Assumed errata

# Appendix E, FindCandS Stumpff-function table, z = -39.47842 row (p. E-12)

confirmed in print open

Printed

C = 5.83559577, S = 0.97444596

We derive

C = 6.75677528, S = 1.05406777

The printed C and S for z = -39.47842 appear inconsistent with the standard Stumpff definitions (for z < 0: C(z) = (1 - cosh sqrt(-z))/z and S(z) = (sinh sqrt(-z) - sqrt(-z))/(-z)^(3/2)). We derive C = 6.75677528, S = 1.05406777 three independent ways — the project's universal-variable implementation, a direct power-series evaluation, and the closed cosh/sinh forms — all agreeing to better than 1e-9, and no nearby z reproduces both printed values simultaneously. The page was re-read character-by-character twice; the printed z itself is -39.47842 (not mis-printed), and the other four rows of the same table (z = 0, 0.57483, 39.47842, 50.0) reproduce to <= 4e-9. We would welcome correction if a different Stumpff convention explains the printed pair. EXTERNAL CONFIRMATION (2026-06-13): the author's own current code release ("Fundamentals of Astrodynamics and Applications" 5th-ed companion, github.com/CelesTrak/fundamentals-of-astrodynamics, findc2c3) evaluated at z = -39.47842 returns C = 6.756775284482481, S = 1.0540677718375635 — bit-identical to our derived values, agreeing with this erratum and not with the 1991 print.

# Appendix E, KEPLER test case 4 (BMW example D.3-3, hyperbolic), propagated position component R_y (p. E-14)

confirmed in print open

Printed

R = (13.9623306, -0.1172043, 0) DU; R_y = -0.1172043

We derive

R_y = -0.11822049 (R_x agrees with print to ~5e-5 relative)

For the printed inputs Ro = (0.3, 1, 0), Vo = (3, 0, 0), Dt = 5, mu = 1, the printed propagated R_y appears inconsistent with the propagation itself: the project's universal-variable propagator (single-shot AND 1000-substep), and an independent high-precision RK4, all give R_y = -0.11822049 (delta ~= 1.0e-3). The printed orbital elements a = -0.1411563, e = 8.0473056 reproduce exactly from the same inputs, so the geometry is consistent; only the propagated R_y disagrees, and by far more than the report's own stated ~1e-5 cross-machine tolerance (p. iv). The page was re-read character-by-character twice; no single-digit or sign variation of the printed R_y or any input closes the gap. The report's four other Kepler cases reproduce cleanly. EXTERNAL CONFIRMATION (2026-06-13): the author's own current code release ("Fundamentals of Astrodynamics and Applications" 5th-ed companion, github.com/CelesTrak/fundamentals-of-astrodynamics, kepler) run at the same canonical inputs returns R_y = -0.11822048981640433 — agreeing with our derived value to 1.8e-15 and not with the 1991 print.

# Appendix E, interplanetary Hohmann-transfer table, Mars row (p. E-36)

provable internal inconsistency open

Printed

Mars heliocentric distance 227,800,000 km with vh1 = 4.1745 km/s, vh2 = 3.5696 km/s, transfer time 311.804 days

We derive

The printed outputs match a Mars distance of 277,800,000 km exactly; a Hohmann transfer from 1 AU to the printed 227.8e6 km (with the table's own mu_Sun = 132715440000.0 km^3/s^2 and stated 200-km burnout setup) gives vh1 ~= 2.94 km/s and ~= 258.7 days

The Mars row is internally inconsistent under the table's own stated construction: its printed outputs cannot follow from its printed input distance, but follow exactly from 277.8e6 km — consistent with a 227.8/277.8 digit transposition somewhere in the run that produced the table. The Venus, Mercury, and Jupiter rows of the same table agree with their printed inputs and with the classic textbook Hohmann values. We would welcome the authors' confirmation of which figure (input distance or outputs) the transposition affected.

