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Opinion: Teachers should require our students to use textbooks
There is a growing trend in schools to ditch textbooks, and have students rely instead on videos, lectures, handouts, and free online texts.
While every way of learning has its place, what would be the result of students leaving high school without learning how to read books and take notes on what they have read? What impact will this have on their ability to do well in college?
Shay Westlake writes – I am a retired teacher. I taught for 25 years. I am sorry in advance for saying this: I think teachers that do not use the textbook are not doing their students any favors. Imagine if your teachers never used a textbook. How would you have read textbooks in college?
When teaching high school we always had the kids read the chapters. We started the year out showing several different ways to take notes. Then we told them to choose the way they want to take them. At that point we started doing open notes quizzes. When they are done we have them staple their notes to the back of a quiz.
That is how I caught a ring of students that took turns reading and taking notes and giving the typed notes to like 20-25 people. At that point we made them do handwritten notes.
Every year after we told the story and told them we would allow them to type their notes until someone shares typed notes with someone else then everyone would have to do handwritten notes. It never failed in either the first or second quiz we would find the exact typed notes.
As the person above mentioned we would have numerous kids come back and thank us for having them read and take notes. They told us the majority of students did not do that and several would fail in their college classes. They also said it was so much easier to study for tests.
This is not judgmental. I just do not understand why you would teach high school kids and not make them do the hard work to prepare for college.
About the author: Shay Westlake taught for 25 years in Plano ISD. I taught U. S. History, World History and World Geography.
El Nino and La Nina
El Niño is the name given to the periodic warming of the ocean that occurs in the central and eastern Pacific.
At irregular intervals of three to seven years, these warm countercurrents become unusually strong and replace normally cold offshore waters with warm equatorial waters.
A major El Niño episode can cause extreme weather in many parts of the world.
What is La Niña? When surface temperatures in the eastern Pacific are colder than average, a La Niña event is triggered that has a distinctive set of weather patterns.
and
and
How does it form?
How do the ocean and atmosphere come together to create thus? This problem took nearly fifty years to solve, even after all of the basic ingredients were uncovered.
The Rise of El Niño and La Niña
How this affects the USA – SciJinks – what is La Niña?
How this affects Africa – Weather conditions over the Pacific, including an unusually strong La Niña, interrupted seasonal rains for two consecutive seasons. Between July 2011 and mid-2012, a severe drought affected the entire East African region. Said to be “the worst in 60 years”, it caused a severe food crisis across Somalia, Djibouti, Ethiopia and Kenya that threatened the livelihood of 9.5 million people. Many refugees from southern Somalia fled to neighboring Kenya and Ethiopia. Other countries in East Africa, including Sudan, South Sudan and parts of Uganda, were also affected by a food crisis. Many people died.
Live video of El Nino
El Niño, Chris Farley, on Saturday Night Live
The full skit is here 🙂 NBC Saturday Night Live classic clip
Links
19.3 Regional wind systems breezes El Nino PowerPoint
Chap 19 Air Pressure Coriolis Global winds El Nino
19.3 regional wind systems PDF worksheets
19.3 Regional Wind Systems Teacher chapter
Learning Standards
NGSS
HS-ESS2-2. Analyze geoscience data to make the claim that one change to Earth’s surface can create feedbacks that cause changes to other Earth systems.
Disciplinary Core Ideas – ESS2.A: Earth Materials and Systems
Earth’s systems, being dynamic and interacting, cause feedback effects that can increase or decrease the original changes.
Crosscutting concepts: stability and change – Feedback (negative or positive) can stabilize or destabilize a system.
HS-ESS2-4. Use a model to describe how variations in the flow of energy into and out of Earth’s systems result in changes in climate
DCI – ESS2.D: Weather and Climate – ESS2.A: Earth Materials and System
The foundation for Earth’s global climate systems is the electromagnetic radiation from the sun, as well as its reflection, absorption, storage, and redistribution among the atmosphere, ocean, and land systems, and this energy’s re-radiation into space.
Seaspiracy – documentary or propaganda?
Seaspiracy is a 2021 documentary about the impact of fishing on marine wildlife directed by Ali Tabrizi. The film investigates the effects of plastic marine debris and overfishing around the world and argues that commercial fisheries are the main driver of marine ecosystem destruction. Is this an even-handed piece of journalism, based on science, or is this propaganda? Here we go through criticism of this movie by scientists working in the field, who see this film as misleading, and intellectually dishonest.
They also discuss implicit (albeit, unintended) racism, with upper middle class white people making movies, demanding that huge numbers of people in the Pacific Islands and off the coasts of Asia and Africa must all lose their jobs, in order to make everyone vegan.
What teachers should say to our students
Be aware that all documentaries come with some view and bias.
Students should take care to see if the film makers make specific claims, citing peer-reviewed sources, or if they just more boardly make statements of fact that are hard to (or impossible) to source.
If the filmmakers do cite a peer-reviewed article, is that article representative of the field, or is it an outlier that the great majority of scientists disagree with.
Are the filmmakers citing papers that were later retracted?
We should discuss how the peer review process is all part of science. This includes papers being revised, or occasionally withdrawn. Revision or withdrawing a paper, by the way, isn’t a sign of a problem: that is exactly what one would expect to find in an open, transparent system. Problems only arise if problems are discovered but the author refuses to revise, or if a paper is retracted, but a documentarian nonetheless cites the retracted paper without noting that it is no longer considered correct.
Global Aquaculture Alliance rebuttal to Seaspiracy
Seaspiracy film assails fishing and aquaculture sectors that seem ready for a good fight, Lauren Kramer, Global Aquaculture Alliance, 3/26/2021
“We know the producer is trying to convince an audience not to eat seafood. He’s gone into filmmaking with a desired outcome for his audience, and that’s not documentary making, it’s propaganda,” Gavin Gibbons, VP, communications at NFI, told the Advocate. “We know from Tabrizi’s previous movies, Cowspiracy and What The Health, that the facts are very relative when it comes to this filmmaker.”
Soon after its release, NFI began debunking some of the key arguments the film makes. “The idea that the oceans will be empty by 2048 is based on a completely debunked 2006 statistic, refuted by the author of the original study. The 2048 statistic was put to rest by a follow-up report in the journal Science released in 2009 under the title New hope for fisheries,” it noted.
