ARCHIVE: VIDAR SECTOR – HYPNOTH SYSTEM

ARCHIVE: VIDAR SECTOR – HYPNOTH SYSTEM

Classification: Structural & Orbital Reference

Compiled For: Vôrun Strategic Continuity Council

Revision: 7.442.Σ

I. Stellar Architecture

Primary Star

• Type: K-dwarf (K1V equivalent)

• Mass:
  M_\star = 0.85 M_\odot = 0.85 \times 1.989\times10^{30}\text{ kg}
  = 1.69\times10^{30}\text{ kg}

• Luminosity: ~0.45 L☉

• Estimated Age: 7–9 Gyr

Companion Star

• Type: M-dwarf

• Mass:
  M_c = 0.25 M_\odot = 4.97\times10^{29}\text{ kg}

• Semi-major axis:
  a_c = 10\text{ AU}

• Eccentricity:
  e_c = 0.35

• Orbital period (Kepler’s Third Law):

P^2 = \frac{4\pi^2 a^3}{G(M_\star + M_c)}

Using AU/solar-mass simplification:

P = \sqrt{\frac{a^3}{M_\star + M_c}} = \sqrt{\frac{10^3}{1.10}} \approx 30\text{ years}

This establishes the ~30-year debris modulation cycle.

II. Planetary System (Circumprimary)

All planets orbit the primary star inside the binary stability boundary (~2.16 AU for this configuration).

Kepler’s law in solar units:

P(\text{years}) = \sqrt{\frac{a^3}{M_\star}}

with M_\star = 0.85.

Planetary Table

#

Name

a (AU)

Period (days)

1

Ferrum Minor

0.050

4.43

2

Ferrum Major

0.083

9.47

3

Pyros

0.137

20.09

4

Volundr

0.214

39.22

5

Kheltar

0.332

75.79

6

Arkh Relay

0.530

152.86

7

Hypnoth (Cygnus)

0.750

257.32

8

Haldris

1.120

469.58

9

Nox Prime

1.740

909.29

These are near-resonant but not locked — a dynamically relaxed system.

III. Hypnoth (Cygnus)

Physical Parameters

Mass:

M_p = 1.6 M_\oplus = 1.6 \times 5.97\times10^{24} = 9.56\times10^{24}\text{ kg}

Radius:

R_p = 1.1 R_\oplus = 1.1 \times 6.37\times10^6 = 7.01\times10^6\text{ m}

Surface gravity:

g = \frac{GM_p}{R_p^2}

g = \frac{6.674\times10^{-11} \times 9.56\times10^{24}} {(7.01\times10^6)^2} \approx 12.8 \text{ m/s}^2

≈ 1.3g.

Rotation period: 10 hours.

IV. Moons of Hypnoth

Moon I – Shepherd

Semi-major axis:

a_1 = 60,000\text{ km}

Orbital period:

P = 2\pi \sqrt{\frac{a^3}{GM_p}}

= 2\pi \sqrt{\frac{(6.0\times10^7)^3} {6.674\times10^{-11}\times9.56\times10^{24}}}

\approx 32.1\text{ hours}

Radius:

110 km.

Mass:

M_1 \approx 2\times10^{19}\text{ kg}

Moon II – Irregular

a_2 = 250,000\text{ km}

Period:

≈ 11.4 days.

Mass:

~6×10²⁰ kg.

Moon III – Hypnoth Tertius (Destroyed)

Pre-destruction:

a_3 = 95,200\text{ km}

Period:

≈ 64.2 hours (2:1 resonance with Shepherd).

Radius:

500 km.

Mass:

M_3 = 1.68\times10^{21}\text{ kg}

V. Roche Limit Calculation

For rubble body:

d_R \approx 2.5 R_p

= 2.5 \times 7,008\text{ km} = 17,520\text{ km}

Conservative fluid estimate ≈ 22,000 km.

Hypnoth Tertius reached eccentricity:

e = 0.77

so that:

r_{peri} = a(1-e) \approx 22,000\text{ km}

Catastrophic tidal shredding followed.

VI. Ring Mass

Original moon mass:

1.68\times10^{21}\text{ kg}

Persistent ring fraction (0.1–1% retained):

10^{18} – 10^{19}\text{ kg}

Ring lifetime (shepherded):

10^7 – 10^8\text{ years}

VII. Vôrun-Hold Asteroid

Orbital Position

a_{hold} = 35,000\text{ km}

Period:

P = 2\pi\sqrt{\frac{(3.5\times10^7)^3}{GM_p}}

≈ 14.31 hours

Eclipse Duration

Orbital velocity:

v = \sqrt{\frac{GM_p}{r}} \approx 4.27\text{ km/s}

Planet diameter:

2R_p = 14,016\text{ km}

Umbra crossing time:

t = \frac{14,016}{4.27} \approx 3,280\text{ s} \approx 55\text{ minutes}

Shadow-Shift = 55 minutes per 14.31 hours.

VIII. Asteroid Physicals

Radius:

80 km.

Volume:

V = \frac{4}{3}\pi R^3 = 2.14\times10^{15}\text{ m}^3

Density:

3,000 kg/m³.

Initial mass:

6.43\times10^{18}\text{ kg}

30% hollowed:

Remaining mass ≈ 4.5×10¹⁸ kg.

Surface gravity (after hollowing):

g \approx 0.047\text{ m/s}^2

Tidal acceleration from Hypnoth:

a_t \approx 0.0024\text{ m/s}^2

≈ 5% of self-gravity.

This necessitates mass-balancing doctrine.

IX. Fossil Belt

Location:

1.30–1.58 AU.

Total mass:

\sim 10^{20}\text{ kg}

Dominant type:

C-type carbonaceous.

Hydrate Band:

1.36–1.49 AU.

Decadal modulation driven by companion periastron (30-year cycle).

Impact flux increases but remains bounded.

X. Shepherd’s Cut

Moon I radius: 110 km.

Distance from Hold during transit:

25,000 km.

Angular size:

0.252°.

Star angular radius:

0.295°.

Max dimming:

(0.252/0.295)^2 \approx 70\%

Duration:

~4 minutes.

Occurs 2–4 times per Hypnoth year.