Mass may be ejected either 1. via internal molecular collisions (i.e., through thermodynamic expansion),

or 2. by applying an external force directly to atoms/molecules.

These two different strategies are common to all space propulsion systems

The Tsiolkowski equation (1) is the form taken by the second Newton’s principle when the mass of an object being accelerated varies with time. In fact, the physics we can bring to bear to solve the problem of faster travel is based solely on Newton’s three principles. The third, Nuclear Propulsion 385 the most important in all kinds of propulsion, states that in space velocity of an object can be increased only by ejecting mass, that is, accelerating it from 0 to Ve (in the spacecraft reference system): so far, no massless ‘space drive’ has been invented.

1. CP is based on the first strategy: in special relativity, the relativistic potential energy PE = (Δm) c2 of a mass Δm becomes kinetic energy (KE) of the remaining mass m, that is ½ m (Ve)2. The percentage Δm/(m + Δm) of mass converted into KE depends on the fundamental force used. CP uses the potential of the second force (electro-weak), the potential energy released when chemical bonds are broken and rearranged.

In fact, the Standard Model of physics includes only three fundamental forces: gravity, electroweak (the result of unifying electro-dynamic and weak forces in the ‘80s), and the strong, or nuclear, force. The electroweak force binds molecules and atoms together, and is responsible for the existence of matter as we know it. The strong force binds sub-atomic particles (nucleons) together, preventing them from disintegrating due to Coulomb repulsion.

The Δm/m fraction varies from 10-27 of gravity to about 10-3 of the nuclear force. In classic mechanics, the simple 0-D relationship between PE change and KE gain is Delta PE= ½ mVe sq predicting that the Ve (the Isp) scales with the square root of Δ(E)/m, a weak dependence.

(Note the equation above does not refer necessarily to a fluid.)

Comparing these three forces shows that the J of CP, based on the second, is eighteen orders of

magnitude larger than gravitation, but six smaller than the third. Dividing J of the second force by the specific heat of chemical reactions products yields the maximum temperature of a CP cycle, not much higher than 3500 K, and anyway limited by the melting point of materials (ruled by the same force). When using realistic numbers, Eqn. (2) shows that the Ve and Isp are correspondingly limited to 4-5 km/s. Hence, as said, Isp is of order of the ΔV needed to change orbit, and Eqn (1) predicts large mass consumption: for instance, the ΔV from ground to LEO (in practice, 9-9.5 km/s) results in a (Min – Mfin)/Min ratio, the payload fraction, of order of a few percent. Thus, during a satellite launch, almost all propellants mass and energy release is used to lift and accelerate the propellants themselves, not the payload.

2. When adopting the second strategy, [ionized] molecules/atoms are still accelerated by electroweak forces, but the Coulomb or Lorentz force is external to the plasma and requires an external electric power source. The Ve possible are much larger than in a thermodynamic expansion, since they are neither limited by the upper and lower temperatures of the cycle, nor by the melting point of materials. Accelerating ionized matter by Coulomb or Lorentz is, in principle, limited only by relativity, although in practice voltages and magnetic fields cannot be made large at will by arcing, magnet mass, critical current density and Meissner effect.

Using classical (Newton’s) mechanics, the conclusions for space propulsion are as follows:

Isp scales with Ve

Thrust, F, scales with (flowrate) times (Ve), thus with (Ve)2

Power of the ejected flowrate is the kinetic energy (of the mass ejected) per unit time, or

½ (flowrate) times (Ve) sq, and thus scales with (Ve) cb.

(Relativistic relationship are formally different, but predictions differ only when Ve is > 0.99c,

and will be ignored here).

Based on these simple scaling laws, to reduce mission time F must be increased. This implies Ve must be as large as possible; when doing so also mass consumption decreases. There is a price, however, and that is the power required, scaling with (Isp)3. As said, CP is fundamentally limited in Isp (in Ve) by J = Δ(E)/m that can be extracted from rearranging chemical bonds.

