ASTR 474 Lab 03: Three-Body Conservation and Encounter Choice

Purpose and learning objectives

L04 · REBOUND N-body dynamics. This investigation develops a numerical method and tests its output against a declared benchmark, invariant, uncertainty model, or independent implementation.

Run a specified scientific workflow from the pinned environment.
Measure an explicit numerical or statistical diagnostic with units and provenance.
Separate numerical error from physical model discrepancy and interpret a limitation.

Preparation, setup, and inputs

Software: CPython 3.14.6; dependencies in requirements.txt. From repository root run .venv/Scripts/python.exe materials/ASTR474/src/astr474_computations.py. Then use the corresponding CSV/JSON under materials/ASTR474/data/generated/. Required data: generated/nbody_conservation.csv.

Apparatus: computer with local CPU, terminal, text editor, and browser; no telescope, GPU, network account, or paid service is required. Preserve the generated input files and record file hash/version.

Model scope: Three-body orbital geometry is idealized; Astropy solar/Earth/Jupiter mass parameters are published physical constants.

Procedure

Run the 12-year Sun-Earth-Jupiter WHFast experiment at 64, 128, and 256 steps per Earth year.
Record relative energy error, relative angular-momentum error, scaled center-of-mass momentum error, particle masses, geometry, and total steps.
Plot each invariant diagnostic against timestep; estimate the convergence slope from adjacent resolutions.
Introduce a test close approach and explain why the hierarchy assumptions of WHFast may fail; select IAS15 or a hybrid integrator and state the required checks.
Repeat one run from a saved initial-condition file and compare the state and checksums.

Measurement record

Quantity	Value or field	Unit/convention	Source/method
Input configuration	Record solver, version, seed, timestep/grid/tolerance	As defined by the experiment	Command line and source file
Primary diagnostic	Record every resolution/sample/fit row, not just the preferred result	State units and normalization	Generated CSV/JSON
Independent reference	Across 12 years, the three-body WHFast relative energy error falls from 8.56e-12 at dt=5.707 d to 5.33e-13 at dt=1.427 d; angular-momentum and scaled momentum errors are tabulated separately.	As stated in the generated example	Analytic/JPL/invariant cross-check
Uncertainty/sensitivity	Repeat with changed resolution, seed, parameter, or method	Report interval or relative change	Student analysis

Analysis and uncertainty

Timestep sweep quantifies discretization sensitivity. This is not a stability proof for arbitrary N-body initial conditions.

Plot the diagnostic against the controlled parameter; label axes, units, normalization, and reference. Explain any non-monotonic point rather than smoothing or dropping it. If propagating independent errors, state why independence is plausible; preserve correlated/common-mode terms separately.

Deliverables and assessment

Runnable source or notebook export with command, package versions, and all input/output paths.
One scientific figure plus a machine-readable table of measurements and convergence/sampling/residual diagnostics.
A 700-1000 word technical report describing model, method, validation, uncertainty categories, and one failed assumption.
A short claim-evidence table separating result, numerical check, and domain limitation.

Rubric: 30% correct method and setup; 25% validation and numerical diagnostics; 20% uncertainty/provenance; 15% physical interpretation; 10% clarity and reproducibility. Revisions and resubmissions are encouraged under the syllabus mastery policy.

Data and source provenance

Three-body orbital geometry is idealized; Astropy solar/Earth/Jupiter mass parameters are published physical constants. Provenance levels, request records, and source verification limits are documented in reference-log.md; generated files and seeds are documented in data/README.md.

References: