Knowledge Library
Scientific Laws, Theories, Models, and Assumptions
Every claim on Evidence Pros depends on some combination of observations, measurements, laws, theories, models, equations, and assumptions. The categories are not interchangeable, and none of them counts as evidence on its own. Use this library to see what each category can and cannot establish — and to trace which assumptions any given argument inherits.
Scientific laws and principles
A law describes a repeatedly observed relationship under stated conditions. It does not explain why. Every entry lists its original wording, formula, variables (measured vs. assumed), the conditions where it applies, its known limits, supporting experiments, and whether it independently distinguishes Earth-shape models.
Newton's First Law of Motion
Used by both models the same way"Every body perseveres in its state of rest, or of uniform motion in a right line, unless compelled to change that state by forces impressed upon it. (Principia, 1687)"
History: Published by Isaac Newton in Philosophiæ Naturalis Principia Mathematica (1687), building on Galileo's inertia work.
Formula
Σ F = 0 ⇒ dv/dt = 0
Variables
- F — Net external force (N, measured)
- v — Velocity (m/s, measured)
Applies when
- Inertial reference frame
- No net external force
Does not apply when
- Non-inertial frames without pseudo-force correction
- Relativistic speeds
Supporting experiments
- Air-track glider trials
- Frictionless puck experiments
Known limitations
- Reference-frame dependent
- Requires operational definition of 'force'
Replication history: Reproduced routinely in undergraduate labs worldwide since the 18th century.
Flat-model usage
Used identically; inertia is model-agnostic.
Globe-model usage
Used identically; inertia is model-agnostic.
Independently distinguishes models?
Used by both models the same way. Inertia by itself does not distinguish Earth's shape.
Newton's Second Law of Motion
Used by both models the same way"The alteration of motion is ever proportional to the motive force impressed. (Principia, 1687)"
History: Newton, 1687.
Formula
F = m · a
Variables
- F — Net force (N, measured)
- m — Inertial mass (kg, measured)
- a — Acceleration (m/s², measured)
Applies when
- Inertial frame
- Constant mass
Does not apply when
- Variable-mass systems without correction
- Relativistic regime
Supporting experiments
- Cart-and-pulley labs
- Rocketry telemetry (with variable-mass correction)
Known limitations
- Requires prior definition of mass and force
Replication history: Universally reproduced across mechanics coursework and engineering practice.
Flat-model usage
Applied identically at surface scale.
Globe-model usage
Applied identically; extended to rotating-frame effects via added Coriolis / centrifugal terms.
Independently distinguishes models?
Used by both models the same way. F = ma is model-independent; the models differ only in what forces they invoke.
Newton's Third Law of Motion
Used by both models the same way"To every action there is always opposed an equal reaction. (Principia, 1687)"
History: Newton, 1687.
Formula
F_AB = -F_BA
Variables
- F — Contact or field force between two bodies (N, measured)
Applies when
- Interacting bodies
- Instantaneous action-at-a-distance idealization or contact
Does not apply when
- Fields with propagation delay treated naively
Supporting experiments
- Rocket propulsion
- Recoil measurements
Known limitations
- Requires field-theoretic reformulation for electromagnetism
Replication history: Ubiquitous.
Flat-model usage
Identical.
Globe-model usage
Identical.
Independently distinguishes models?
Used by both models the same way. Does not distinguish Earth's shape.
Newton's Law of Universal Gravitation
Local observation does not distinguish"Every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. (Principia, 1687)"
History: Newton, 1687; refined by Cavendish (1798) and Einstein's general relativity (1915).
Formula
F = G · m₁ · m₂ / r²
Variables
- G — Gravitational constant (m³·kg⁻¹·s⁻², measured)
- m₁, m₂ — Masses of the interacting bodies (kg, measured)
- r — Center-to-center distance (m, measured)
Applies when
- Weak-field, low-velocity regime
- Point masses or spherically symmetric bodies
Does not apply when
- Strong gravitational fields
- Relativistic speeds
Supporting experiments
- Cavendish torsion balance (1798)
- Lunar laser ranging
Known limitations
- Assumes an attractive mass-based force; alternative downward-force explanations (density, aether pressure) reproduce the local observation of falling objects.
Replication history: Cavendish-style experiments have been reproduced many times, most recently with atom interferometry.
Flat-model usage
Flat/enclosed models typically substitute density-and-buoyancy or an alternative downward mechanism.
Globe-model usage
Central to the globe model's account of orbits, tides, and satellites.
Independently distinguishes models?
Local observation does not distinguish. Local 'things fall' does not distinguish. Cavendish-style small-mass attraction, if replicated independently at high precision, would.
