More than half a century ago, ground tests during Project Rover demonstrated capabilities of re-igniting and clustering nuclear thermal rocket (NTR) engines. The initially envisioned application of NTR engines was to power the upper stages of intercontinental ballistic missiles. After NASA took over the project from the United States Air Force in 1958, Project Rover became part of the Nuclear Engine for Rocket Vehicle Application (NERVA) program. Potential applications of nuclear rocket engines were lunar shuttles and early manned interplanetary round-trip expeditions, as envisioned in NASA roadmaps comprising a round-trip to Mars by 1978, a perpetual settlement on the lunar surface by 1981, and the follow-up missions to outer planets. Those plans could not be realized due to the cancellation of the NERVA project in 1973. In the meantime, the RD-0410 engine was developed by the Soviet Union from 1965 through the 1980s, whose application was also crewed missions to Mars.

Despite the lack of flight records for nuclear engine rockets, there have been continued efforts to study nuclear rocket engines because they are more than twice as efficient as chemical rocket engines. Because the reduced propellant mass can increase the cargo capacity, nuclear propulsion can shorten the interplanetary transit time during which crews are subject to space radiation that is difficult to shield. In 2023, the Defense Advanced Research Projects Agency (DARPA) and NASA announced that they would collaborate in assembling and testing NTR engines from as early as 2027 [1]. The Demonstration Rocket for Agile Cislunar Operations (DRACO) engine will first transport cargo to the Moon, in preparation for crewed missions to Mars.

The advent of mega-constellations and the increasing occurrences of conjunction events would necessitate extreme care throughout the lifecycle of spacecraft with nuclear propulsion systems onboard. At the same time, the increased use of nuclear power propulsion could open up opportunities for novel missions in orbit or on the surface of the Moon and Mars. The improved fuel efficiency will lower the transportation of space logistics, thereby contributing to the circular economy on Earth and in space. The organization of this paper is as follows; Section 2 illustrates the near-future application of nuclear propulsion technologies by comparing their fuel economy with that of chemical propulsion in the Earth-Moon system. In Section 3, we introduce the concept of self-engineering and its applicability to nuclear propulsion systems. In Section 4, we investigate terrestrial architecture and nuclear infrastructures as a reference to establish sustainable habitation on the Moon and beyond.

**2. Where nuclear propulsion would work**

As mentioned above, the early NASA roadmap for NTR engines did not consider cis-lunar transits as its application, whereas DRACO aims at using NTR engines in cislunar space. Both plans are examples of nuclear thermal propulsion where the reactor heat is used for gas expansion. Another nuclear-powered option is nuclear electric propulsion (NEP). The term ‘nuclear electric rockets’ is less favored over NEP since the thrust does not directly originate from the reactor heat; instead, the thermal energy from its nuclear reactor is converted to electricity for powering electric thrusters. While rockets with nuclear thermal engines have not flown in orbit yet, nuclear electric propulsion has spaceflight records dating back to the US experimental satellite SNAP-10A, which marked the first operation of a nuclear reactor and an ion thruster in 1965. The follow-up NEP missions include the SP-100 program in 1983 and Project Prometheus/Prometheanin in 1993, neither of which was implemented in hardware. The Soviet Union ground-tested NEP (“Romashka”) in 1965 and deployed the next generation NEP system (“Buk” or “Bouk”) on over 30 reconnaissance satellites flown in the 1970s [2]. These satellites used the thermoelectric effect, also called the Peltier–Seebeck effect, in their thrusters where the temperature difference is directly converted to the voltage difference. The thermionic effect is another effect adopted in NEP systems to convert heat to electricity. A thermionic generator generates electricity from electrons released from an electrode (Edison effect) at high temperatures, whose efficiency is greater than that of thermoelectric generators. Examples of thermionic thrusters are TOPAZ and YENISEI reactors, which were produced in the Soviet Union and ground-tested in the US. First ground tested in 1971, TOPAZ (or TOPAZ-I) was flown in 1987 onboard the Soviet satellite, Kosmos 1818, which later experienced a coolant leakage problem [3]. YENISEI (or TOPAZ-II) was considered a successful collaboration between the U.S. and Russia, where British and French specialists also participated in ground testing; no flight plans followed despite possible applications of powering spacecraft radars and propulsion systems [4, 5, 6]. To evaluate the potential of nuclear propulsion, its performance relative to chemical propulsion could be analyzed in terms of orbital mechanics (“delta-V”) and scaling laws.