New hope for fisheries. Scientists document prospects for recovery, call for more global action, AAAS, 7/30/2009
Seaspiracy director Tabrizi interviews Richard Oppenlander, owner of a vegan company and animal rescue sanctuary, who endorses the call to ban fishing in 30 percent of the oceans by 2030 based on his calculation that “less than 1 percent of our oceans are being regulated,” a point that NFI retorted is “not only inaccurate, it’s nonsensical.”
In his coverage of illegal, unregulated and unreported (IUU) fishing in Africa, Tabrizi claims that one in every three wild caught fish imported into the United States were caught illegally and therefor sold illegally, a statistic that prominent U.S. fisheries researcher Ray Hilborn wrote was not credible, and that the retraction of the approach has been a long, drawn-out process.
Pramod et al. methods to estimate IUU are not credible
Ray Hilborn et al
Marine Policy, Volume 108, October 2019, 103632
https://www.sciencedirect.com/science/article/abs/pii/S0308597X19303318
and
Retraction drama continues, Max Mossler, Sustainable Fisheries, University of Washington, 7/14/2019
Response by Christina Hicks
Environmental social scientist at Lancaster Environment Centre, adjunct at JCU
Unnerving to discover your cameo in a film slamming an industry you love & have committed your career to. I’ve a lot to say about #seaspiracy- but won’t. Yes there are issues but also progress & fish remain critical to food & nutrition security in many vulnerable geographies.
Absolutely they raise important issues that need addressing, but there was no real conversation (intersectional or otherwise) and their conclusion-to stop eating fish a) doesn’t address the systematic injustices & b) threatens livelihoods and food security.
Here is a resource put together by academics at UW. I work on fisheries contributions to food and nutrition security. There are important messages in the film. And we do need to challenge corporate control. I just don’t think all fishers are the villains
Rebuttal by Josette Emlen Genio
Sustainable Markets Consultant at Sustainable Fisheries Partnership (SFP)
She writes
No scientist would support the assertion that all fish stocks will be collapsed by 2048. There are threats, however.
https://sustainablefisheries-uw.org/fisheries-2048/
“The latest FAO State of World Fisheries and Aquaculture report (25) indicates that the fraction of overfished stocks has increased since 2000 (from 27% to 33%), while this study suggests that abundance of stocks is increasing.”
“Effective fisheries management instrumental in improving fish stock status” Ray Hilburn et al., Proc Natl Acad Sci USA, 2020 Jan 28;117(4):2218-2224 doi: 10.1073/pnas.1909726116. Epub 2020 Jan 13.
Thoughts by Francisco Blaha
An institutional fisheries advisor. IUU, PSM & Labor issues for FFA/FAO/NZMFAT & others.
Here it is: for all of those that tell me to watch “Seaspiracy” I started and got feed up very soon… Is a kick in the guts for most of the people I work with here in the WCPO that are doing the right thing and managing their fisheries. Be outside and point fingers stuff. Of course, there are many problems! No one doubts that. But also things progressively working in many regions like the WCPO, I choose to focus my work on those. “Gloom sells but does not help”.
Furthermore. to be totally honest: I’m over the set up where, the “bad guys” are predominantly Asian, the “victims” predominantly black/brown, and the “good guys” talking about it and saving the ocean are predominantly white. While I’m sure is well intended, still drags cliche stereotypes and racist overtones.
As for the science background research of the film… as an example… a couple of minutes on google would have shown him that even the lead author of the paper retracted the claim.
Yes, I understand you may choose to not eat fish for whatever reasons you choose to believe. Is your privilege to have a choice. Yet all food production systems have impacts, and it is easy to dismiss one when your livelihood does not depend on them, like for most Pacific Islands
These countries are managing their fisheries sustainably because they are capable and understand better than anyone else, the implications of a failure. They don’t need the uncalled opinion of privileged people to tell them that doesn’t matter what they can scientifically prove.
FFA 2019 Tuna Economics Indicators Brochure
Click to access FFA%202019%20Tuna%20Economic%20Indicators%20Brochure%202019.pdf
The western and central Pacific tuna fishery: 2019 overview and status of stocks, Fisheries, Aquaculture and Marine Ecosystems
https://fame1.spc.int/en/component/content/article/251
Rebuttal by Josette Emlen Genio
I renewed my Netflix subscription just for this, and I was disappointed. Besides the many inaccuracies, I have a gazillion thoughts and sentiments about this documentary, but I’ll be more interested to hear what my fellow colleagues in marine conservation NGOs, many of which have been discredited in the film, have to say😞 But here’s my 2 cents (beware of spoilers!):
While I agree on several of the cases they presented, you cannot ask people to just “stop eating fish and go vegan” (yes that’s exactly the docu’s message) WITHOUT considering the socio-economic impacts of this in MANY fisheries-dependent, food-deficit communities. Overfishing and Illegal, Unreported and Unregulated (IUU) fishing are not only driven by greed, but also by POVERTY.
There’s a distinct line between industrial and artisanal fishing. It’s easy to say “boycott seafood” when options are afforded to you or you do not understand the complexities of the struggles and plight of fishermen. In many coastal communities in Asia and Latin America, the oceans are their LIFEBLOOD that provides them MAIN source if not the ONLY source of livelihood and food security. More than 90% of world’s fishers are NOT from industrial fishing fleets- they are smallholder, subsistence fishers – and thus stand to benefit from eating more sustainable and responsibly-caught seafood.
When it comes to sustainability, the type, size, source, and harvest method of fish always matter. Eating matang-baka or tanigue vs “industrial” salmon or tuna will GREATLY VARY in terms of impacts. And marine conservation NGOs are working hard, so consumers have informed choices. Drastic, blanket recommendations will have drastic, unimaginable consequences. Remember that.
Accusations of racism
I dare them to tell small-scale fishers, esp the ones in the developing countries that they must stop eat and do something that keeps them alive Face with look of triumph This kind of approach – is just another example of white savior complex. I am still enraged!
The documentary outright says that the large scale fishering fleets are taking the food from the small-scale fishers and causing hunger. The dumb “just don’t eat fish” message is obviously made for the viewers that are 90% first world rich people NOT dependant on fish at all.
Magnus Johnson writes
Le Chatelier’s principle
In the early parts of a chemistry class we think of a chemical reaction as a one-time event: either compounds react, or they don’t react. Nothing.
But quite often the reality is dynamic: Chemical A and B combine to make AB…. but AB breaks apart back into A and B. Then those individual A and B can eventually recombine again into AB.
