ASTR 474 Problem Set 02: Orbital Integration and Ephemeris Validation

Objectives and instructions

Practice computational reasoning, quantitative analysis, validation, and scientific communication for lecture 03.

Use SI or explicitly stated astronomical units consistently; show conversions and significant figures.
Cite all data, software, and adapted code. Distinguish supplied measured data from synthetic records.
Include runnable code and record environment, command, and seed where used.
Collaboration on concepts is permitted; each submitted derivation, code, and interpretation must be the student's own and contributors must be named.

Revisions and resubmissions are encouraged to improve mastery and grade under the course policy.

Problem 2.1

Using Astropy GM_sun, derive the circular 1-AU period and report the value in days with the conversion steps.

Deliver: derivation or code, units/conventions, a reproducible result, uncertainty or validation evidence, and a short physical interpretation.

Problem 2.2

Integrate the supplied JPL Earth state from Jan 1 to Jan 2 with REBOUND and SciPy. Reconcile the Sun-relative frame, report both residuals in km, and explain why neither residual is a pure solver error.

Deliver: derivation or code, units/conventions, a reproducible result, uncertainty or validation evidence, and a short physical interpretation.

Problem 2.3

For the WHFast sweep, compare relative energy error and endpoint error against timestep. Recommend a step only after naming the quantity and error tolerance you need.

Deliver: derivation or code, units/conventions, a reproducible result, uncertainty or validation evidence, and a short physical interpretation.

Reproducibility check

Use this generated reference result as one consistency check, not as a substitute for showing reasoning: Using Astropy GM_sun, the circular 1-AU Kepler period is 365.25690 d. After one day, REBOUND and independent SciPy two-body runs differ from the DE441 Earth-center vector by 126.0 km and 126.1 km respectively; the residual is model/frame scope, not an accuracy claim.

No textbook exercise is adopted for this course; problems are original and cite the primary software/data sources in the reference log.

Submission

Submit a readable PDF report, source code, environment/version record, and any generated tables/figures. The assignment is complete only when another student can rerun the command and identify the inputs and validation test.