Orbits Within the Nucleus

By Paul VanRaden

© 2026

Since 1913, an atom has a small nucleus and electrons orbiting the nucleus. Chemistry describes different types of atoms, classifies them into elements and their isotopes, groups them into classes such as metals or noble gases, and explains how atoms combine into molecules. Hydrogen has one electron and helium has a second electron which travels in 2 cone shaped areas above and below its nucleus according to the chemistry I learned in high school and college almost 50 years ago. That second orbit makes sense only if the second electron travels up and down thru the empty space in the middle of each helium atom’s nucleus. Each larger element also includes that second electron shell and if so, each element larger than helium also must also have a hole in the middle of its nucleus.

In 2023, NASA announced that harmonic orbits among planets can be more stable than orbits that are less well tuned. The hydrogen atom, the hydrogen molecule, and helium have relative masses ratios of 1 to 2 to 4. The 4 bodies in helium’s nucleus line up in a straight line at 6 different points in their harmonic orbits spinning in opposite direction with a ratio of 1 to -2. Each nucleus has an inner orbit with 2 bodies (like a binary star) and a second orbit with 2 bodies that takes twice as long to travel 360 degrees but going the opposite direction. Each nucleus then has the hole for the second electron that I had imagined 50 years ago during chemistry classes. Finding those 2 harmonic nuclear orbits in helium took me about 1 day using 1 sheet of graph paper, a pencil, and a calculator.

The periodic table then lists 8 more elements in a row leading up to neon that has relative mass of 20. The next orbits 3 and 4 must also be a pair of harmonic nuclear orbits with opposite spin but with 4 instead of 2 bodies per orbit. Those first 4 orbits with 2 + 2 + 4 + 4 = 12 bodies can explain the nuclear orbits in carbon 12. I verified on graph paper that the 8 bodies in orbits 3 and 4 can line up with the 4 bodies in orbits 1 and 2 at those same 6 points, just like the hexagon shaped molecules that carbon often forms. The neon atom with a mass of 20 requires another pair of harmonic orbits 5 and 6 with 4 more bodies each.

The harmonic nuclear orbits look nice both in graphs and in real life. Seeing is believing, and a real picture of a real nucleus matches the nuclear orbit math and the graphs. Instead of writing a paper, I made about 40 slides with graphs and pictures of the nuclear orbits. Those slides explain how atoms really look and work and are available at:

Orbits Within the Nucleus

First meeting

The first ever meeting on paired harmonic nuclear orbits was held January 26, 2026, 11am Eastern Standard Time until noon.

The attendees were:

Mark VanRaden, PhD in Statistics, 2008, George Washington University, retired

Miriam McKenna, B.S. in Civil Environmental Engineering, 1995, University of Southern California, retired

Deb Noordhoff, Assoc. of Science, 1976, Highland Community College, Freeport, IL, retired

Judy Winship, B.S. in Mathematics, 1980, Illinois Wesleyan University, self employed

Paul VanRaden, PhD in Animal Breeding, 1986, Iowa State University, retired

Zoom’s Artificial Intelligence generated notes from our meeting and that unedited meeting report follows:

Meeting assets for Sibling Meeting are ready!

Meeting summary

Quick recap

The meeting began with Mark sharing his recent COVID-19 diagnosis and mild symptoms, followed by a discussion about staying active while infectious and avoiding contact with others. The group then discussed personal updates, including Deborah's new bell choir and Paul's discovery of a pattern in atomic orbits that resembles the periodic table of elements. Paul presented his theory on atomic structure and harmonic orbits, explaining how he discovered a pattern in the orbits of protons and neutrons that resembles a hexagonal or snowflake shape, and discussed the implications of his findings with the group.

Next steps

• Paul: Decide on next steps for formally publishing or presenting the new atomic/nuclear orbit theory, including consideration of peer review, computer programming verification, and possible venues for publication.
• Paul: Send slides/presentation to interested meeting participants (notably Miriam) for review and feedback.
• Miriam: Schedule a review session with Paul to go over the presentation materials in detail.
• All participants: Provide Paul with further thoughts or suggestions on how to proceed with publishing or protecting the new theory (if any arise after the meeting).
• Miriam: Send the AI-generated meeting summary to Paul after the meeting.

Summary

Mark's COVID-19 Update and Deborah's Bell Choir

Mark shared that he tested positive for COVID-19 12 days ago and is experiencing mild symptoms, including congestion and eye aches. He mentioned reading that staying active is safe for those with mild symptoms, and he plans to continue gentle exercise. The group discussed the importance of avoiding contact with others while infectious, with Mark noting that home tests are likely to detect enough virus to be infectious. The conversation then shifted to personal updates, with Deborah sharing that she is starting a bell choir in Mount Carroll, which begins tomorrow at the Methodist Church.

Atomic Orbit Pattern Discovery

Paul shared his recent discovery of a pattern in atomic orbits that resembles the periodic table of elements. He created a visual representation of carbon's orbit and suggested that this pattern might explain the arrangement of elements in the periodic table. The group discussed the stability of different elements, with Paul explaining how neon and argon are stable because their electron orbits are fully occupied. Paul also mentioned that he had created slides to further illustrate his findings, which he planned to present at an upcoming meeting.

