![[Merch.png]] When authority is challenged, the modern academic is reduced to gas lighting and appealing to their own authority. While it may seem that the boasting, mocking, insults and shaming is directed at the Challenger, it assuredly is not. It's a warning message to the reader, the public. For those who can't read subtext his true message is: *"Dare challenge my authority and I'll publicly humiliate you. After you've suffered my humiliation, I'll ignore your existence. Disagreement with me is equivalent, to mental incompetence. You're not incompetent, are you?"* After years of specialized training and then teaching that specialized training, maybe the academics deserves an allowance for some arrogance? After all, how could *they* be wrong? Let's take a look at what's being said. Half of the argumentation is written in math while the other half is in definitions. Since the definitions precede the math, I'll cover that first. Definition is key. In any conversation, for it to be productive, definitions must be agreed upon. Some equations are provided and then the end, several statements are made. We'll start as we'll see if the equations match the provided definitions to prove the argument. *"I taught dynamics for 3 years"* *"Dynamics = kinematics + kinetics"* *"Kinematics = geometry of motion: position, velocity, acceleration."* *"Kinetics = motion + forces behind it (Newton's 2nd Law, F=ma)"* *"Dynamics always includes both"* We'll grab some definitions from physics text books and compare. --- ![[The_Current_State_of_Modern_Academia.png]] Notes: Shankar, Ramamurti. _Fundamentals of Physics I: Mechanics, Relativity, and Thermodynamics_. Yale University Press, 2019. --- ![[Pasted image 20250924144525.png]] Watson, William. _A Text-Book of Physics_. 1911. --- ![[Pasted image 20250924144821.png]] Notes: Watson, William. _A Text-Book of Physics_. 1911. --- ![[Pasted image 20250924150317.png]] Notes: Question: In the equations provided by the Academic: Where is the variable that describes a change in momentum or defines how mass there is for there to be any sort of proportionality changes? Not a single one of the equations provided enable us to derive a force. Watson, William. _A Text-Book of Physics_. 1911. --- ![[The_Current_State_of_Modern_Academia-1.png]] Notes: Giancoli, Douglas C. _Physics for Scientists and Engineers with Modern Physics_. Vol. 2. Pearson Education, 2008. --- # Kinematic Equations: # $v = v_0 + a t$ # $\Delta x = \left(\frac{v + v_0}{2}\right) t$ # $\Delta x = v_0 t + \tfrac{1}{2} a t^2$ # $v^2 = v_0^2 + 2 a \Delta x$ The equations of kinematics, which all describe change in position over time. First time derivative = velocity, and second = acceleration. No causal mechanism for the motion assume. Relative motion is ALWAYS true in kinematics. We can demonstrate that isn't the case in dynamics. https://www.pasco.com/resources/articles/kinematic-equations?srsltid=AfmBOopvttRz-CXrJKbRK5gGxz4doXP92x_YVf67s94XaXfFmcYJUwfk --- Lets now take a look at the equations of dynamics. # Dynamics ![[Pasted image 20250925022202.png]] ![[Pasted image 20250925022242.png]] ![[Pasted image 20250925022316.png]] Notes: https://academics.uccs.edu/rtirado/Giancoli_6e_Study_Guide/Ch_4_Dynamics_Newton%27s_Laws_of_Motion.pdf https://ocw.mit.edu/courses/16-07-dynamics-fall-2009/6c3adbdf48feaf3580731511ee9cb776_MIT16_07F09_Lec12.pdf --- Now that its been firmly established that mechanics is divided into two distinctly different. Let's a gander at the current mainstream equations that govern solar system dynamics. --- ![[The_Current_State_of_Modern_Academia-2.png]] Newton’s great insight was to show that if any two masses attract with a universal inverse-square gravitational force $F = G\,\frac{m_1 m_2}{r^2}$ and obey Newton’s laws of motion, then the relative orbit is a conic section. As a result, Kepler’s laws follow: (1) equal areas in equal times from conservation of angular momentum, (2) elliptical orbits with the primary at a focus for bound energy, and (3) $T^2 = \frac{4\pi^2}{G(M+m)}\,a^3$ (≈ $\frac{4\pi^2}{GM}\,a^3$ when $m \ll M$). Murray, C. D., Dermott, S. F. (1999). Solar System Dynamics. United Kingdom: Cambridge University Press. https://assets.cambridge.org/97805215/72958/sample/9780521572958wsn01.pdf --- ![[20240914-4.png]] ![[20241030-11.png]] By algebraic canceling, it is easy to see that the dynamic cause, mass is canceled out and the Newtonian equation (dynamics) falls back into the Kepler's equations (kinematics) which is a ratio of $\pi /T$ which is based off (empirical observation). T = periodicity of the celestial body (i.e., how many days does it take to return to the same spot in the sky) --- ![[Pasted image 20250925030848.png]] https://physics.bu.edu/~redner/211-sp06/class16/kepler3.html --- If the causal mechanism of your formula cancels out, it's not the causal mechanism. It doesn't require