# Chapter 7, Table 7.1 (Outbound Cycler Vehicle 1, p. 148), encounters 20-24 (Mars-20 2031-07-15 through Earth-24 2038-05-06), V-infinity and closest-approach columns

provable internal inconsistency open

Printed

V-infinity 7.85 / 4.21 / 4.20 / 5.87 / 7.23 km/s; closest approach 8,802 / 24,870 / 2,756 / 1,770 / (blank) km, against Table 7.1's own printed encounter dates

We derive

Table 7.5 (p. 159) prints, for encounter dates identical to the printed day, V-infinity 7.70 / 3.78 / 3.76 / 4.68 / 5.54 km/s and closest approaches 10,573 / 22,970 / 9,633 / 15,695 km; a DE440 per-leg reproduction from Table 7.1's own dates emerges Table 7.5's values

Tables 7.1 and 7.5 print encounter dates identical to the printed day from Earth-3 through Earth-22, yet from Mars-20 they print incompatible V-infinity and closest-approach values. Identical dates force the same Lambert conics (the discrete alternative conics are 6.7-16.3 km/s apart), so both tails cannot be right for these dates — Table 7.1's tail is internally inconsistent with the table's own dates and times of flight. Our DE440 reproduction of the full 24-encounter itinerary from Table 7.1's printed dates reproduces rows 1-19 cleanly and emerges Table 7.5's values for the tail, as does the independent Russell 2004 Appendix C itinerary that overlaps these dates. Our transcription of both tables was re-read character-by-character against the page (image and embedded text layer agree). Whether the production error sits in Table 7.1's date column or its V-infinity/closest-approach columns is unresolvable from the print alone — a question we would welcome the author's input on.

# Table 3 (p. 11), C^stable lower bound for the (2,1) family, vs Eq. 8 with Table 1's tangency constants (p. 8)

provable internal inconsistency open preprint — may be fixed in VoR

Printed

C^stable_(2,1) = 3.1297495000000 (Table 3; trailing zeros as printed)

We derive

Eq. 8 evaluated with the paper's own Table 1 constants gives 3.129751730201047 (exact difference 2.2302e-6, Decimal arithmetic)

The printed Table 3 bound appears inconsistent with the paper's own Eq. 8 + Table 1: evaluating the published formula with the published constants gives a value 2.2302e-6 larger than the Table 3 entry. Table 4's Delta-C_(2,1) = 5.859161e-2 reconciles with the Table 3 value (C1 - 3.1297495 = 5.8591605e-2), so the paper is self-inconsistent between Table 3/Table 4 on one side and Eq. 8 + Table 1 on the other. Both sides were re-read twice; the discrepancy is pinned by a regression test so we will notice if a corrected version changes either side. The family's C^stable/C^max/T^stable golden columns are unaffected (they re-verify as internally consistent). We would welcome the authors' indication of which side carries the slip.

Version of record: Read from the AAS 25-621 manuscript publicly posted by the authors. A 2026 journal version ("Stable Prograde Earth-Moon Multi-Orbiter Cyclers via Three-Body Dynamics", Roberts-Tsoukkas & Ross) exists but has not yet been acquired/checked.

Affected catalogue entry: Ross/Roberts-Tsoukkas stable Earth-Moon (2,1) prograde cycler (CR3BP)

# Table 3 (p. 11), C_(3,1) bound, vs Table 4 (p. 13) Delta-C reconciliation

provable internal inconsistency open preprint — may be fixed in VoR

Printed

C_(3,1) = 3.1833333078762 (Table 3); Delta-C_(3,1) = 1.272710e-2 and Delta-C^max_(3,1) = 1.381776e-2 (Table 4)

We derive

Table 4's two deltas reconcile only with C_(3,1) = 3.175614005 (C1 - 1.272710e-2 = 3.175614005; 3.175614005 - C^stable_(3,1) = 1.3817758e-2); exact difference vs Table 3 is 7.7193e-3

Table 3's printed C_(3,1) equals C^(u2)_1, the Eq. 8 minimum, but it does not reconcile with Table 4's printed Delta-C_(3,1) and Delta-C^max_(3,1), both of which reconcile (to printed precision, Decimal arithmetic) only with C_(3,1) = 3.175614005. The two tables are therefore self-inconsistent as printed (difference 7.7193e-3). Both sides were re-read twice and the discrepancy is pinned by a regression test. The family's C^stable/C^max/T^stable golden columns are unaffected. We would welcome the authors' indication of which table carries the intended value.