Atomic Structure and Harmonic Orbits

Paul presented his theory on atomic structure and harmonic orbits, explaining how he discovered a pattern in the orbits of protons and neutrons that resembles a hexagonal or snowflake shape. He demonstrated this theory using PowerPoint graphics and discussed how it could explain the periodic table of elements and the structure of snowflakes. The group discussed the implications of Paul's findings, with Miriam and others providing feedback and questions about the scientific validity of his theory.

Carbon Atom Structure and Reactivity

Paul discussed the structure and stability of atoms, particularly focusing on carbon and its hexagonal shape. He explained how carbon's four electron orbits contribute to its reactivity, unlike helium's perfect symmetry. Paul also explored how hydrogen atoms share electrons in a Figure 8 orbit to form stable H2 molecules. The discussion touched on the relationship between an atom's structure and its chemical properties, with Paul noting that his mathematical model aligns with the periodic table's arrangement of elements.

Atomic Structure Model Discussion

Paul discussed his model of atomic structure, explaining how electrons in a figure-eight orbit are attracted to the nucleus while being pushed apart by other electrons, creating a balance of forces that keeps the atoms stable. He compared this to binary stars and suggested that his model could help people understand atoms and molecules. The group also discussed the possibility of varying sizes of protons, electrons, and neutrons, with Paul noting that the reported averages might mask individual variations. They briefly touched on the terminology used to describe protons and neutrons, with Paul suggesting a need to potentially create new terms to accurately describe these subatomic particles.

New Orbital Pattern Discovery

Paul discussed his discovery of a new orbital pattern, similar to Copernicus' heliocentric model, which could revolutionize our understanding of atomic structures. He plans to publish and present this formally, but emphasized that it is not affiliated with any organization. Mark inquired about the figure-eight orbit and its relation to hydrogen, which Paul explained was a simplified representation of a more complex three-dimensional structure. Paul also expressed doubts about the stability of the proposed atomic structure due to potential collisions between adjacent atoms.

Carbon Atom Model Discussion

Paul presented his recent work on a new atomic model involving carbon atoms with "donut holes" and perpendicular orbits, which he developed over a week of focused work. The group discussed the scientific implications and potential next steps, with Paul considering whether to publish the findings or share them through a presentation. Miriam offered to review the material with Paul, and the group agreed to explore options for presenting the work while protecting Paul's intellectual property.

AI can make mistakes. Review for accuracy.

Please rate the accuracy of this summary.

Those same 5 siblings have met almost each week since 2020 to share news, learn about problems, help solve them, check Paul’s math, and remember the good old days. For example, Deb helped Paul develop better math to predict milk production of cows milked at uneven intervals and coauthored their 2023 scientific report, Judy suggested color coding for the VanRaden pedigree, and Miriam photographed Paul’s protest in front of the U.S. Supreme Cult building, but none of us 5 have prior training in nuclear physics. Paul never took physics in high school or college and studied agriculture instead.

Scientific Review

The powerpoint presentation was then sent to 3 potential reviewers and 2 returned these comments just one day later: Tom Lawlor, PhD in Animal Breeding from Cornell University, retired, and Ignacy Misztal, PhD from Polish Academy of Science, partially retired.

Paul

Thanks for sharing. I found your thoughts on orbitals to be quite interesting. My knowledge on this topic is quite limited, however, since you asked for questions and comments I'll give it a try.

The idea that one of the orbits is through the center is certainly plausible and may indeed occur with some elements, eg He. However, it becomes more difficult to visualize this for larger elements. You would need to stack a lot of donuts on top of each other to get the larger elements.

Current orbital theory talks about attraction and repulsion being a key component in understanding the shapes of the orbits. They then go on to link the size of the outermost orbital with its bonding ability. I don't see where your theory provides much information on bonding. Your theory does a nice job of explaining stability versus instability.

It seems to me that current theory on energy subshells provides a nice way of grouping different elements in the periodic table into groups with similar properties and characteristics.

Does your theory include the distance of the orbit from the nucleus? Or the nuclear charge? These two components are very valuable in understanding the structure of the heavier elements.

Again, thanks for sharing. It'll be interesting to hear the feedback from others.

All the best, Tom

Paul,

Seems you try to occupy your mind with things unrelated to your work.  New horizons. 

When we do it, we are in a position of an entry level undergraduate. Interesting but long way to discovery.

Interesting story with Copernicus and Galileo. The biggest sponsor of research in the Middle Ages was the catholic church, with a goal of research to explore God’s creations. But things became complex if the discoverers were too fast and too bold making the claims when they interfered with the contemporary teaching. Also things got heated after the reformation, especially when > 4 million people were killed in the 30-year religious war. 

I am bad sleeper so to get myself to sleep I listened to many courses on a variety of topics. A fraction of them displayed below. Of astronomy, there was a course with 96 lectures, where I dropped at about 70. Two very good courses on discoveries with Hubble. You may like “impossible physics”. 

Since the courses are academic, no advertising or sensation just pure knowledge. 

One of the most exciting places for astronomy around DC is a radio telescope complex in Green Bank, WV; see the course below. Perhaps you can visit them and then ask you to be their pro-bono statistician! https://en.wikipedia.org/wiki/Green_Bank_Telescope

My other side is at no9e.com. But few people are reading. The competition for attention is immense, and little chance to succeed without "sensations". 

Ignacy

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