture is from here. Fred Wierum, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0&gt;, via Wikimedia Commons.

Terror Birds and Other Giant Birds

After the Cretaceous-Paleogene extinction event 66 million years ago birds continued evolving. Some of them became large standing 1 – 3 meters (3-10 feet) and weighing hundreds or even thousands of pounds. From about 53 million years ago until 100,000 years ago there were large birds that we refer to as Terror Birds. They lived at the same time as humans. However, there were other large and scary birds. Dromornis stirtoni was a flightless bird that lived 7-8 million years ago, it was over three meters in height (10 feet) and weighed 500-600 kilograms (1,100 to 1,300 pounds). Below are some illustrations.

pencil drawing, digital coloring of Paraphysornis brasiliensis, a Terror Bird. | Birds are Avian Dinosaurs
Paraphysornis brasiliensis, a Terror Bird, 8 feet tall weighing 400–530 pounds, this is a terror bird from the Early Miocene of Brazil,: Snowmanradio (talk)Paraphysornis_BW.jpg:  Nobu Tamura (http://spinops.blogspot.com), CC BY 3.0 <https://creativecommons.org/licenses/by/3.0&gt;, via Wikimedia Commons.
The Kelenken, Devincenzia, Phorusrhacos, and Titanis birds are all larger than the human standing on the left hand side. Kelenken guillermoi is the largest.
Size comparison of some phorusrhacids (Terror Birds), including Kelenken, Devincenzia, Phorusrhacos, and Titanis. Picture taken from here. PaleoNeolitic, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0&gt;, via Wikimedia Commons.
A flightless bird with huge yellow beak. | Birds are Avian Dinosaurs
A pencil-drawn reconstruction of Dromornis stirtoni. Picture is taken from here. Nobu Tamura (http://spinops.blogspot.de), CC BY-SA 3.0 http://creativecommons.org/licenses/by-sa/3.0/, via Wikimedia Commons

Shared False Memories Are Common – Mandela Effect

Super fact 83 : Everyone experiences false memories. They are a normal part of how human memory works and are very common. There are also false memories that are shared among large groups of people and that are often socially reinforced. This is called the Mandela effect.

Pop art style comic book panel doubtful wondering woman can't tell reality from fantasy, daydreaming, dreams, delusion, vector illustration. She says “W-Was … it … just a dream?!?” | Shared False Memories Are Common – Mandela Effect
Shutterstock Asset id: 717504940 by durantelallera

As I mentioned, false memories are very common. However, what may come as a surprise is that some false memories are widespread and socially reinforced. It is important to know this, and we know it is true, so it is a super fact. The effect is named after the former President of South Africa, Nelson Mandela, who died in 2013. However, a lot of people distinctly remember him dying in prison in the 1980s.

It was paranormal researcher Fiona Broome who named the effect after having a personal experience with the phenomenon. She wrongly recalled Nelson Mandela dying in the 1980s and she could even remember the news coverage of his funeral, and yet it never happened. After talking to other people, she realized that she was far from alone with her false memory.

Another example is that a lot of people remember Darth Vader in Star Wars telling Luke “Luke, I am your father”. What Darth Vader said was “No, I am your father”. Yet another movie example is that Forrest Gump did not say “Life is like a Box of Chocolates”. He said, “Life was like a box of chocolates”. Also, the Monopoly man never had a monocle, Curious George doesn’t have a tail, many remember the “Berenstein Bears” but it’s the “Berenstain Bears”. C-3PO is not all gold, he has a silver leg. You can easily find hundreds of examples of the Mandela effect online.

The photo shows a scene from Star Wars. C-3PO and R2-D2. C-3PO has a silver leg.
Shutterstock Asset id: 558350728 by Willrow Hood

People have asked me, “do you remember in the 1970’s and 1980’s when scientists were  convinced that global cooling was happening”, to which I answer, “no I don’t remember that and neither do you”. In the 1970’s much less was known about the climate, but the possibility of anthropogenic warming dominated the peer-reviewed literature even then. There were a few contrarian climate scientists who claimed there was global cooling and there were some articles in popular media about global cooling, but the statement that scientists were  convinced there was global cooling is simply false. You can read more about this in this book. Yet some people “remember” this. I believe this is another example of a socially reinforced Mandela Effect.