So on a microscopic level, individual reactions never cease.
Yet at the macroscopic level, the reaction seems to have come to a stop.
What does happen, is that at any given pressure and temperature, we’ll end up with an equilibrium: there will be a constant, certain amount of separate pieces, and a constant, certain amount of combined pieces.
We can make a ratio of [separate pieces] compared to [combined pieces.]
This ratio is called an equilibrium constant.
Here is a visual of a situation, not about chemical reactions, but about locations. We create a ratio of how much is one one side compared to how much is on another side.
from blendspace.com/lessons/NiOSxDaHOeAhQA/copy-of-equilibrium-ap-chemistry
Online lessons
CK-12 Chemistry LeChatelier’s Principle
CK-12 LeChatelier’s Principle and the Equilibrium Constant
Dynamic Equilibrium and Le Chatelier’s Principle
Opentextbc.ca Shifting Equilibria: Le Chatelier’s Principle
Libretexts Chemistry – Le Chatelier’s Principle
Here is a fantastic infographic by Compound Interest
Apps & interactives
PhET apps – Reactions & Rates, and Reversible Reactions
interactives CK-12 Scroll down to “Flat vs Fizyy Soda”
elearning at Cal Poly Pomona – Kinetics, Equilibrium, and then Le Chatelier.
PLIX Le Châtelier’s Principle and the Equilibrium Constant
The Law of Mass Action, Wolfram
Le Chatelier’s Principle in Chemical Equilibrium, Wolfram
Constructing an equilibrium expression
See the lesson here Dynamicscience.com equilibrium4
Learning Standards
NGSS
HS-PS1-6. Refine the design of a chemical system by specifying a change in conditions that would produce increased amounts of products at equilibrium. Clarification Statement: Emphasis is on the application of Le Chatelier’s Principle and on refining designs of chemical reaction systems, including descriptions of the connection between changes made at the macroscopic level and what happens at the molecular level.
Massachusetts
HS-PS1-6. Design ways to control the extent of a reaction at equilibrium (relative amount of products to reactants) by altering various conditions using Le Chatelier’s principle. Make arguments based on kinetic molecular theory to account for how altering conditions would affect the forward and reverse rates of the reaction until a new equilibrium is established.*
Massachusetts State Assessment Boundaries:
• Calculations of equilibrium constants or concentrations are not expected in state assessment.
• State assessment will be limited to simple reactions in which there are only two reactants and to specifying the change in only one variable at a time.
Who invented the…Engine, Auto, Radio, TV, Computer, Smartphone, GPS?
The Difference Engine of Charles Babbage, progenitor to the computer.
Who invented the …
power loom? telephone?
internal combustion engine? automobile?
radio? television? computer?
smartphone? GPS?
technology for organ transplantation?
modern light bulb?
Myth – Each of these was invented by someone.
Reality – None of these were developed by just one person. Instead, each technology developed over time – with contributions from many people.
Consider a recent meme shared on social media about Dr. Gladys West. It is well-intentioned, but ends up concealing as much as it reveals.
While doing important work, she didn’t invent GPS – no one person did.
Instead, we follow the contributions of many people. Here, from left to right are Friedwardt Winterberg, Bill Guier, Frank McClure, and George Weiffenbach.
And here are Roger Easton, Ivan Getting, Bradford Parkinson, and Gladys West.
Let’s look at the story more deeply, which covers decades:
One of the fathers of GPS was Friedwardt Winterberg. Back in 1955 he proposed a test of Einstein’s theory of general relativity.
Winterberg realized that it should be possible to detect the predicted slowing of time in a strong gravitational field; this could be done by using atomic clocks placed in Earth orbit inside artificial satellites.
From “The Elegant Universe”, PBS series NOVA. 2003.
Contrary to the predictions of classical physics, relativity predicts that the clocks on the GPS satellites would be seen by the Earth’s observers to run 38 microseconds faster per day than the clocks on the Earth.
Image found on Gyfcat. Looking for the source.
His experiment was eventually experimentally verified by Hafele and Keating in 1971 by flying atomic clocks on commercial jets.
Without taking such relativistic corrections into account, any position calculated from satellite technology – such as GPS – would quickly drift into error. The error in estimated position would be as much as 10 kilometers per day (6 miles/day.)
The next people who helped create what would become GPS were William Guier and George Weiffenbach. They worked at Johns Hopkins University’s Applied Physics Laboratory (APL.)
When the Soviet Union launched the first artificial satellite (Sputnik 1) in 1957, they decided to monitor its radio transmissions.
Guier and Weiffenbach realized that, because of the Doppler effect, they could pinpoint where the satellite was along its orbit.
In 1958, Frank McClure, the deputy director of the APL, asked Guier and Weiffenbach to investigate the inverse problem – pinpointing the user’s location, given the satellite’s location.
At the time, the US Navy was developing the submarine-launched Polaris missile, which required them to know the submarine’s location.
This led Guier and Weiffenbach, along with other scientists at APL to develop the TRANSIT system. Transit was used by the U.S. Navy to provide location information to its Polaris ballistic missile submarines.
It was also used as a navigation system by Navy surface ships, as well as for surveying. This system went online in 1960.
The next father of GPS would be Roger L. Easton of the Naval Research Laboratory. During the 1960s and early 1970s he developed a navigational system with passive ranging, circular orbits, and space-borne high precision clocks placed in satellites.
Ivan A. Getting of The Aerospace Corporation
In the 1950s, as head of research and engineering at Raytheon Corp., Waltham, Mass., Getting led a project to develop a mobile ballistic missile guidance system called Mosaic, which was to work like the Loran system.
But Getting envisioned another concept. Though the railroad mobile version of the intercontinental ballistic missile was cancelled, he realized that if a similar system were used, one that based the transmitters on satellites, and if enough satellites were lofted so that four were always in sight, it would be possible to pinpoint locations in three dimensions anywhere on earth. This theory led to Navstar.
For GPS, Also Thank Ivan Getting; He Got “the Damn Thing Funded, Tekla Perry, IEEE Spectrum, 4/19/2018
Bradford Parkinson of the Applied Physics Laboratory was the lead architect, advocate and developer of GPS. He was given full, direct control of the development of the demonstration system, which included satellites, a global ground control system, nine types of user receivers, and an extensive land, sea and air test program
Gladys West analyzed data from satellites, putting together altimeter models of the Earth’s shape. She became project manager for the Seasat radar altimetry project, the first satellite that could remotely sense oceans.