super intelligence to understand that, yet Newtonian dynamics is asserted as mutually exclusive proof as to why the celestial bodies move. Now that we've gone over the basics of kinematties and dynammies we can conclude that $kinematics \neq dynamics$. Two separate fields of studying motion, governed by completely equations. Let's now move on to the math side of the argument, now that we know what variables we're looking for to determine how to interpret what's being said. --- # $\theta(t) = \omega_e \, \cdot t, $ ## $\quad \omega_e \approx 7.29 \times 10^{-5} \,\text{rad/s} \space {(sidereal \space rotation)}$ # $\varphi(t) = \omega_{orb} \, \cdot t,$ ## $\quad \omega_{orb} \approx 2.0 \times 10^{-7} \,\text{rad/s} \space {(yearly \space revolution)}$ # $\text{Solar day }= \omega_{solar} = \omega_e - \omega_{orb}$ # $\varepsilon = 23.44^{\circ} \space (Axial \space tilt)$ # $\text{Sun}(t) = R_z(\theta) \cdot R_x(\varepsilon) \cdot R_z(\varphi) \cdot r_{\odot}$ ## $r_{\odot} = \text{Earth--Sun position vector (mean length } \approx 1 \,\text{AU})$ # $R_z(\alpha) = \begin{bmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\0 & 0 & 1 \end{bmatrix}$ - $R_z(\alpha)$ is a **rotation in 3D space about the z-axis**. - It rotates vectors in the **x–y plane** by an angle $\alpha$, counterclockwise if you’re looking down the positive z-axis (right-hand rule). - The **z-component is unchanged**, so this is a “flat” rotation that only affects x and y. *"Polaris stays fixed, since Earth's axis points to it (only drifts with 26k-yr procession)"* ---- These equations tell us the angular position of the sun as a function of time. The backbone of what's being said is that the angle created by the relative motion between the earth -> sun and earth -> stars around $\varepsilon$, the common z-axis between Earth and the sky (polaris) based on their respective angular frequencies given by $\omega$ . This is the most kinematic, non-mutually exclusive way to describe the suns position that could ever be done. It's entirely driven by a change in position over time, not WHY it's changing position over time. So what can we do with that? Well as we learned earlier, kinematics, relative motion is always true. So let's add a minus sign to some of these equations, change the name of a few variables and suddenly with the same equation that makes the relative motion between the sun and firmament with respect to a stationary earth. The axial tilt with be the tilt of the firmament. # $\theta(t) = -\,\omega_e \cdot t$ ## $\;\omega_{Firm} \approx 7.29 \times 10^{-5}\ \text{rad/s}$ (magnitude; sky appears westward) # $\varphi(t) = \omega_{orb} \cdot t$ ## $\;\omega_{orb} \approx 2.0 \times 10^{-7}\ \text{rad/s}$ (annual westward drift of the Sun vs. stars) # $\omega_{\text{solar}} = -\big(\omega_e - \omega_{orb}\big)$ ## Solar-day apparent rate in the Earth-fixed frame # $\varepsilon = 23.44^{\circ}$ (Sun's ecliptic) # $\text{Sun}(t) = R_z(-\theta)\ \cdot\ R_x(\varepsilon)\ \cdot\ R_z(\varphi)\ \cdot\ r_{\odot}$ ## $r_{\odot} = \text{Earth--Sun position vector (mean length } \approx 1\,\text{AU})$ # $R_z(\alpha) =\begin{bmatrix}\cos \alpha & -\sin \alpha & 0\\\sin \alpha & \cos \alpha & 0\\0 & 0 & 1\end{bmatrix}$ --- ## "Take a dynamics course!" Agreed. It's always nice go to back to the source material and double check if we're correct in the physical interpretation of what we're calculating. I left lots of citations for people to follow so they can learn all about kinematties and dynammies without conflating the two as equivalent. Now we're going to go through some slides that give a dynamic analysis to reference frames. It will be shown that only a stationary, non-rotating Earth will correctly satisfy the laws of dynamics (conservation of energy, momentum, kinetics, etc). --- ![[Attachments/13.png]] Notes: First we define a reference frame (by mainstream standards) Not to be confused with how I define an inertial frame, which is stationary, non-rotating. --- ![[Attachments/14 1.png]] --- ![[Attachments/22 1.png]] --- ![[Attachments/23 1.png]] --- ![[Attachments/24 2.png]] Notes: This is not a Foucault pendy. The analysis is for a something Newton's cradle. Apologies for the mislabel. --- ![[Attachments/25 1.png]] --- ![[Attachments/26 2.png]] --- Conclusion: At the end of the day, using dynamics to make future predictions of motion reveals that the Earth is stationary, non-rotating. As it's the only frame that when all motion is relative to it, does the the correct energy and conservation output get derived. The disproportional and emotional response from the Academics comes from fear of us not needing them. In the same way this Academic publicly excommunicated Yoders, he fears we will do the same when we find out that the the mixture of cosmology and physics is mathematical role-play not unlikely fantasy rules for Dungeons & Dragons. ---