False Beliefs and False Memories

The existence of false beliefs is another phenomenon that is very common. There are hundreds of common beliefs that we know are false based on carefully vetted data, large amounts of studies, and scientific experiments. I think we all have some false beliefs. We have all been bamboozled at some point. The way to know is to check and compare the evidence and the data and papers from reputable sources. Find out what the experts in the field say. Some examples of false beliefs are:

We adopt false beliefs because of misinformation, propaganda (politics), social reinforcement, a wish to believe certain things, our own lack of critical thinking, etc. False memories, including collective false memories are due to the fact that memories aren’t perfect recordings, memory reconstruction, social reinforcement (also true for false beliefs), and confusion with similar events.

Woman near inscriptions false and true reflects trying to choose from two options and make difficult decision. Woman put fingers on temples and closed eyes considering pros and cons fateful decision.
Shutterstock Asset id: 2593117091 by Drawlab19

Both false beliefs, false memories and the Mandela effect distort our understanding of the world. That is BTW one important inspiration for this fact finding blog – superfactful. It is difficult to accept that what you believe to be true may simply be false. We want to believe that we know better than others, not that we have been bamboozled or that we misremember things. But we need to be open to look at and compare evidence, be curious and willing to understand how things work, and be willing to change our beliefs and accept that some of our memories may be false. That is one way to grow as a human.

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All Life Have a Common Ancestor

Super fact 82 : All known cellular life descends from a single Last Universal Common Ancestor (LUCA). All animals, all plants, fungi, algae, green and red algae, kelp, phytoplankton, cyanobacteria, amoebas, amoebozoa, diatoms, stramenopiles, rhizaria, hacrobia, all eukaryote, all archaea, all bacteria, all the millions of species on Earth come from one single ancestor known as the Last Universal Common Ancestor – LUCA. Viruses are an exception, but viruses are not considered life.

This AI generated image shows a cell in an ocean and in the background, there are hundreds of other cells or possible life structures. | All Life Have a Common Ancestor
Last Universal Common Ancestor creation Shutterstock Asset id: 2666598705 by Shutterstock AI

LUCA, the Last Universal Common Ancestor, was not the first life form. It was preceded by earlier, simpler life forms that did not survive. LUCA was a single-celled, bacteria-like microorganism that existed roughly 4.2 billion years ago, or about 400 million years after planet Earth first formed. It was the final common ancestor for all currently living organisms. It thrived near hydrothermal vents as part of a larger microbial community before the three domains of life bacteria, archaea, and Eukarya diverged. This is a super fact because it is true, or at least highly probable, it is surprising and amazing and kind of important.

How Do We Know All Life Has a Common Ancestor ?

The answer is genome mining. By surveying nearly 2000 genomes of modern microbes we not only know that all life has a common ancestor (LUCA), that lived roughly 4.2 billion years ago, but we also know that it thrived near hydrothermal vents as part of a larger microbial community. This is analogous to another of my posts “Humans and Chimpanzees Have a Common Ancestor”. By sequencing human DNA and chimpanzee and bonobo DNA we know that humans and chimpanzees have a common ancestor. No fossils, or other information from the past is needed. DNA is a great tool for determining relationships between species and for finding information about past life, without the need of fossils.

To be more specific, the detailed biochemical similarity of all current life makes the existence of LUCA widely accepted by biochemists. There is a Universal Genetic Code, which means that nearly all living things use the same DNA/RNA-based genetic code to translate genetic information into proteins. There is a shared molecular machinery, for example, all life relies on ribosomes for protein synthesis, similar energy carriers like ATP, and the same 20 amino acids. All life uses the same mirror-image form of molecules, a signature of a single, common ancestry. In addition, there is a “core” set of 355 gene families present in both modern bacteria and archaea, which were likely inherited from LUCA. Finally, we have phylogenetic mapping, protein-sequence-based phylogenetic trees converge on a single root, indicating a common ancestry for all life. See the phylogenetic tree of life below.