## 2.1 Cis-lunar transfers

NTR engines and NEP engines can be classified into different categories of rocket propulsion. NTR engines are similar to chemical propulsion (high-thrust) and have a high specific impulse (Isp) of approximately 1000 seconds. Their thrust level might enable take-off under limited low-gravity conditions. On the other hand, NEP engines have higher efficiencies (Isp = 7000s) but much lower thrust levels, thus limiting their application to in-orbit operations. As shown in Eq. (1) and Eq. (2), the same rocket equation may be written for high-thrust (HT) engines and low-thrust (LT) engines [7].

\(\:{\left(\frac{{m}_{pl}}{{m}_{0}}\right)}^{HT}=1-{\left(\frac{{m}_{f}}{{m}_{0}}\right)}^{HT}=exp\left(-\frac{\varDelta\:{V}^{HT}}{{I}_{sp}^{HT}{g}_{0}}\right)\) Eq. 1

\(\:{\left(\frac{{m}_{pl}}{{m}_{0}}\right)}^{LT}=1-{\left(\frac{{m}_{f}}{{m}_{0}}\right)}^{LT}=exp\left(-\frac{\varDelta\:{V}^{LT}}{{I}_{sp}^{LT}{g}_{0}}\right)\) Eq. 2

In the equations above, the ratio of the payload mass to the total initial mass decreases for a larger delta-V and increases for a larger specific impulse. When the payload ratio is subtracted from 1, we obtain the ratio of the propellant (fuel) mass to the total initial mass. The specific impulse value is for low-thrust propulsion, but the low-thrust delta-V tends to be also higher than the high-thrust counterparts. As shown in Eq. (3), a generalization can be made for a hybrid rocket by multiplying the payload ratios of HT phases and LT phases:

\(\:{\left(\frac{{m}_{pl}}{{m}_{0}}\right)}^{hyb}={\prod\:}_{i}^{}exp\left(-\frac{{\sum\:}_{j}^{}\varDelta\:{V}_{j}^{i}}{{I}_{sp}^{i}{g}_{0}}\right)=exp\left(-{\sum\:}_{i}^{}\frac{{\sum\:}_{j}^{}\varDelta\:{V}_{j}^{i}}{{I}_{sp}^{i}{g}_{0}}\right)\) Eq. 3

where \(\:\varDelta\:{V}^{HT}\) and \(\:\varDelta\:{V}^{LT}\) are represented by \(\:\varDelta\:{V}_{i}^{j}\) instead, with *i* for flight legs and *j* for propulsion types. While the above equations would apply to deep space transfers, we focus on cislunar space, i.e. the space within the Moon’s orbit around Earth, where nuclear propulsion will be tested and operated first.

## 2.1.1 Lunar surface to Earth-Moon-Lagrange points

The delta-V requirements for high-thrust transfers between the Moon and its vicinity are summarized in Table 1. A low-lunar orbit (LLO) is a Moon-bound orbit with an altitude of 100 km (in this case) or below. Landing on the lunar surface from an LLO or launching from the lunar surface to an LLO has a delta-V requirement of 1900 m/s. The flight legs between an LLO and an Earth-Moon Lagrange (EML) point tend to have lower delta-V requirements. Altogether, those requirements translate into the payload proportion of 42.4% out of the total rocket mass if only chemical propulsion, with a specific impulse (Isp) of 300 seconds, is used from the lunar surface to an EML. The same trip would yield a much higher payload fraction of 77.3% if only nuclear thermal propulsion is used, with a higher Isp value of 1000 seconds. However, this NTR-only option means that nuclear rockets must lift off from or land on the lunar surface, which would be exposed to radioactive emissions.