Conservation of Energy
Used by both models the same way"Energy is neither created nor destroyed; it changes form."
History: Consolidated by Mayer, Joule, and Helmholtz (1840s–1850s).
Formula
ΔE_total = 0
Variables
- E — Total energy (kinetic + potential + thermal + …) (J, measured)
Applies when
- Closed system
Does not apply when
- Open systems without accounting for exchange
Supporting experiments
- Joule's paddle-wheel experiment
Known limitations
- Requires all energy channels to be accounted for
Replication history: Reproduced throughout thermodynamics coursework and engineering.
Flat-model usage
Applied identically.
Globe-model usage
Applied identically.
Independently distinguishes models?
Used by both models the same way. Does not distinguish Earth's shape.
Conservation of Linear Momentum
Used by both models the same way"The total momentum of an isolated system is constant."
History: Descartes, Newton, then formalized in classical mechanics.
Formula
Σ p = constant
Variables
- p — Momentum m·v (kg·m/s, measured)
Applies when
- No external net force
Does not apply when
- External forces present
Supporting experiments
- Collision carts
- Ballistic pendulum
Replication history: Standard laboratory demonstration.
Flat-model usage
Identical.
Globe-model usage
Identical.
Independently distinguishes models?
Used by both models the same way. Does not distinguish Earth's shape.
Conservation of Angular Momentum
Used by both models the same way"In the absence of external torque, angular momentum is conserved."
History: 18th-century mechanics.
Formula
L = I · ω, dL/dt = τ
Variables
- L — Angular momentum (kg·m²/s, measured)
- I — Moment of inertia (kg·m², measured)
- ω — Angular velocity (rad/s, measured)
- τ — External torque (N·m, measured)
Applies when
- Isolated rotating system
Does not apply when
- External torques
Supporting experiments
- Ice-skater spin demonstration
- Gyroscope rigs
Replication history: Standard.
Flat-model usage
Identical.
Globe-model usage
Identical; central to orbital and rotational mechanics.
Independently distinguishes models?
Used by both models the same way. Does not distinguish Earth's shape directly.
Inverse-Square Law
Distinguishes competing models"The intensity of a field or effect radiating from a point source decreases as 1/r²."
History: Recognized in gravitation (Newton), electrostatics (Coulomb), and radiometry.
Formula
I = P / (4π r²)
Variables
- I — Intensity at distance r (W/m², measured)
- P — Source power (W, measured)
- r — Distance from source (m, measured)
Applies when
- Isotropic point source
- Non-absorbing medium
Does not apply when
- Directional sources
- Absorbing media
- Near-field regime
Supporting experiments
- Photometry
- Coulomb torsion balance
Known limitations
- Assumes point source and no absorption
Replication history: Extensively reproduced.
Flat-model usage
Sometimes cited to argue sunlight falloff supports a near sun.
Globe-model usage
Applied to a distant sun with negligible falloff across Earth's diameter.
Independently distinguishes models?
Distinguishes competing models. Careful measurement of solar irradiance vs. angular size across latitudes can constrain sun distance; both models must produce a consistent number.
Archimedes' Principle
Used by both models the same way"Any body wholly or partially immersed in a fluid experiences a buoyant force equal to the weight of the fluid displaced. (On Floating Bodies, ~250 BCE)"
History: Archimedes, 3rd century BCE.
Formula
F_b = ρ_fluid · V_displaced · g
Variables
- ρ_fluid — Fluid density (kg/m³, measured)
- V_displaced — Volume of fluid displaced (m³, measured)
- g — Local gravitational (or downward-force) field (m/s², measured)
Applies when
- Static fluid
- Body fully or partially submerged
Does not apply when
- Highly accelerated fluid
- Surface-tension-dominated regime
Supporting experiments
- Displacement of water by dense/less-dense objects
Known limitations
- Requires a valid downward field g; does not by itself explain what g is.
Replication history: Directly reproducible at home.
Flat-model usage
Often cited as a complete downward-force account: 'density and buoyancy explain why things fall.'
Globe-model usage
Used identically; buoyant force acts within a gravitational field g.
Independently distinguishes models?
Used by both models the same way. Archimedes' principle presumes g; it does not itself establish the origin of g.
Laws of Buoyancy
Used by both models the same way"Objects less dense than the surrounding fluid rise; denser objects sink."
History: Formalized from Archimedes.
Formula
F_net = (ρ_fluid - ρ_object) · V · g
Variables
- ρ — Density (kg/m³, measured)
- V — Object volume (m³, measured)
- g — Downward field (m/s², measured)
Applies when
- Fluid at equilibrium
Does not apply when
- Non-fluid media
Supporting experiments
- Helium balloon, ice-in-water tests
Known limitations
- Requires g; density explains relative behavior in a field, not the field itself.
