The engineering ledger of a time machine: mass, wrap, siting, and the resource class of an acquired relic

This paper is the engineering ledger for a time machine. It quantifies the mass and density rungs, the wrap, the siting distance and the resource class of an acquired relic.

The canonical tube mass is 6.45 times 10 to the 26 kilograms, or 0.34 Jupiter masses; the full envelope is 2.9 to 5.4 times 10 to the 27 kilograms, or 1.5 to 2.8 Jupiter masses. The canonical density is 4.0 times 10 to the 25 kilograms per cubic metre, about 1.7 times 10 to the 8 nuclear saturation, with a peak near 5 times 10 to the 8. The ordinary-density rung is 778 kilograms per cubic metre at the deep rung, but it is asteroid-scale in total mass.

The siting derivation uses an environmental-curvature limit: the tidal curvature must stay below 10 percent of the gate margin, a safety factor of 10. The factor 2 from radial geodesic deviation gives r_min = (20 GM / (c squared m)) to the one third, so the net distance factor is 2.71. The two curvature cases give 1.8 times 10 to the 7 metres, 2.8 Earth radii and 0.008 AU, and 2.6 times 10 to the 8 metres, 41 Earth radii and 0.12 AU. The text uses 0.008 to 0.12 AU.

The wrap is asteroid-industry scale. The survey for a natural relic is civilization-scale. The energy conditions are scoped to the verified interior band, with the collar and upper envelope stated as open.

Key results

• Mass rungs: 0.34 Jupiter-mass tube, 1.5 to 2.8 Jupiter-mass envelope.
• Density rungs: about 1.7 times 10 to the 8 nuclear at the canonical corner (peak near 5 times 10 to the 8), 778 kilograms per cubic metre at the deep rung.
• Siting: 0.008 to 0.12 AU from the environmental-curvature limit.
• Resource class: asteroid-industry wrap, civilization-scale survey.

Status and limits

This is an 18-page content-complete engineering ledger. The siting derivation is a safety-factor model, and the resource class is an estimate. It has not been submitted or peer reviewed.