Table 1

delta-V requirements (m/s) for high-thrust transfers near the Moon

From\To | Lunar surface | LLO | EML1/2 | EML4/5 |

Lunar surface | X | 1900 | 2520 | 2580 |

LLO | X | X | 640 | 980 |

For the same scenario, chemical propulsion (from lunar surface to LLO) and NTR (from LLO to EML1/2) might be combined to avoid contaminating the lunar surface with radioactive emissions from NTR engines. Compared to the chemical-propulsion-only option, the payload fraction increases in the chemical-NTR hybrid to 49.1% from Eq. (3). The increase is not drastic because the flight leg from/to the lunar surface accounts for most of the delta-V to overcome the lunar gravity. If we hybridize chemical propulsion with nuclear electric propulsion, the resulting payload fraction is still around 51%, whose value is not sensitive to the range of Isp in NEP engines (7000 to 10000 seconds). The higher efficiency of NEP is offset by the increased delta-V requirement for low-thrust propulsion, which is approximately twice the high-thrust counterpart in this example. Overall, constrained operations of nuclear rockets to Moon-bound orbits and their vicinity, excluding the lunar surface, will not make significant improvements in the fuel efficiency of a mission or campaign.

## 2.1.2 Low-Earth-orbit to Earth-Moon-Lagrange points

In the next scenario, the operations of nuclear propulsion are extended to Earth-Moon transfers. During early phases of lunar settlements, materials and equipment should be carried from Earth; once habitation is established, materials may be sourced from the Moon to EML points to support exploration to Mars and beyond. Table 2 summarizes high-thrust and low-thrust delta-V requirements from the low-Earth orbit (LEO) and the geosynchronous equatorial orbit (GEO) to the select destinations in Table 1. Each entry in this table has two delta-V values; high-thrust (HT) values are calculated from Hohmann transfers, and low-thrust (LT) values are approximated using Edelbaum’s approach [8].

Table 2

delta-V requirements (m/s) for high-thrust (HT) and low-thrust (LT) transfers between the Moon and Earth [8]

From\To | LEO | EML1 | EML4/5 | LLO |

LEO | X | 3770 (HT) 7000 (LT) | 4000 (HT) 7500 (LT) | 4040 (HT) 8000 (LT) |

GEO | 3900 (HT) 4800 (LT) | 1400 (HT) 3000 (LT) | 1700 (HT) | X |

If nuclear propulsion is allowed in LEOs for Earth-Moon transfers, its advantages in terms of fuel efficiency are clear. Taking a LEO-EML1 transfer as an example, the payload ratio of 27.7% in chemical propulsion increases to 68.1% in NTR engines and 90.3% in NEP engines. If nuclear rocket operations are only permitted at higher altitudes, around a GEO for example, its advantage is less pronounced; the payload ratio of 62.1% in chemical propulsion increases to 86.7% in NTR and 95.7% in NEP.

If a LEO-LLO transfer is considered, the payload ratios are 25.3% for chemical engines, 66.2% for NTR engines, and 89.0% for NEP engines, as shown in Fig. 4. For scenarios where nuclear engines are banned in lower altitudes (LEOs), one way of dividing a LEO-LLO transfer is dividing into a sub-flight from a LEO to an EML1 (chemical) and a sub-flight from an EML1 to a LLO (nuclear) as a first-order approximation. The resulting increases in payload fraction are minimal, 26.0% for the chemical + NTR option and 27.5% for the chemical + NEP option, meaning that starting nuclear engines near an EML point does not provide fuel-saving advantages. Starting nuclear engines earlier would offer more advantages but is more challenging to characterize. Dividing a flight leg from a LEO to an EML into a sub-flight from LEO to GEO and a sub-flight from GEO to an EML based on Table 2 is not valid due to excessive delta-V requirements for arriving (re-circularizing the orbit) at and departing from the geosynchronous orbit. The diversity of LEO-LLO transfer trajectories poses challenges in analyzing HT-LT hybrid options comprehensively in their tradespace. While we will leave the details of design and optimization as future work, HT-LT hybridization might be an economically competitive alternative in space logistics and space domain awareness. Another option is to use solar electric propulsion (SEP) closer to Earth and NTR elsewhere, but this architecture may have too high complexity relative to its fuel-efficiency gain.