Replication history: Reproduced daily.
Flat-model usage
Frequently offered as the primary downward-cause explanation.
Globe-model usage
Same behavior, embedded in a gravitational field model.
Independently distinguishes models?
Used by both models the same way. See buoyancy comparison exhibits in Fundamentals.
Hydrostatic Pressure
Used by both models the same way"Pressure in a static fluid increases with depth in proportion to fluid density and the downward field."
History: Stevin, Pascal (17th century).
Formula
P = P₀ + ρ · g · h
Variables
- P — Pressure at depth h (Pa, measured)
- P₀ — Surface pressure (Pa, measured)
- ρ — Fluid density (kg/m³, measured)
- g — Downward field (m/s², measured)
- h — Depth below surface (m, measured)
Applies when
- Static incompressible fluid
Does not apply when
- Compressible-gas depth over kilometers without correction
Supporting experiments
- Pressure gauges at varying depth
Known limitations
- Requires g
Replication history: Standard hydraulics practice.
Flat-model usage
Applied at surface scale identically.
Globe-model usage
Applied identically.
Independently distinguishes models?
Used by both models the same way. Does not distinguish shape at everyday scales.
Ideal Gas Laws (Boyle, Charles, Gay-Lussac, combined)
Used by both models the same way"For an ideal gas, PV = nRT."
History: Boyle (1662), Charles (1780s), Gay-Lussac (1802), unified 19th century.
Formula
P · V = n · R · T
Variables
- P — Pressure (Pa, measured)
- V — Volume (m³, measured)
- n — Moles of gas (mol, measured)
- R — Gas constant (J·mol⁻¹·K⁻¹, constant)
- T — Absolute temperature (K, measured)
Applies when
- Dilute gas, moderate T and P
Does not apply when
- Near condensation, high pressure, molecular attraction dominant
Supporting experiments
- Sealed-syringe pressure tests, hot-air balloon behavior
Known limitations
- Ideal-gas assumption breaks near phase transitions
Replication history: Reproducible with a syringe and a thermometer.
Flat-model usage
Applied identically.
Globe-model usage
Applied identically.
Independently distinguishes models?
Used by both models the same way. Does not distinguish Earth's shape.
Laws of Thermodynamics
Used by both models the same way"0th: bodies in thermal equilibrium share temperature. 1st: energy conservation with heat. 2nd: entropy of an isolated system does not decrease. 3rd: entropy → 0 as T → 0 K."
History: 19th-century synthesis (Carnot, Clausius, Kelvin, Boltzmann).
Formula
dU = δQ - δW; dS ≥ 0
Variables
- U — Internal energy (J, measured)
- S — Entropy (J/K, measured)
Applies when
- Macroscopic systems
Does not apply when
- Single-particle scale without statistical treatment
Supporting experiments
- Heat engines, calorimetry
Known limitations
- 2nd law is statistical, not absolute
Replication history: Foundational to engineering.
Flat-model usage
Identical.
Globe-model usage
Identical.
Independently distinguishes models?
Used by both models the same way. Does not distinguish Earth's shape.
Snell's Law
Used by both models the same way"n₁ sin θ₁ = n₂ sin θ₂"
History: Ibn Sahl (984), rediscovered by Snellius (1621).
Formula
n₁ · sin(θ₁) = n₂ · sin(θ₂)
Variables
- n — Refractive index of medium (dimensionless, measured)
- θ — Angle from normal (rad, measured)
Applies when
- Interface between two isotropic media
Does not apply when
- Anisotropic or gradient-index media without extension
Supporting experiments
- Ray-box optics kits
Known limitations
- Assumes sharp interface
Replication history: Universally reproduced.
Flat-model usage
Cited to explain apparent lifting of distant objects.
Globe-model usage
Cited to explain terrestrial and astronomical refraction.
Independently distinguishes models?
Used by both models the same way. Applies in either model; the argument shifts to atmospheric refraction magnitude.
Law of Reflection
Used by both models the same way"The angle of incidence equals the angle of reflection."
History: Euclid's Catoptrics, ~300 BCE.
Formula
θ_i = θ_r
Variables
- θ — Angle from surface normal (rad, measured)
Applies when
- Smooth reflective interface
Does not apply when
- Diffuse surfaces (Lambertian)
Supporting experiments
- Mirror-and-laser demonstrations
Replication history: Universally reproduced.
Flat-model usage
Identical.
Globe-model usage
Identical.
Independently distinguishes models?
