Appendix A: Notes On 2788 Propulsion Technology

Assumptions:

Let us assume humanity developed antigravity technology that could both create artificial gravity and reduce a structure's effective inertia -- by, say, 60-70% or so, before the energy costs became prohibitive. Let's further assume we had fusion reactors with self-contained plasma reactions (using their own magnetic field), enabling gratuitous use of fusion rockets such as the Direct Fusion Drive. How fast would spaceships operating around, say, Jupiter's moons, would be able to move around?

Well, let's see...

Technology Impact:

The antigravity tech is capable of comfortably reducing effective inertia to 35% of normal (midpoint of 60-70% reduction), increasing acceleration by ~2.86× for the same thrust. Assuming a baseline fusion drive capable of 1g (10 m/s²) sustained acceleration (inspired by speculative designs like those in The Expanse and theoretical fusion rockets), the effective acceleration becomes ~30 m/s² (3g), which can be dialed up further in desperate situations of for more advanced ship models. We can assume that artificial gravity allows the crew to experience a comfortable 1g (give or take) inside while this is happening.

Trajectory:

Constant acceleration to midpoint, then deceleration (brachistochrone path) could be the standard way to handle longer-distance travel. The formula is:

Time \( t = 2 \sqrt{\frac{d}{a}} \), max speed \( v_{\max} = \sqrt{a d} \).

This, of course, ignores gravity wells and orbital mechanics for simplicity, as high acceleration dominates over those things easily.

Distances: For simplicity, let us use minimum straight-line distances (optimal alignments) for optimistic speculative times. Speeds are all non-relativistic approximations (v << c for most trips).

Acceleration Value: \( a = 30 \) m/s². Higher reductions in mass are possible with greater energy expenditure, and fusion is assumed to provide effectively limitless sustained power (constrained only by the number and size of the reactors).

Travel in Jupiter's Moon System:

Any of these would be considered quite short hops, with times being measured in mere hours rather than days. Local ships -- without much of a "runway" to accelerate for a long time -- could reach speeds of 10^3–10^4 m/s (0.00003–0.0001c). Here are some sample trips.

Io to Europa:

Distance: 249,000 km (2.49 × 10^8 m; orbital radii difference). Time: 1.6 hours. Max speed: 86,000 m/s (0.00029c). Reasoning: \( t = 2 \sqrt{\frac{2.49 \times 10^8}{30}} \approx 5,760 \) s.

Europa to Ganymede:

Distance: 399,000 km (3.99 × 10^8 m; orbital radii difference). Time: 2.1 hours. Max speed: 109,000 m/s (0.00036c).

Io to Callisto:

Distance: 1,461,000 km (1.46 × 10^9 m; orbital radii difference). Time: 4.4 hours. Max speed: 209,000 m/s (0.0007c).

Interplanetary Travel

For longer routes that span multiple AU-scale distances, travel times will be measured in days rather than weeks or months. This is because ships would have time to accelerate, reaching 0.01–0.04c, thus enabling quick system traversal. Fusion sustains thrust; inertia reduction cuts energy needs.

Callisto to Mars:

Distance: 3.68 AU (5.51 × 10^11 m; min Jupiter-Mars separation, Callisto's orbit negligible). Time: 3.1 days. Max speed: ~4.07 × 10^6 m/s (0.014c). Reasoning: \( t = 2 \sqrt{\frac{5.51 \times 10^{11}}{30}} \approx 271,000 \) s.

Jupiter to Titan (as in, Saturn's moon):

Distance: 4.38 AU (6.55 × 10^11 m; min Jupiter-Saturn separation). Time: 3.4 days. Max speed: ~4.43 × 10^6 m/s (0.015c).

Titan to Triton (Neptune's moon):

Distance: 20.52 AU (3.07 × 10^12 m; min Saturn-Neptune separation). Time: 7.4 days. Max speed: ~9.59 × 10^6 m/s (0.032c).

Jupiter to Triton:

Distance: 24.9 AU (3.73 × 10^12 m; min Jupiter-Neptune separation). Time: 8.2 days. Max speed: ~1.06 × 10^7 m/s (0.035c).

This raises interesting implications. In the "old" days, with less advanced antigrav technology, the distances between worlds would have been vast enough to encourage the formation of highly autonomous local governments. With more modern technology and faster travel times, however, a tighter colonial control becomes a practical possibility. This can be a great source of intra-stellar political tensions.​​