Thus the next logical step is to seek other potentials providing larger energy density J. Of the three fundamental forces we know, only the nuclear force remains, since gravity is so weak that only assist (flybys) manoeuvres, exploiting the mass of entire planets, can supply enough energy to a spacecraft, at the expense of lengthening, not shortening, mission time.

The nuclear force, see Table 1, converts about 0.09% of the ‘fuel’ mass into KE in the case of 235U fuel, and 0.3% in the case of D-T (deuterium-tritium) fusion, a factor ~106 larger than possible in chemistry. It is logical to look at nuclear reactions as the only solution to the need to increase J, thus Isp, thus thrust, finally enabling faster missions with drastically lower mass consumption. Thrust, and travel time, scaling with (Ve)2, will depend on the NP strategy outlined already. The first, nuclear thermal propulsion, or NTP, has produced in time the family of NP devices called nuclear thermal rockets (NTR), the second, nuclear electric rockets, or thrusters, or (generally) nuclear thermal propulsion (NTP). Strategy 1 began to be explored in the ‘50s. Strategy 2 was explored by Stuhlinger during WW II, but started being investigated only much later.

Amongst the missions of interests:

**Heavy robotic missions to outer planets**

**Asteroid deflection missions**

**Interplanetary manned mission (at longer term)**

These missions involve high speed increments, generally beyond the capability of chemical propulsion (except if gravitational swing-by can be used). For missions beyond Mars orbit, the fission nuclear energy sources become competitive with solar panels.

Two electrical power levels have been considered: 30 kW and 200 kW.

The lowest power level (30 kW) is more suited to surface energy source (Moon or Mars manned base) or to relatively small automatic platforms.

The 200 kW power level is more suited to heavy robotic missions, including asteroid deflection.

NTP (Nuclear Thermal Propulsion) has been also considered, especially for asteroid deflection. NTP may be compatible with late detection acting by direct impact.

The public acceptance of these new technologies has been analysed, showing the necessity to provide safe ground testing facilities as well as a mission scenario excluding re-entry of an activated space nuclear reactor.

**APPLICATIONS AND MISSIONS**

**Background**

Applications requiring or able to benefit from space nuclear power generation have been researched. At the lower end of the scale are high power instruments such as ground penetrating radar. The higher power tends to be more needed for propulsion. Some applications, such as asteroid/NEO mining or powerplants

for surface infrastructure (say, on the moon or Mars) may be achieved with lower or higher power levels. Although not specifically listed there are secondary benefits from high power such as high data rate for very long distance (laser) communications.

The lower power level of 30 kWe was selected for DiPoP study to investigate which applications might be benefited in practice, and whether there were advantages in terms of technical options, European capability, resources, public acceptance, safety and sustainability.

The higher power level (200 kWe) was selected in the HiPER and DiPoP studies because current European studies indicate this is the maximum consistent with the lift capability of the Ariane 5 ECA launcher. Current alternative launchers (such as the Atlas V heavy lift) or more efficient power conversion may permit some

increase but not enough for the megawatts of power normally associated with manned missions.

The NPPS and heavy spaceship development is linked to manned space missions with access to a larger launch lift capability. The HiPER Concept Design is scalable from 100 kWe to 2 MWe. Thus, although manned missions were not considered in DiPoP, many of the capabilities and resources required are directly applicable.

Also, with a 200 kWe NEP-powered spacecraft it would be possible to send the infrastructure required at the destination (say a landing and re-ascent module) ahead separately in slower time. A smaller (than combined infrastructure and human) module for the humans can then be sent separately by fast chemical or nuclear thermal propulsion once it is known that the infrastructure has safely arrived at for the destination.

**Range of Potential Applications**

Identified potential applications are:

- Nuclear electric propulsion.

- Ground Penetrating Radar and High Power Lasers for surveying remote planets,

- Planetary outpost surface Infrastructure including electrical and thermal support,

- Asteroid and comet deflection

- Asteroid Management: surveying and mining

- Removing ‘Dead’ Spacecraft or Debris (a ROSCOSMOS study).

The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n°284081 for the Disruptive Technologies for Power and Propulsion (DiPoP) Study.