Used by both models the same way. Does not distinguish Earth's shape.
Atmospheric Refraction
Distinguishes competing models"Light bends when traveling through media of varying density; Earth's atmosphere refracts light along near-horizontal paths."
History: Documented by Ptolemy; quantified by Bouguer (1729), Bessel, and standardized in modern surveying with k ≈ 0.13.
Formula
Δh ≈ (1 - k) · d² / (2R) (surveyor's refraction-adjusted horizon-drop, globe model)
Variables
- Δh — Apparent lift due to refraction over distance d (m, model derived)
- k — Refraction coefficient (standard ≈ 0.13, variable) (dimensionless, assumed)
- d — Line-of-sight distance (m, measured)
- R — Effective Earth radius (m, assumed)
Applies when
- Near-horizontal viewing
- Standard atmospheric profile
Does not apply when
- Strong thermal inversions
- Non-standard vertical density profiles
Supporting experiments
- Geodetic surveying corrections
- Astronomical refraction tables
Known limitations
- k varies with weather and temperature gradient; a single assumed value can produce large errors.
Replication history: Applied routinely in surveying and astronomy for two centuries.
Flat-model usage
Sometimes invoked to explain why distant objects remain visible beyond a globe's predicted horizon.
Globe-model usage
Central to reconciling long-distance sightings with globe geometry; requires a specific k.
Independently distinguishes models?
Distinguishes competing models. Only if k is measured independently at the time of sighting rather than assumed to match the desired outcome.
Perspective and Angular Resolution
Distinguishes competing models"The apparent size of an object shrinks with distance; two points can be distinguished only above a resolution angle."
History: Optical resolution formalized by Rayleigh (1879).
Formula
θ_min ≈ 1.22 · λ / D
Variables
- θ_min — Minimum resolvable angle (rad, model derived)
- λ — Wavelength (m, measured)
- D — Aperture diameter (m, measured)
Applies when
- Diffraction-limited optics
Does not apply when
- Atmospheric seeing dominates
Supporting experiments
- Telescope and binocular resolution tests
Known limitations
- Does not by itself explain a horizon; explains angular disappearance only.
Replication history: Standard optics.
Flat-model usage
Sometimes invoked as the sole cause of objects disappearing at distance.
Globe-model usage
One of several factors along with horizon geometry and refraction.
Independently distinguishes models?
Distinguishes competing models. Zoom tests can partially distinguish angular vanishing from geometric occlusion.
Electromagnetic Propagation (Maxwell's Equations)
Used by both models the same way"Electromagnetic fields propagate at c in vacuum; described by Maxwell's equations."
History: Maxwell (1865), Hertz (1887).
Formula
∇·E = ρ/ε₀; ∇×B - μ₀ε₀ ∂E/∂t = μ₀J (etc.)
Variables
- E, B — Electric and magnetic fields (V/m, T, measured)
- c — Speed of light in vacuum (m/s, constant)
Applies when
- Classical regime
Does not apply when
- Quantum-optical single-photon regime
Supporting experiments
- Radio propagation, GPS timing
Known limitations
- Requires quantum extension for photon-level effects
Replication history: Foundational to modern electronics.
Flat-model usage
Applied identically.
Globe-model usage
Applied identically.
Independently distinguishes models?
Used by both models the same way. Does not by itself distinguish Earth's shape.
Doppler Effect
Used by both models the same way"The frequency of a wave shifts when source and observer are in relative motion."
History: Doppler (1842), Fizeau (1848) for light.
Formula
f' = f · (c ± v_obs) / (c ∓ v_src)
Variables
- f, f' — Emitted and observed frequency (Hz, measured)
- v — Relative velocity (m/s, measured)
Applies when
- Waves in a defined medium or vacuum
Does not apply when
- Highly relativistic without Lorentz correction
Supporting experiments
- Radar, medical ultrasound, astronomical spectroscopy
Replication history: Universal.
Flat-model usage
Applied identically.
Globe-model usage
Applied identically; used to argue stellar recession.
Independently distinguishes models?
Used by both models the same way. The physics is model-independent; the interpretation of astronomical redshift is where models diverge.
Coriolis Effect
Distinguishes competing models"In a rotating reference frame, moving objects experience an apparent deflection perpendicular to their velocity."
History: Coriolis (1835).
Formula
a_c = -2 · Ω × v
Variables
- Ω — Angular velocity of rotating frame (rad/s, assumed)
- v — Velocity in rotating frame (m/s, measured)
Applies when
- Rotating reference frame
Does not apply when
- Non-rotating frames
Supporting experiments
- Long-range artillery corrections, ocean and atmospheric circulation modeling
Known limitations
- Requires an actual Ω; magnitude and sign predict specific latitude-dependent effects.