Version of record: Read from the AAS 25-621 manuscript publicly posted by the authors. A 2026 journal version ("Stable Prograde Earth-Moon Multi-Orbiter Cyclers via Three-Body Dynamics", Roberts-Tsoukkas & Ross) exists but has not yet been acquired/checked.

Affected catalogue entry: Ross/Roberts-Tsoukkas stable Earth-Moon (3,1) prograde cycler (CR3BP)

# Eq. 16 (p. 11 of the 22-page author draft), t_e1 coefficient

provable internal inconsistency open preprint — may be fixed in VoR

Printed

t_e1 = 22 * n_cycle * S_G,E (Ganymede-Europa synodic period)

We derive

S_C,E (Callisto-Europa synodic period, ~4.511 d): Fig. 4 labels the same interval "11*2 S_C,E" and the p. 10 text states "4 C-G synodic periods or 11 C-E synodic periods"

Eq. 16's printed subscript appears inconsistent with the paper's own figure and text: Fig. 4 and the accompanying p. 10 prose both describe the t_e1 interval in Callisto-Europa synodic periods (11 per cycle, hence the 22 for two cycles), while Eq. 16 prints the Ganymede-Europa synodic period S_G,E. The cycle timing only closes with S_C,E. Both readings were confirmed in two independent passes over the draft. No catalogue row ingests Eq. 16, so this is recorded for reproducibility of the construction only. The defect may already be corrected in the journal version of record.

Version of record: Page/equation numbers refer to the 22-page author draft; the JGCD version of record (DOI 10.2514/1.G008387) is unchecked (paywalled).

# Eq. 13 (p. 6 of the 22-page author draft), denominator of the flyby-defect angle gamma

provable internal inconsistency open preprint — may be fixed in VoR

Printed

gamma = arccos[(1+nu_1) / sqrt((1+nu_1)^2 + nu_2^2 + nu_2^2)] (nu_2^2 repeated)

We derive

nu_2^2 + nu_3^2 in the last two denominator terms, per the Delta-v projection definition of Eqs. 9-10 (components nu_1, nu_2, nu_3)

The printed denominator repeats nu_2^2 where the projection definition the paper itself sets up in Eqs. 9-10 (a three-component decomposition nu_1, nu_2, nu_3) requires the norm to include nu_3^2 — as printed, the nu_3 component never enters, which is inconsistent with the stated definition. This reads as a subscript typo; any reproduction must use nu_2^2 + nu_3^2. Confirmed in two independent passes over the draft. No catalogue row ingests Eq. 13. The defect may already be corrected in the version of record.

Version of record: Page/equation numbers refer to the 22-page author draft; the JGCD version of record (DOI 10.2514/1.G008387) is unchecked (paywalled).

# Introduction in-text citations and reference list (author draft)

confirmed in print minor / typographical open preprint — may be fixed in VoR

Printed

"Lynan and Longuski [9]"; "Drew et al. [6]"; "Naoya et al. [7]"; reference-list "Sttange" [8]

We derive

Lynam (ref. 9); Jones (ref. 6, "Drew" is the first name); Ozaki (ref. 7, "Naoya" is the first name); Strange (ref. 8)

Minor/typographical only — no numerical content is affected. The in-text names appear inconsistent with the cited works' author surnames: "Lynan" for Lynam, "Sttange" for Strange, and two first-name citations ("Drew et al." for Jones et al., "Naoya et al." for Ozaki et al.). All four were confirmed in print in two independent passes. Recorded so that forward-citation searches from this note resolve to the right authors; the typos may already be corrected in the version of record.

Version of record: Read from the 22-page author draft; the JGCD version of record (DOI 10.2514/1.G008387) is unchecked (paywalled).

# Sec. VI.A Earth-Mars example, p. 30 (arXiv pagination): prose total-time statement vs the feasibility check on the same page

provable internal inconsistency fixed in version of record

Printed

"becomes 701.2694 days and 1405.8939 days" (prose), then "793 - 720.2694 = 72.7306 < T_0" (feasibility check, same page)

We derive

720.2694 days — the same-page subtraction 793 - 720.2694 = 72.7306 is arithmetically consistent, so the prose 701.2694 appears to be the slip

The two printed statements of the same total time on p. 30 disagree (701.2694 vs 720.2694 days) and cannot both be right; the page's own feasibility arithmetic (793 - 720.2694 = 72.7306) supports 720.2694. Both readings were confirmed in two independent passes over the arXiv PDF. We would welcome the authors' confirmation of which figure was intended, and whether the journal version of record already corrects it.