From the mid-1970s through the 1980s, West worked on precise calculations to model the shape of the Earth – a geoid – an ellipsoid with irregularities.
NOAA National Geodetic Survey, from a PPT by Hawaii Geographic Information Coordinating Council
Generating an extremely accurate model required her to employ complex algorithms to account for variations in gravitational, tidal, and other forces that distort Earth’s shape. This was essential for the Global Positioning System (GPS).
Whew…. and all that is just the short version of who invented the GPS. The longer version would literally take a book, a dozen hours of video, and include dozens more people.
Student project
Students will work individually or in groups, researching, and then creating a presentation on the evolution of any of these technologies.
You may propose another technology to investigate; clear it with your teacher first.
power loom? telephone?
internal combustion engine? automobile?
radio? television? computer?
smartphone? GPS?
technology for organ transplantation?
modern light bulb?
Many ways to create your report!
Select one of these options
Create a written report using MS Word/Google Docs. This will have images, text, perhaps short animations if you like. If you like, you can use the built-in voice-to-text; this will transcribe your words.
Create a video, using your favorite software & apps. This will have images, text, perhaps short animations if you like. You’ll narrate it. Share the project as a video file with us.
Create a PowerPoint/Google Slides presentation. This will have images, text, perhaps short animations if you like.
Create an Infographic. There are many websites and apps out there to do this. Choose your favorite apps. This will have images, text, perhaps short animations if you like.
Resources
Engineering & Technology History, People, and Milestones PBS Learning Media
Learning Standards
NGSS Science
HS-PS3-3. Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy.*
Crosscutting concepts – Influence of Science, Engineering and Technology on Society and the Natural World. Modern civilization depends on major technological systems. Engineers continuously modify these technological systems by applying scientific knowledge and engineering design practices to increase benefits while decreasing costs and risks.
Disciplinary Core Idea Progression Matrix – ETS2.B Manufacturing
Grade 6-8. The design and structure of any particular technology product reflects its function. Products can be manufactured using common processes controlled by either people or computers.
Grade 9-10 – Manufacturing processes can transform material properties to meet a need. Particular manufacturing processes are chosen based on the product design, materials used, precision needed, and safety.
History C3 Framework and the National Social Studies Standards
D2.Eco.13.9-12. Explain why advancements in technology and investments in capital goods and human capital increase economic growth and standards of living.
D2.Geo.7.6-8. Explain how changes in transportation and communication technology influence the spatial connections among human settlements and affect the diffusion of ideas and cultural practices.
D2.His.1.9-12. Evaluate how historical events and developments were shaped by unique circumstances of time and place as well as broader historical contexts.
Common Core
CCSS.ELA-LITERACY.W.8.4
Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
CCSS.ELA-Literacy.WHST.9-10.6
CCSS.ELA-Literacy.WHST.11-12.6
Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically.
Molecular Orbitals
Content objective (What are we learning & why?)
Lewis theory and the octet rule are not enough to describe the shapes of molecules and many of their properties.
To go beyond such limitations we learn molecular orbital theory.
Prerequisites (What do we need to know before starting this unit?)
Lewis structures; the octet rule; covalent & ionic bonds
sub-atomic particles; s, p, d, and f orbitals
the wave nature of matter; Schrödinger model of the atom
Shorthand notation reminder
e- = electron
Introduction
By this time it may be no surprise to you that the name of this theory – molecular orbitals – is a misnomer. There are no orbitals involved.
We should really call this
“Three dimensional electron-clouds, overlapping with other three dimensional electron-clouds, to make even more complicated and pretty electron-clouds theory”
But that’s way too many words. So “molecular orbitals” it is 😉
Remember, electrons are not solid objects like billiard balls.
And e- don’t really orbit an atom’s nucleus.
Electrons are better described as a rippling waves.
How does the Schrödinger equation create orbitals?
When we interact with e- in certain ways, sure they have particle-like properties.
But most of the time they have wave-like properties.
If you feel like it, you can learn a bit about quantum mechanics here.
What does this mean? When atoms get close to each other, the 3D wave function of one e- overlaps with the 3D wave function of another e-.
This creates constructive interference and destructive interference:
high parts of one wave combine with high parts of another wave to make even higher waves
A high part of a wave can be canceled out by hitting a low point of another wave.
Electrons work like this – except they have three dimensional waves (the GIF above is only 2D.)
In this unit we’re going to see what happens to the shape of orbitals when atoms come close enough to bond with each other.
===========================================
This next section has been adapted from Prentice Hall Chemistry by Wilbraham, Staley, Matta and Waterman.
Sigma Bonds
Atomic orbitals can combine to form a molecular orbital that is symmetrical around the axis connecting atomic nuclei. This is called a sigma bond.
We use the Greek letter sigma (σ).
Covalent bonding results from an imbalance between the attractions and repulsions of the nuclei and e- involved.
This next image is from Valence Bond Theory, LibreTexts
Because their charges have opposite signs, the nuclei and e- attract each other.
Because their charges have the same sign, nuclei repel other nuclei, and e- repel other e-.
In a hydrogen molecule (H2), the nuclei repel each other, as do the e-.
In a bonding molecular orbital of hydrogen, however, the attractions between the H nuclei and the e- are stronger than the repulsions.
The balance of all the interactions between the H atoms is thus tipped in favor of holding the atoms together.
The result is a stable, diatomic molecule of H2.
Atomic p orbitals can also overlap to form molecular orbitals.
A fluorine atom, for example, has a half-filled 2p orbital.
When two fluorine atoms combine then the p orbitals overlap to produce a bonding molecular orbital.
There is a high probability of finding a pair of e- between the positively charged nuclei of the two fluorines.
The fluorine nuclei are attracted to this region of high e- density.
This attraction holds the atoms together in the fluorine molecule (F2).
The overlap of the 2p orbitals produces a bonding molecular orbital that is symmetrical when viewed around the F⎯F bond axis connecting the nuclei.
Therefore, the F⎯F bond is a sigma bond.
Pi bonds, π bonds
“Pi” is symbolized by the Greek letter π.
In the sigma bond of the F2 molecule, the p atomic orbitals overlap end-to-end.
In some molecules, however, orbitals can overlap side-by-side.
The side-by-side overlap of atomic p orbitals produces pi molecular orbitals.
When a pi molecular orbital is filled with two electrons, a pi bond results.