The picture shows how the three domains of life bacteria, archaea, eukaryote, and the relationships between the different phylum in each domain leads back to LUCA.
User: Crion, CC BY 3.0 https://creativecommons.org/licenses/by/3.0, via Wikimedia Commons.

Below is another view of the diversification of life that focuses on the inventions made by life.

This tree of life picture shows a root representing a common ancestor and from it sprouts various inventions of life DNA, mitochondria, nuclei, chloroplasts, organs, hair, and much more.
The evolutionary tree of life showing diversification, branching and key characteristics of each branch. Shutterstock Asset id: 228953155 by Zern Liew

It should be noted that in addition to viruses there were likely other forms of life that existed alongside LUCA or before it. There was likely non-cellular life as well as cellular life that died out, RNA-based life, self-replicating nucleic acids, etc. It should also be noted that if some of the large viruses were to be reclassified as life, or a life form not based on LUCA were to be discovered then our “current LUCA” would no longer be LUCA, but just the ancestor of “almost all life”. That would still be amazing, just slightly less so.

The existence of LUCA brings up an interesting question. What would happen if we found DNA based life on another planet and its DNA showed that it also originated from LUCA ?

Other Evolution Related Super Facts

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Conic Sections are the Shapes that Shape Our World

Super fact 80 : A conic section is a shape formed by slicing a cone with a plane. There are four such shapes, circle, ellipse, parabola, and hyperbola. The conic sections universally describe motion under gravity. The orbits of planets around their stars are circles or ellipses, comets fly around space in elliptical orbits, or parabolic or hyperbolic paths. Objects thrown up in the air follow parabolic paths. They are the basis for a huge amount of engineering applications.

Esther’s writing prompt: January 21 : Shapes

Click here or here  to join in.

Four cones each shown with a plane section forming a specific conic section. | Conic Sections are the Shapes that Shape Our World
Types of conic sections : circle , ellipse , parabola , hyperbola Shutterstock Asset id: 2377159367 by ProfDesigner

The four conic sections, circle, ellipse, parabola and hyperbola are fundamental and very useful shapes in mathematics, physics and engineering. Well, a circle is a special case of an ellipse, so it is really only three conic sections. The motion of the planets and other stellar objects are described by the conic shapes. Isaac Newton derived his law of gravitation from Kepler’s laws, which describe planetary orbits as ellipses.

The conic sections are all described by second degree equations (quadratic equations) and are in that sense the simplest shapes aside from points and lines. It is important to understand that there is an infinite amount of shapes that are almost conic sections and look like conic sections, but it is the exact mathematical properties of the four conic sections that make them so common in physics, mathematics, nature and engineering.

The picture shows a cone with four planes slicing the cone in four ways. The resulting shapes are circle (red), ellipse (green), parabola (blue), hyperbola (orange).
The black boundaries of the colored regions are conic sections. Not shown is the other half of the hyperbola, which is on the unshown other half of the double cone. by Magister Mathematicae, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=18556148

It may not come as a surprise that the circle is a fundamental and important shape, but I believe that the fact that the other conic sections are also fundamental in mathematics, physics and engineering come as a surprise to people outside of the STEM fields. It is a true and an important fact regarding how our world works.

Conic Sections

As mentioned, the conic sections are fundamental shapes that appear in a lot of places in STEM. Below are a few examples.

Parabola

Math function parabola graphics illustration with a dark background. | Conic Sections are the Shapes that Shape Our World
Math function parabola. Shutterstock Asset id: 1628916337 by EleonoraDesigner

A parabola is formed when a plane cuts a cone, so the plane is parallel to a side of the cone. Parabolas are shapes that are roughly U-shaped and described by the equation y = x^2 or more generally by y = ax^2 + bx + c. Parabolas have a so called focus point. See the picture below. If you throw a ball, or any object, up in the air its trajectory will be a parabola (ignoring distortions caused by friction and wind). I should say the parabola you get in this case is upside down. The parabola is important when you design any kind of projectile.