Version of record: FIXED IN VoR (checked 2026-06-13). The J. Astronaut. Sci. version of record (DOI 10.1007/s40295-025-00528-0, 38 journal pages) was diffed against the arXiv:2501.01583 preprint: the entire Sec. VI.A Earth-Mars rendezvous worked example that carried this cell was removed in production and replaced by a new CAPSTONE-inspired orbit-raising example (VoR Sec. 5.4, pp. 29-32). The prose total time, the same-page feasibility subtraction, and the mission time of 793 days appear nowhere in the VoR, so the in-print inconsistency does not survive. No fault is implied: this is the routine kind of section revision between preprint and publication; the defect simply no longer exists in the version of record.

# Sec. VI.A Earth-Mars example, pp. 30-31 (arXiv pagination): Delta-v total of the iso-impulse solution (Fig. 21c sentence on p. 30 vs p. 31)

provable internal inconsistency fixed in version of record

Printed

Delta-v_total = 5.6109 km/s (p. 30) vs 5.6108 km/s (p. 31)

We derive

The two printed statements of the same quantity differ by 0.1 m/s; at most one is correct (our independent bracket 5.5865 <= Delta-v <= 6.047 km/s is consistent with either)

The same solution's total Delta-v is printed as 5.6109 km/s on p. 30 and 5.6108 km/s on p. 31 — a 0.1 m/s internal inconsistency, confirmed in two independent passes over the arXiv PDF. Our reproduction cannot discriminate at that precision (the value sits inside our independently computed lower/upper bracket either way), so this is recorded purely as an in-print inconsistency for the authors to adjudicate. The values wired as goldens from this paper (the 3.9618011 km/s two-impulse base and its breakdown) are unaffected and reproduce cleanly.

Version of record: FIXED IN VoR (checked 2026-06-13). The J. Astronaut. Sci. version of record (DOI 10.1007/s40295-025-00528-0, 38 journal pages) was diffed against the arXiv:2501.01583 preprint: the entire Sec. VI.A Earth-Mars rendezvous worked example that carried both the p. 30 (5.6109) and p. 31 (5.6108) statements of this quantity was removed in production and replaced by a new CAPSTONE-inspired orbit-raising example (VoR Sec. 5.4, pp. 29-32). Neither 5.6109 nor 5.6108 appears anywhere in the VoR, so the 0.1 m/s in-print inconsistency does not survive. No fault is implied: this is the routine kind of section revision between preprint and publication; the defect simply no longer exists in the version of record. The goldens wired from this paper (3.9618011 km/s and its breakdown) survive verbatim in the VoR (Fig. 8 text, p. 19).

# Table 3 (p. 18), 2-Impulse Lambert (a) rows: cost-effective (J_c*) and minimum-impulse (J_m*) labels

provable internal inconsistency open preprint — may be fixed in VoR

Printed

J_c* = 5.1176 km/s (at t_f = 2894 s); J_m* = 7.9455 km/s

We derive

Labels exchanged: 5.1176 km/s reproduces as the min-over-t_f of the MAX impulse norm (J_m, Eq. 27) at exactly the printed t_f = 2894 s, and 7.9455 km/s as the min-over-t_f of the SUM of impulse norms (J_c, Eq. 26)

As printed the row pair is mathematically impossible: by the paper's own definitions the maximum impulse norm (J_m, Eq. 27) can never exceed the sum of impulse norms (J_c, Eq. 26) on the same transfer, yet the printed J_m* = 7.9455 exceeds J_c* = 5.1176. Both values reproduce exactly (at printed precision) with the labels exchanged, using our independent Lambert solver on the case-2 fixed-endpoint geometry; the paper's own discussion on p. 19 (Lambert (a) gives the "worst (highest) costs") matches the exchanged reading. The reproduction is wired as regression tests. We would welcome the authors' confirmation that the two labels were transposed in production.