In a pi bond, the bonding e- are most likely to be found in sausage-shaped regions above and below the bond axis of the bonded atoms.
It is not symmetrical around the F⎯F bond axis.
Atomic orbitals in pi bonding overlap less than in sigma bonding.
Therefore, pi bonds tend to be weaker than sigma bonds.
===========================================
Bonding and antibonding
When orbitals interact, the result can be bonding or antibonding.
Bonding molecular orbitals
Occurs when the interactions between the orbitals are constructive.
They are lower in energy than the orbitals that combine to produce them.
Antibonding molecular orbitals
Occurs when the interactions between the orbitals are are destructive (out-of-phase.)
The destructive interference creates a long, thin, region where the probability of finding an e- is effectively zero. We call this region a nodal plane.
They are basically an orbital containing an e- outside the region between the two nuclei.
They are higher in energy than the orbitals that combine to produce them.
Do both bonding and antibonding orbitals exist in the same molecule at the same time?
Yes. They both can develop as atoms come together to form a molecule. Both exist at the same time.
The resultant behavior of the molecule depends on how all the orbitals – bonding and antibonding – add together.
Let’s watch Pi orbitals develop
Here we see the Pi bonding orbital forming as P orbitals, from two atoms moving closer, slowly come together.
Pi bonding molecular orbital
Here we see two P orbitals come together to form what is known as the antibonding Pi orbital. Notice that we see a nodal plane develop!
Pi antibonding molecular orbital showing nodal plane
These two animations were created by Mohammad Alhudaithi using Wolfram Alpha. See Visualizing Molecular Orbitals for One Electron Diatomic Molecules.
Example: two O atoms bonding
Here we see 2 O atoms bonding together to create an O2 molecule.
Each atom has its own three-dimensional e- orbitals.
As the atoms get closer the wave functions overlap. The subsequent constructive and destructive interference creates a new three dimensional shape, one for the molecule as a whole.
The original 2s and 2p atomic orbitals merge to create Sigma and Pi orbitals. These bind the atoms together.
The 1s orbitals do not combine and still show the individual atoms.
This GIF is from O2 Molecular Orbitals Animation at Wikimedia by Kilohn Limahn.
________________________________________
Deep thoughts
Because arguments based on atomic orbitals focus on the bonds formed between valence electrons on an atom, they are often said to involve a valence-bond theory.
The valence-bond model can’t adequately explain the fact that some molecules contains two equivalent bonds with a bond order between that of a single bond and a double bond.
The best it can do is suggest that these molecules are mixtures, or hybrids, of the two Lewis structures that can be written for these molecules.
This problem, and many others, can be overcome by using a more sophisticated model of bonding based on molecular orbitals.
Molecular orbital theory is more powerful than valence-bond theory because the orbitals reflect the geometry of the molecule to which they are applied. But this power carries a significant cost in terms of the ease with which the model can be visualized.
Molecular Orbital Theory, Purdue, Chemical Education Division Groups, Bodner Research Web, General Chemistry Help, The Covalent bond
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Deep thoughts
Molecular Orbital theory (MO) is the most important quantum mechanical theory for describing bonding in molecules. It is an approximate theory (as any theory that utilizes “orbitals”), but it is a very good approximation of the bonding.
The MO perspective on electrons in molecules is very different from that of a localized bonding picture such as valence bond (VB) theory.
In VB we describe particular bonds as coming from the overlap of orbitals on atomic centers.
In MO this idea is not completely gone, but now rather than just looking at individual bonds, MO describes the whole molecule as one big system.
The orbitals from MO theory are spread out over the entire molecule rather than being associated with a bond between only two atoms.
Each MO can have a particular shape such that some orbitals have greater electron density in one place or another, but in the end the orbitals now “belong” to the molecule rather than any particular bond.
For diatomic molecules (which we look at a lot), the VB picture and the MO picture are very similar. This is because the whole molecule is simply two atoms bonded together. The difference become more apparent when we look at MO in larger molecules.
Molecular orbitals, Chemistry 301 , Univ of Texas
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Teaching molecular orbitals with the relationships analogy:
This is a great lesson which starts of simple and then brings you into a series of analogy that eventually lets you understand the topic:
From the introduction – “A lot of people say they’re happy being single, and I believe that many likely are. But in the back of their mind of many single people is the thought that if they just found the right person, they might be even happier – or less unhappy, which is a crappy way to look at it psychologically but necessary if you wish to draw a diagram where a “happy couple” is occupying a “potential energy well”, below.”
and then analogies and diagrams grow from here…
Bonding And Antibonding Pi Orbitals, by James Ashenhurst, Master organic chemistry
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Relating molecular orbital theory to quantum mechanics and standing waves
The Lewis Structure approach provides an extremely simple method for determining the electronic structure of many molecules. It is a bit simplistic, however, and does have trouble predicting structures for a few molecules.
Nevertheless, it gives a reasonable structure for many molecules and its simplicity to use makes it a very useful tool for chemists.
A more general, but slightly more complicated approach is the Molecular Orbital Theory. This theory builds on the electron wave functions of Quantum Mechanics to describe chemical bonding.
To understand MO Theory let’s first review constructive and destructive interference of standing waves starting with the full constructive and destructive interference that occurs when standing waves overlap completely.
Molecular Orbital Theory by Philip J. Grandinetti
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Very advanced questions
Valence electrons are associated with molecular orbitals and hybridizations. Do core electrons have molecular/hybridized orbitals, or the original atomic orbitals?
Do core electrons have molecular orbitals?
Apps and interactives
Real-Time Visualization of the Quantum Mechanical Atomic Orbitals, Dauger Research, Atom In A Box, app for Macintosh and iPad
Octet rule exceptions
When we draw electron structures or orbital box diagrams, we are following a pattern, the octet “rule.” But there are many exceptions to this pattern, especially with heavier atoms and transition metals.
See page 190, Prentice Hall Chemistry, Wilbraham et al. Section 7.1 ions.
Article
This section excerpted from 9.6: Exceptions to the Octet Rule, from Chemistry: Principles, Patterns, and Applications by Bruce A. Averill and Patricia Eldredge.
General exceptions to the octet rule include molecules that have an odd number of electrons and molecules in which one or more atoms possess more or fewer than eight electrons.
Molecules with an odd number of electrons are relatively rare in the s and p blocks but rather common among the d– and f-block elements.
Compounds with more than an octet of electrons around an atom are called expanded-valence molecules.