Replication history: Ballistics and meteorology depend on it.
Flat-model usage
A stationary flat Earth predicts no Coriolis-like deflection from Earth rotation.
Globe-model usage
Coriolis magnitude scales with sin(latitude) and Earth's Ω = 7.29e-5 rad/s.
Independently distinguishes models?
Distinguishes competing models. Precisely measured latitude-dependent artillery drift or Foucault precession tests Ω directly.
Foucault Pendulum
Distinguishes competing models"A freely swinging pendulum's plane of oscillation appears to rotate in a rotating reference frame."
History: Foucault (1851).
Formula
T_precession = 24 h / sin(latitude)
Variables
- T_precession — Time for one full plane rotation (h, model derived)
- latitude — Observer latitude (deg, measured)
Applies when
- Long-period pendulum, minimal friction
Does not apply when
- Pendulum with elliptical swing or asymmetric suspension
Supporting experiments
- 1851 Paris Panthéon demonstration; countless replications
Known limitations
- Suspension asymmetries can produce apparent precession without rotation; controls needed.
Replication history: Public installations worldwide.
Flat-model usage
Predicts no latitude-dependent precession from Earth rotation.
Globe-model usage
Predicts precession rate exactly following 24h / sin(lat).
Independently distinguishes models?
Distinguishes competing models. Independently replicated latitude scans are among the strongest direct tests of Earth's rotation.
Gyroscopic Precession
Distinguishes competing models"A spinning gyroscope subjected to a torque precesses at right angles to the applied torque."
History: Formalized in 19th-century rotational dynamics.
Formula
Ω_p = τ / (I · ω_spin)
Variables
- Ω_p — Precession rate (rad/s, model derived)
- τ — Applied torque (N·m, measured)
- I — Moment of inertia (kg·m², measured)
- ω_spin — Spin rate (rad/s, measured)
Applies when
- Rapidly spinning rigid body
Does not apply when
- Non-rigid or slow-spinning bodies
Supporting experiments
- Ring-laser gyroscopes, mechanical gyros
Replication history: Aviation and navigation.
Flat-model usage
A ring-laser gyroscope on a stationary flat Earth should show zero Earth rate.
Globe-model usage
A ring-laser gyroscope measures Earth's Ω directly, ≈ 15°/h · sin(lat).
Independently distinguishes models?
Distinguishes competing models. A calibrated ring-laser gyroscope independently measures Earth-rate; results are reported in surveying.
Kepler's Laws of Planetary Motion
Distinguishes competing models"1) Orbits are ellipses with the sun at one focus. 2) Equal areas in equal times. 3) T² ∝ a³."
History: Kepler (1609–1619) from Tycho Brahe's data.
Formula
T² = (4π² / (G · M)) · a³
Variables
- T — Orbital period (s, measured)
- a — Semi-major axis (m, measured)
- M — Central mass (kg, assumed)
Applies when
- Two-body gravitational systems, weak-field
Does not apply when
- Multi-body strong perturbation, strong-field GR
Supporting experiments
- Planetary ephemerides, spacecraft trajectory prediction
Known limitations
- Depends on heliocentric geometry and Newtonian gravity or its GR extension.
Replication history: Ephemerides validated to sub-arcsecond precision.
Flat-model usage
Typically rejected outright, or reframed under non-heliocentric geometry.
Globe-model usage
Core to modern celestial mechanics.
Independently distinguishes models?
Distinguishes competing models. Spacecraft trajectory predictions to outer planets are a Kepler + Newton test on decade timescales.
Tidal Forces
Distinguishes competing models"Differential gravitational attraction across an extended body produces tidal deformation."
History: Newton (1687); refined by Laplace.
Formula
F_tidal ≈ 2 · G · M · r / R³
Variables
- M — Mass of tide-raising body (moon/sun) (kg, assumed)
- r — Radius of Earth (m, assumed)
- R — Distance to tide-raising body (m, assumed)
Applies when
- Extended body in an external gravitational gradient
Does not apply when
- Isolated body far from gradient
Supporting experiments
- Tide gauges worldwide, harmonic tidal analysis
Known limitations
- Regional tides depend heavily on basin geometry; force alone does not fully predict amplitude.
Replication history: Tide tables validated over centuries.
Flat-model usage
Various alternative explanations are proposed; competing quantitative predictions are typically not published.
Globe-model usage
Tidal harmonic analysis matches measured tide-gauge data.
Independently distinguishes models?
Distinguishes competing models. Only if the competing model publishes a quantitative tide prediction that can be checked against gauge data.