Version of record: Values cite arXiv:1905.04543v1; any Acta Astronautica version of record is unchecked.

# Table 2 (p. 14) and Table 3 (p. 18): the 1-Impulse row; the Remark-2.7 row's t_f cell; the 2-Impulse Lambert (b) rows; and the t_f = 3570 s cell of Table 3's 7.9455 km/s optimum

unresolved — question for the authors open preprint — may be fixed in VoR

Printed

(a) Table 2, 1-Impulse row: J_c = 2.6305 km/s, coast times 2631 / 3463 s; (b) Table 2, 2-Impulse (Remark 2.7) row: t_f = 2315 s; (c) Tables 2-3, 2-Impulse Lambert (b) rows: 1.4677 / 0.7831 km/s (case 1) and 2.5604 / 1.3344 km/s (case 2); (d) Table 3: t_f = 3570 s for the 7.9455 km/s cell

We derive

Our reproductions: (a) single-impulse cost 2.7864 km/s at BOTH orbit intersections (true anomaly 120/240 deg), coast times 4039 / 14623 s; (b) the transfer is a half revolution of the a_2 = 10317 km intermediate ellipse, half-period 5214 s; (c) with the departure point fixed at theta_12 our optimum is 1.93 km/s, and with the departure anomaly also free our optima fall BELOW the printed values (1.337 / 0.782; 2.508 / 1.283 km/s); (d) our minimiser of the impulse sum sits at t_f ~= 5126 s, and our J_c(3570 s) = 8.2459 km/s

These cells are open QUESTIONS for the authors, not claimed errata: our reproductions disagree with the printed values, but we hold no internal-consistency proof and a convention difference may explain them. Specifically we would ask: (a) under what geometry does the 1-Impulse row reach J_c = 2.6305 km/s with coast times 2631 / 3463 s? No interpretation we tried (either omega sign convention, either coast direction, time measured from perigee) reproduces the printed row, and the same row's orbits intersect where our single-impulse cost is 2.7864 km/s. (b) How is the Remark-2.7 transfer time t_f = 2315 s defined, given the closed-form transfer is a half revolution of the intermediate ellipse (half-period 5214 s) and the row's J_c / J_m cells reproduce exactly? (c) What feasible set defines the Lambert (b) rows ("allows the spacecraft to remain in its initial orbit before applying the first impulse", p. 12)? With the departure fixed we land above the printed optima and with it free we land below them. (d) For Table 3's 7.9455 km/s value (see the label-swap entry), is the printed t_f = 3570 s a typo? Our minimiser of the impulse sum sits near 5126 s. The reproduction code paths are public and we would welcome correction of any mistaken assumption on our side.

Version of record: Values cite arXiv:1905.04543v1; any Acta Astronautica version of record is unchecked.

# Appendix, Eqs. A1-A6 (gradients of the Eq. 4 flyby minimum-altitude constraint w.r.t. the v-infinity vectors)

provable internal inconsistency open

Printed

Each printed term carries an additional 1/r_periapse factor (A1-A3 and the first terms of A4-A6) or 1/r_flyby factor (final terms of A4-A6) relative to the gradient of Eq. 4 as printed

We derive

The unscaled gradient d(c_alt)/d(v-infinity) of Eq. 4 (units km per km/s); the printed expressions match it term by term — same numerator vectors, same cos(acos(alpha)/2), (alpha - 1), and power factors — except for the extra radius factors

The printed appendix gradients appear to be of an r-scaled (nondimensionalised) form of the Eq. 4 constraint rather than of Eq. 4 as printed — and the scaling radius is printed inconsistently between terms of the same gradient (1/r_periapse in some terms, 1/r_flyby in others), so as printed the expressions are not the gradient of any single scaling of Eq. 4 and are dimensionally inconsistent with it. Our unscaled implementation of d(c_alt)/d(v-infinity) matches the printed expressions term by term once the extra radius factors are removed, and validates against central differences — the paper's own recommended verification pattern for derivative code (Sec. VI). The paper prints no unit-level numeric gradient values, so a direct numeric check against the print is not possible; we would welcome the authors' statement of the intended constraint scaling.