One model to explain their existence uses one or more d orbitals in bonding in addition to the valence ns and np orbitals.
Such species are known for only atoms in period 3 or below, which contain nd subshells in their valence shell.
Learning Objective: assign a Lewis dot symbol to elements not having an octet of electrons in their compounds.
Lewis dot structures provide a simple model for rationalizing the bonding in most known compounds. However, there are three general exceptions to the octet rule:
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Molecules, such as NO, with an odd number of electrons;
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Molecules in which one or more atoms possess more than eight electrons, such as SF6; and
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Molecules such as BCl3, in which one or more atoms possess less than eight electrons.
Odd Number of Electrons
Because most molecules or ions that consist of s– and p-block elements contain even numbers of electrons, their bonding can be described using a model that assigns every electron to either a bonding pair or a lone pair.
Molecules or ions containing d-block elements frequently contain an odd number of electrons, and their bonding cannot adequately be described using the simple approach we have developed so far.
There are, however, a few molecules containing only p-block elements that have an odd number of electrons.
Some important examples are nitric oxide (NO), whose biochemical importance was described in earlier chapters; nitrogen dioxide (NO2), an oxidizing agent in rocket propulsion; and chlorine dioxide (ClO2), which is used in water purification plants.
Consider NO, for example. With 5 + 6 = 11 valence electrons, there is no way to draw a Lewis structure that gives each atom an octet of electrons.
Molecules such as NO, NO2, and ClO2 require a more sophisticated treatment of bonding.
Example 1: The NO Molecule. Draw the Lewis structure for the molecule nitrous oxide (NO).
5. There are currently 5 valence electrons around the nitrogen.
A double bond would place 7 electrons around the nitrogen, and a triple bond would place 9 around the nitrogen. We appear unable to get an octet around each atom.
More Than an Octet of Electrons
The most common exception to the octet rule is a molecule or an ion with at least one atom that possesses more than an octet of electrons. Such compounds are found for elements of period 3 and beyond.
Examples from the p-block elements include SF6, a substance used by the electric power industry to insulate high-voltage lines, and the SO42− and PO43− ions.
Let’s look at sulfur hexafluoride (SF6), whose Lewis structure must accommodate a total of 48 valence electrons [6 + (6 × 7) = 48].
If we arrange the atoms and electrons symmetrically, we obtain a structure with six bonds to sulfur; that is, it is six-coordinate.
Each fluorine atom has an octet, but the sulfur atom has 12 electrons surrounding it rather than 8.
The third step in our procedure for writing Lewis electron structures, in which we place an electron pair between each pair of bonded atoms, requires that an atom have more than 8 electrons whenever it is bonded to more than 4 other atoms.
Basis of the octet rule
The octet rule is based on the fact that each valence orbital (typically, one ns and three np orbitals) can accommodate only two electrons.
To accommodate more than eight electrons, sulfur must be using not only the ns and np valence orbitals but additional orbitals as well.
Sulfur has an [Ne]3s23p43d0 electron configuration, so in principle it could accommodate more than eight valence electrons by using one or more d orbitals.
Thus, species such as SF6 are often called expanded-valence molecules.
Whether or not such compounds really do use d orbitals in bonding is controversial, but this model explains why compounds exist with more than an octet of electrons around an atom.
There is no correlation between the stability of a molecule or an ion and whether or not it has an expanded valence shell.
Some species with expanded valences, such as PF5, are highly reactive, whereas others, such as SF6, are very unreactive.
In fact, SF6 is so inert that it has many commercial applications. In addition to its use as an electrical insulator, it is used as the coolant in some nuclear power plants, and it is the pressurizing gas in “unpressurized” tennis balls.
An expanded valence shell is often written for oxoanions of the heavier p-block elements, such as sulfate (SO42−) and phosphate (PO43−).
Sulfate, for example, has a total of 32 valence electrons [6 + (4 × 6) + 2]. If we use a single pair of electrons to connect the sulfur and each oxygen, we obtain the four-coordinate Lewis structure
(a). We know that sulfur can accommodate more than eight electrons by using its empty valence d orbitals, just as in SF6.
An alternative structure (b) can be written with S=O double bonds, making the sulfur again six-coordinate.
We can draw five other resonance structures equivalent to (b) that vary only in the arrangement of the single and double bonds.
In fact, experimental data show that the S-to-O bonds in the SO42− ion are intermediate in length between single and double bonds, as expected for a system whose resonance structures all contain two S–O single bonds and two S=O double bonds.
When calculating the formal charges on structures (a) and (b), we see that the S atom in (a) has a formal charge of +2, whereas the S atom in (b) has a formal charge of 0.
Thus by using an expanded octet, a +2 formal charge on S can be eliminated.
Less Than an Octet of Electrons
Molecules with atoms that possess less than an octet of electrons generally contain the lighter s- and p-block elements.
Especially so for beryllium, typically with just four electrons around the central atom, and with boron, typically with six.
One example, boron trichloride (BCl3) is used to produce fibers for reinforcing high-tech tennis rackets and golf clubs.
The compound has 24 valence electrons and the following Lewis structure:
The boron atom has only six valence electrons, while each chlorine atom has eight.
A reasonable solution might be to use a lone pair from one of the chlorine atoms to form a B-to-Cl double bond:
This resonance structure, however, results in a formal charge of +1 on the doubly bonded Cl atom and −1 on the B atom.
The high electronegativity of Cl makes this separation of charge unlikely and suggests that this is not the most important resonance structure for BCl3.
This conclusion is shown to be valid based on the three equivalent B–Cl bond lengths of 173 pm that have no double bond character.
Electron-deficient compounds such as BCl3 have a strong tendency to gain an additional pair of electrons by reacting with species with a lone pair of electrons.
Example 8
Draw Lewis dot structures for each compound.
(a) BeCl2 gas, a compound used to produce beryllium, which in turn is used to produce structural materials for missiles and communication satellites.
(b) SF4, a compound that reacts violently with water
Include resonance structures where appropriate.
Given: two compounds
Asked for: Lewis electron structures
Strategy:
(A) Use the procedure given earlier to write a Lewis electron structure for each compound. If necessary, place any remaining valence electrons on the element most likely to be able to accommodate more than an octet.
(B) After all the valence electrons have been placed, decide whether you have drawn an acceptable Lewis structure.