U-shaped parabola with the focus shown. The pciture has an x-axis and a y-axis.
Part of a parabola (blue), with various features (other colours). The complete parabola has no endpoints. In this orientation, it extends infinitely to the left, right, and upward. Picture is from Wikipedia Melikamp, CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0, via Wikimedia Commons.

Antennas shaped like parabolas (in 3D) will direct incoming radiation and waves towards their focus point. If the surface is reflective a light located at the focus point will reflect to create a straight beam. Parabolas are used for radio telescopes, satellite dishes, car headlights, flashlights, solar cookers, solar power plants, water fountains, suspension bridges, business modelling and thousands of engineering applications. Parabolas like circles and the other conic sections shape our modern world (pun intended).

A parabola dish with equipment located at the focus.
Würzburg-Riese radar built by Germany in WW2 had a 7.4 meter (24 foot) dish. From this page. Alan Wilson from Stilton, Peterborough, Cambs, UK, CC BY-SA 2.0 https://creativecommons.org/licenses/by-sa/2.0, via Wikimedia Commons

Ellipse and circle

As mentioned, a circle and an ellipse are conic sections formed by intersecting a plane with a cone. You get a circle when the cuts perpendicular to the cone’s axis (see pictures above) and an ellipse form when the plane intersects the cone at a slant but not slanted so much that it becomes a parabola or a hyperbola. An alternative for an ellipse is that the sum of the distances from any point on the curve to two fixed points (called the foci) is a constant. See the picture below. The two definitions are identical. For a circle the two foci are merged into one point at the center.

The picture shows an ellipse and its two foci points. From the foci points there are lines going to a point P on the ellipse. The length of the two lines are added together and is the sum “2a” no matter where on the ellipse the point P is located. | Conic Sections are the Shapes that Shape Our World
Ellipse: definition by sum of distances to foci. Ag2gaeh, CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0, via Wikimedia Commons

There are a lot of real world examples of ellipses. Planets orbit the Sun in elliptical paths. The sun is in one of the foci points. The orbits of other stellar objects and satellites are also elliptical. Charged particles follow elliptical paths within magnetic fields.  Elliptical patterns are observed in the rotation of ocean currents, elliptical models and algorithms are used in medical imaging, computer science and encryption. Also whispering galleries.

Hyperbola

Comets and spacecraft that are not orbiting another body, in other words, they have enough speed to escape the gravitational pull and continue into deep space, will travel along a hyperbola. The boundary of a shockwave from a supersonic jet (a sonic boom) creates a hyperbolic curve on the ground as it moves. The intersection of two sets of concentric ripples in water makes a hyperbola. The light beam from a lamp or flashlight makes an ellipse or an hyperbola on a plane depending on the angle.

Newton’s Law of Gravitation

Johannes was an early 17th century German mathematician who derived three laws that describe how planetary bodies orbit the Sun using the observational data collected by the Danish astronomer Tycho Brahe. The three laws are the following:

  • Planets move in elliptical orbits with the Sun as a focus.
  • A planet covers the same area of space in the same amount of time no matter where it is in its orbit.
  • A planet’s orbital period is proportional to the size of its orbit (its semi-major axis).
Kepler’s three laws are illustrated in a diagram for two planets.
Illustration of Kepler’s laws with two planetary orbits.
The orbits are ellipses, with foci F1 and F2 for Planet 1, and F1 and F3 for Planet 2. The Sun is at F1.
The shaded areas A1 and A2 are equal and are swept out in equal times by Planet 1’s orbit.
The ratio of Planet 1’s orbit time to Planet 2’s is (a1/a2)^3/2
Hankwang, CC BY-SA 3.0 <http://creativecommons.org/licenses/by-sa/3.0/&gt;, via Wikimedia Commons

Later Isaac Netwon would use Kepler’s three laws to derive his law of gravity. Newton showed that an inverse-square force (gravity) directed toward the sun was necessary to explain the orbits.

My Other Responses to Esther’s Prompts

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