## 2.2 Unconventional orbits

Nuclear propulsion has relative advantages over chemical propulsion in terms of fuel efficiency, as analyzed above, and in terms of thrust time as well. The total duration of the trajectory correction maneuvers (TCMs), or burn time during which thrust is generated, is 20–40 minutes for an Earth-to-Mars transfer with chemical propulsion and is expected to be around 80 minutes with NTR (Microsoft Word - Mission Spacecraft and Instrument.docx (nmsu.edu)). Using the rocket equations, NEP for the same mission will yield a burn time of 460 minutes for Isp = 7000s. Another example, the Prometheus 1 Spacecraft in the Jupiter Icy Moons Orbiter (JIMO) mission envisioned a 3-year thrust duration with its NEP system on for its trip from Earth to Jupiter. These examples illustrate the potential for increased thrust duration. Furthermore, the scaling law analysis in this section suggests that the levels of thrust and acceleration would scale up as the size of a nuclear propulsion system increases. As a result, adopting nuclear propulsion might realize novel types of orbits, previously seen as infeasible due to perturbation forces, in cislunar space missions as well as in deep space exploration.

Comparing the specifications of several flown and proposed nuclear fission systems, the system specific mass (kilogram per watt) appears to be decreasing as the system power (watt) increases. Figure 5 describes this relationship in a logarithmic scale; in the figure, the specific power (watt per kilogram) is used instead, which is increasing with the system power [9, 10]. The data points, from the left to the right, represent SNAP-10A, RORSAT, TOPAZ, SP100, JIMO, Mars Cargo, Mars Human, and Longhurst’s concept [11, 12, 13]. Although the larger spacecraft missions are unimplemented prototypes, strong linear dependency is consistent in their modeling, continued from the data of smaller reactor sizes implemented in the past.

Table 3

Specifications of nuclear propulsion systems in Fig. 5 [9, 10, 11, 12, 13]

Mission | Meaning or other names | Power (kWe) | Year |

SNAP-10A | Systems for Nuclear Auxiliary Power, Space Nuclear Auxiliary Power Shot, OPS-4682 | 0.5 | 1965 |

RORSAT | Radar Ocean Reconnaissance Satellites | 1.8 | 1980 |

TOPAZ | TOPAZ-I | 5.0 | 1987 |

SP-100 | Space reactor Prototype (concept) | 100 | 1994 |

JIMO | Jupiter Icy Moons Orbiter (concept) | 200 | (concept) |

Mars Cargo/Human | - | 1000/2500 | (concept) |

Longhurst | - | 50000 | (concept) |

Denoting the specific power (kg/W) and the power (W) by s and P, respectively, the linearity between log(s) and log(P) yields a power law that can be expressed as

\(\:s={k}_{1}{m}^{{k}_{2}}\) Eq. 4

where k1 and k2 denote the scaling coefficient and the exponent of a power law, respectively. By definition, the power is a product of the specific power (s) and the reactor mass (m).

\(\:P=sm={k}_{1}{m}^{{k}_{2}+1}\) Eq. 5

Given the fitted value of k2 = 1.975 in Fig. 4, it can be said that the specific power is roughly proportional to the square of the reactor mass in Eq. (4) and that the power is proportional to the cube of the reactor mass in Eq. (5). The thrust of a rocket engine is represented as

\(\:F=\frac{2P\eta\:}{{I}_{sp}{g}_{0}}=\frac{2\eta\:{k}_{1}{m}^{{k}_{2}+1}}{{I}_{sp}{g}_{0}}=ma\) Eq. 6

where eta is efficiency, Isp is specific impulse, and g0 = 9.8 m/s2. Therefore, the thrust is proportional to the cube of the power. Dividing the thrust by the reactor mass, the acceleration is proportional to the square of the mass. Eq. (7) also shows that the acceleration is proportional to (reactor power)0.66 where the exponent is evaluated from k2/(k2 + 1).