Solution:
(A) Because it is the least electronegative element, Be is the central atom. The molecule has 16 valence electrons (2 from Be and 7 from each Cl). Drawing two Be–Cl bonds and placing three lone pairs on each Cl gives the following structure:
(B) Although this arrangement gives beryllium only 4 electrons, it is an acceptable Lewis structure for BeCl2. Beryllium is known to form compounds in which it is surrounded by less than an octet of electrons.
Now let’s draw a structure for SF4:
Sulfur is the central atom because it is less electronegative than fluorine.
The molecule has 34 valence electrons (6 from S and 7 from each F).
The S–F bonds use 8 electrons, and another 24 are placed around the F atoms:
The only place to put the remaining 2 electrons is on the sulfur, giving sulfur 10 valence electrons:
Sulfur can accommodate more than an octet, so this is an acceptable Lewis structure.
Example: Draw Lewis dot structures for XeF4 .
Notes
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In oxoanions of the heavier p-block elements, the central atom often has an expanded valence shell.
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Molecules with atoms that have fewer than an octet of electrons generally contain the lighter s- and p-block elements.
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Electron-deficient compounds have a strong tendency to gain electrons in their reactions.
This section of this resource is available as Creative Commons Non Commercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
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Resources
8.7: Exceptions to the Octet Rule, Chemistry: The Central Science by Brown, LeMay, Busten, Murphy, and Woodward
9.6: Exceptions to the Octet Rule Chemistry: Principles, Patterns, and Applications by Bruce A. Averill and Patricia Eldredge
9.11 Exceptions to the Octet Rule, CK-12 Chemistry for High School FlexBook
Exceptions to the Octet Rule, General Chemistry I, Dr. Michael Blaber
8.8 Exceptions to the Octet Rule Chemistry, Prentice Hall
CoreChem:Exceptions to the Octet Rule
Why are there exceptions to the octet rule?
Because the octet “rule” was never a rule in the first place.
https://www.quora.com/What-is-the-octet-rule-in-chemistry-Are-there-any-exceptions-to-it
https://www.quora.com/Why-does-boron-violate-the-octet-rule
Advanced Placement Chemistry discussion
Exceptions to the octet rule and resonances
Trihydridoboron, also known as borane or borine, is an unstable and highly reactive molecule with the chemical formula BH
3. The preparation of borane carbonyl, BH3(CO), played an important role in exploring the chemistry of boranes, as it indicated the likely existence of the borane molecule.[1] However, the molecular species BH3 is a very strong Lewis acid. Consequently it is highly reactive and can only be observed directly as a continuously produced, transitory, product in a flow system or from the reaction of laser ablated atomic boron with hydrogen.
See https://www.quora.com/Why-do-incomplete-octets-occur
Resonance (Chemistry)
Introduction (all levels)
Abbreviations: e- = electron
In chemistry we make simple drawings showing the location of each atom in a molecule.
We call these Lewis diagrams or dot diagrams.
Examples:
Here is a slightly more complicated Lewis diagram. This is Tyrosine. Don’t worry about what the molecule is; the point is only that we draw it with simple shapes.
Single lines represent single-bonds between atoms
Double-lines represent double-bonds between atoms
We use Lewis diagrams all the time.
Yet once in a while the rules for making Lewis structures don’t work
Here are three ways that the rules break down, even for a simple molecule:
1. A molecule might have 2 or 3 different ways of being drawn. How do we decide which way is correct? The rules don’t tell us.
2. Using the same example (ozone) the rules seem to want us to draw it as a straight line. Yet experimental measurements show that ozone is bent.
Hmm, the rules fail to predict if a molecule is straight or bent.
electron clouds of ozone molecule
3. The rules sometimes compel us to make double bonds on side of a molecule, and single bonds on the other side.
Double bonds are stronger, holding atoms closer together, so they are shorter length.
Single bonds are weaker, holding atoms less close together, so they are longer length.
Yet sometimes experimental measurements of a molecule show that all bonds are the same length.
Consider the possible Lewis structures for ozone: Either way, some bonds are shorter while others are longer. Yet the 3D electron map for ozone (above) shows that all bond lengths are identical.
The rules, clearly, are incorrect: Neither model is correct enough.
Takeaway: Even for small, simple molecules, Lewis structure rules can fail in multiple ways.
This is a problem yet also an opportunity: In physics, when a rule break down, that means the “rule” is really a simplified case of a more general rule.
Imperfect assumptions -> imperfect rules
What assumptions were behind Lewis structure rules?
Atoms assumed to be like tiny solar system.
protons, neutrons, and e- are assumed to be in in one location or in another. location.
Yet experiments prove that e- aren’t like tiny billiard balls at all.
They aren’t solid objects!
We’ll need some quantum mechanics to figure out what e- really are, but for now we can say this:
e- act like a cloud of energy that spreads out.
Resonance: Fudging drawing rules to make them fit real world measurements
When more than one possible Lewis structure for a molecule can be drawn, resonance is a trick in which we draw all possible forms, and say that the real molecule is an average of each separate drawing.
We call this a resonance hybrid model.
Several Lewis structures are collectively describe the true structure.
Example: Benzene is a hydrocarbon, C6H6. The Lewis rules are ambiguous. We could draw it either way. Which structure is right? Neither!
We just draw both possibilities, and say that the real molecule is an average of the two possibilities.
The real structure is an average of the two different drawings. (See the top 2 drawings here.)
The bottom picture is a way to symbolize that some of these e- aren’t in the left form, or the right form, but are really sort of evenly spread out.
Now combine this idea with what we learned previously in chemistry:
There are many different ways to draw the same molecule.
All of the following are different ways of showing benzene.
Honors: ozone
According to experimental evidence from microwave spectroscopy, ozone is a bent molecule.
The central atom is sp² hybridized with one lone pair.
It can be represented as a resonance hybrid with two contributing structures, each with a single bond on one side and double bond on the other.
Here’s one way to draw the resonance structures of ozone.
Here is a better way of drawing it, with the experimentally determined angles.
External links
TBA
Learning Standards
NGSS
HS-PS1-1. Use the periodic table as a model to predict the relative properties of elements based on the patterns of electrons in the outermost energy level of atoms.
NGSS Evidence Statement – Students predict the following patterns of properties:
i. The number and types of bonds formed (i.e. ionic, covalent, metallic) by an element and
between elements;
College Board Standards for College Success: Science
Objective C.1.2 Electrons
Students understand that the interactions of electrons between and within atoms are the primary factors that determine the properties of matter.
