Further Reading: Kepler's Laws and the Two-Body Problem

The two-body problem is the foundation of every astrodynamics text, and the derivation in §8.2 appears in all of them (in a handful of equivalent forms). The sources below are Tier 1 (canonical works we are confident exist) or Tier 2 (a real, named resource whose exact edition or URL we do not pin down here). Nothing here needs more mathematics than this chapter did — though the professional references go much deeper if you want them.

Core textbook treatments

Curtis, Orbital Mechanics for Engineering Students, Ch. 2–3. Our anchor for Part II. Curtis derives the two-body equation of motion, the conservation of angular momentum, and the orbit equation $r = h^2/\mu\,/(1+e\cos\nu)$ exactly as we did, then devotes a full chapter to the orbital elements and the anomalies, with worked numerical examples and clean code. The best single match to this chapter's level and spirit. Tier 1.

Bate, Mueller & White, Fundamentals of Astrodynamics, Ch. 1–4. The classic, inexpensive Dover text. Its treatment of the two-body problem, the classical elements, and the time-of-flight problem (Kepler's equation) is famously physical and readable, and it is where generations of engineers first solved $M = E - e\sin E$ by hand. If you buy one cheap book for Part II, buy this one. Tier 1.

Vallado, Fundamentals of Astrodynamics and Applications, Ch. 1–2. The professional reference. Heavier than you need here, but the definitive source for the element sets, coordinate frames, the many forms of the anomaly relations, and robust algorithms for solving Kepler's equation (including the awkward near-parabolic cases). Reach for it when you want completeness and production-grade methods. Tier 1.

Wertz, Everett & Puschell, Space Mission Engineering: The New SMAD. The systems-engineering bible. Its orbit chapters connect the elements and periods of this chapter to mission choices — coverage, ground tracks, revisit time — which is exactly how you will use them in your own Mission Design Review. The place to see Kepler put to work for design rather than analysis. Tier 1.

On the two-line element set and real orbits

CelesTrak (Dr. T.S. Kelso) and Space-Track.org. The public homes of two-line element sets for essentially every tracked object, plus clear documentation of the TLE format and the SGP4 propagator that turns elements into positions. Download the ISS's current TLE and repeat Case Study 1 with live data. Tier 2 — long-running, real resources; search the names for current URLs.

On the history

Kepler, Astronomia Nova (1609) and Harmonices Mundi (1619). The first two laws appear in the former (the war on Mars's orbit), the third in the latter (the source of this chapter's epigraph). You need not read the originals, but any good history of astronomy recounts how Kepler wrung three laws from Tycho Brahe's data. Tier 2 — the primary sources are real; accessible accounts vary.

Newton, Philosophiæ Naturalis Principia Mathematica (1687), Book I. Where Kepler's laws became theorems of gravity. Newton's geometric proofs are hard going in the original; Chandrasekhar's Newton's Principia for the Common Reader or any modern mechanics text (Goldstein, Classical Mechanics, Ch. 3) gives the calculus version you worked in §8.2. Tier 1/2.

Watch and play

Scott Manley, YouTube — videos on orbital elements and "how orbits work." Clear, intuitive explanations of what the six elements mean and how the anomalies relate, from an expert who flies them daily in simulation. Pair with §8.4 and §8.6. Tier 2.

Kerbal Space Program (with an orbit/map readout). The fastest way to feel the elements: the game's map view shows your $a$, $e$, apoapsis, periapsis, and a live "time to apoapsis" that is Kepler's equation running in real time. Set up an eccentric orbit and watch the craft race through periapsis and crawl through apoapsis — Kepler's second law in your hands. Tier 2 — a commercial game.

Suggested order

1. Reread §8.2 (the derivation) and §8.6 (the anomalies), then watch Scott Manley on orbital elements to hear a second voice on the same six numbers.
2. Work the Kepler's-equation and element examples in Curtis Ch. 2–3 or Bate/Mueller/White Ch. 1–4 — do them by hand and check against our GTO and ISS numbers.
3. Download a live ISS TLE from CelesTrak and redo Case Study 1 for today's orbit.
4. If you have KSP, build a Molniya-style eccentric orbit and watch the time-to-apoapsis clock; then reread Case Study 2's dwell-time calculation and see your own orbit in it.