\(\:a=\frac{F}{m}=\frac{2P\eta\:}{{I}_{sp}m{g}_{0}}=\frac{2{k}_{1}{m}^{{k}_{2}+1}\eta\:}{{I}_{sp}m{g}_{0}}=\frac{2{k}_{1}{m}^{{k}_{2}}\eta\:}{{I}_{sp}{g}_{0}}={\left({k}_{1}P\right)}^{\frac{{k}_{2}}{{k}_{2}+1}}\frac{2\eta\:}{{I}_{sp}{g}_{0}}\) Eq. 7

It should be noted that this acceleration formula considers the reactor mass only. Using the spacecraft mass when dividing the thrust, the resulting spacecraft acceleration will be less than the acceleration in Eq. (7) as it is. The spacecraft mass is the sum of the propellant mass and the dry mass without propellant. The dry mass is calculated by scaling up the reactor mass. Assuming a scaling factor of k3 multiplied to convert the reactor mass to the spacecraft mass (dry mass), the reactor mass term at the denominator of Eq. 7 is first replaced by k3m. After that, the rocket equation is used to add propellant mass to the dry mass; the resulting gross mass (wet mass) is thus the k3m term multiplied by\(\:(1+{e}^{\varDelta\:V/{I}_{sp}{g}_{0}}){g}_{0}\) as shown in Eq. 8:

\(\:a=\frac{2P\eta\:}{{I}_{sp}{k}_{3}m(1+{e}^{\varDelta\:V/{I}_{sp}{g}_{0}}){g}_{0}}={\left({k}_{1}P\right)}^{\frac{{k}_{2}}{{k}_{2}+1}}\frac{2\eta\:}{{I}_{sp}{k}_{3}(1+{e}^{\varDelta\:V/{I}_{sp}{g}_{0}}){g}_{0}}\) Eq. 8

As a reference, the acceleration of the NEP spacecraft is around 5×10− 5 m/s2 for Jupiter Icy Moons Orbiter (JIMO) whose reactor mass, spacecraft mass, and gross mass are 6 tonnes, 12 tonnes, and 20 tonnes, respectively. This acceleration magnitude is similar to that of the J2 effects and is greater than contributions from higher-order nonspherical harmonics (3×10− 7 m/s2), solar radiation pressure (1×10− 7 m/s2), and third-body effects from the Sun and the Moon (5×10− 6 m/s2). If this acceleration can be continuously or repeatedly applied, space missions with unconventional orbits, deemed inappropriate for chemical propulsion, would become possible as the acceleration benefits from the reactor size effect. Among the envisaged orbits with continuous propulsion is the so-called ‘cylindrical orbit’ depicted in Fig. 6 [14]. The coordinate system is rotating around the Earth’s center such that the x-axis is always coinciding with the geostationary point of interest, marked by a black dot in Fig. 5. Instead of being placed at the geostationary point, a satellite with continuous propulsion could be placed above or below the geostationary point. While the vertical displacement will result in small circular motion, this concept will greatly expand the usability of geosynchronous orbits which is mostly limited to the geostationary points on the Earth’s equatorial plane. The proposed cylindrical orbit concept relies on solar sails for thrust generation, but nuclear propulsion may provide an alternative or complementary option, whose investigation is left for future work. example, very-low-lunar-orbits [15]. Whether conventional or unconventional, orbital operations of nuclear power space vehicles should comply with the global norms such as the International Safety Framework for Nuclear Power Source Application**s** and other prior space treaties [2, 16].