ESSENTIAL KNOWLEDGE – Students apply, as well as engage and reason with, the following concepts in the performance expectations:
• Atoms can bond to form molecules, ionic lattices, network covalent structures or materials with metallic properties. Each of these types of structures has different, yet predictable, properties that depend on the identity of the elements and the types of bonds formed.
• The forces of attraction between the particles in molecules, ionic lattices, network covalent structures or materials with metallic properties are called chemical bonds.
• The bonds in most compounds fall on a continuum between the two extreme models of bonding: ionic and covalent.
• An ionic bond involves the attraction between two oppositely charged ions, typically a positively charged metal ion and a negatively charged nonmetal ion. An ion attracts oppositely charged ions from every direction, resulting in the formation of three-dimensional lattices.
• Covalent bonds typically involve at least two electrons shared between the bonding atoms. Nonmetal atoms usually combine by forming one or more covalent bonds between atoms. Covalent bonding can result in the formation of structures ranging from
small molecules to large molar mass biopolymers and three-dimensional lattices (e.g., a diamond).
Objective C.1.4 Representations of Matter
Students understand that atoms, molecules and ionic substances can be represented with a variety of models.
C-PE.1.4.1 Translate among representations (including molecular formulas, Lewis structures, ball-and-stick models and space-filling models) of macroscopic, atomic–molecular and symbolic levels of matter. Compare and contrast the types of information that can be inferred from the different representations. Choose the most appropriate representation to illustrate a physical or chemical process
C-PE.1.4.2 Construct Lewis structures for simple molecules, showing all bonds and lone pairs of electrons for simple molecules. Using regions of electron density, predict electron pair geometry and the shape of the molecule from the arrangement of the atoms in space.
Plotting Coulomb’s law or the law of gravity – not quite hyperbolas
Here’s a graph of force versus distance using an inverse square law.
This is Coulomb’s law, showing the magnitude of the force between two electrically charged particles.
It looks hyperbolic – but does this actually qualify as a hyperbola?
What is a hyperbola?
There are many different yet equivalent definitions for hyperbolas, see those definitions here:
Hyperbola, Math Is Fun, The Hyperbola, Lumen, Graphs of Hyperbolas Centered at the Origin, CK-12
For our graph:
Force is plotted on the Y-axis.
‘r’ is the distance between two charged objects, plotted on the X-axis.
In the above example we used Coulomb’s law, but mathematically it is the same form as Newton’s law of universal gravitation:
K is just a constant. With gravity this constant is extremely small.
With electric attraction/repulsion the constant is many orders of magnitude larger.
So for any of these cases, is this curve a hyperbola?
No. Hyperbolas – by definition – are conic sections.
And by definition conic sections must be able to be put into this format:
Ax2 + Bxy + Cy2 +Dx + Ey + F = 0
The above equations – Coulomb’s law and Newton’s law – can’t be put into this format. Thus these curves cannot be hyperbolic.
Rational functions
So what kind of curve are these force vs distance curves?
They are not hyperbolas but they are rational functions: the ratio of two polynomials.
It is called “rational” because one is divided by the other, like a ratio.
Notice that rational functions have horizontal and vertical asymptotes, and inverse relationships, so they visually approximate hyperbolas.
One might even say that they share some properties of hyperbolas without fulfilling all the criteria of actually being one.
A special case of rational functions
Although not applicable for Coulomb’s law, one may note that rational functions of the form (ax+b)/(cx+d) are hyperbolas
As long as determinant, ad-bc, and c, are non-zero.
So hyperbolas are special cases of rational functions.
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Thanks for visiting. While you are here see our other articles on mathematics.
#hyperbolas #conic #rationalequations
The Eötvös effect
The Eötvös effect is the change in perceived gravitational force caused by the change in centrifugal acceleration resulting from eastbound or westbound velocity.
The measured effect is caused by the motion of the object traveling with, or against, the rotation of the Earth.
When moving eastbound, the object’s angular velocity is increased (in addition to Earth’s rotation)
thus the centrifugal force also increases, causing a perceived reduction in gravitational force.
When moving westbound, the object’s angular velocity is decreased,
thus the centrifugal force decreases, causing a perceived increase in gravitational force.
From flatearth.ws, debunking flat earth misconceptions
In the early 1900s (decade), a German team from the Institute of Geodesy in Potsdam carried out gravity measurements on moving ships in the Atlantic, Indian, and Pacific oceans.
While studying their results, the Hungarian nobleman and physicist Baron Roland von Eötvös (Loránd Eötvös) noticed that the readings were lower when the boat moved eastwards, higher when it moved westward. He identified this as primarily a consequence of Earth’s rotation.
In 1908, new measurements were made in the Black Sea on two ships, one moving eastward and one westward. The results substantiated Eötvös’ understanding.
Relationship between eötvös effect and Coriolis effect
Some people say that the Eötvös effect is the vertical component of the Coriolis effect. Max on Physics StackExchange explains to us
In many science disciplines, casual versus formal usages become intermixed, and this is certainly one area.
Eötvös is not the vertical component of Coriolis.
The earth is both (a) spherical and (b) spinning. This produces a number of phenomena that affect bodies in motion on or near the surface of the Earth.
In casual usage these phenomena tend to be lumped together into all being called “Coriolis,” but they are actually discrete physical properties that are not related, except for the fact that they are artifacts of (a), (b), or both.
Coriolis is a conservation of angular momentum consideration when objects move north/south across a spinning sphere.
As you move away from the equator latitudinally, the same angular rate of rotation around the Earth’s C/G results in a different velocity in the east/west component, and the effects of this difference is the Coriolis Effect.
Were the Earth a cylinder instead of a sphere, there’d be no Coriolis Force. (*)
Eötvös on the other hand is a centrifugal force/orbital mechanics problem. Eötvös would still occur on a cylinder, where Coriolis would not.
There is an angular momentum force that acts east/west based on the height of an object’s trajectory or orbit, and thus would affect the vertical component of a projectile’s trajectory at long distances involving high trajectories.
But this isn’t Eötvös at all. If I shoot a projectile perfectly vertically a few miles into the air, conservation of angular momentum dictates the projectile will not land back on me, it will land several feet west of me, opposite the direction of the Earth’s spin. It may be more correct to think of this motion as the vertical component of Coriolis.
(*) This gets addressed later on this page. There would be some force, but it would different from what we see on a spherical Earth.
KaiserScience 
