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| Fig. 1: A plot comparing the approximate specific impulse of multiple space propulsion methods, including nuclear thermal propulsion (NTP) and nuclear electric propulsion (NEP). [3-5] (Image Source: Z. Granowitz.) |
One of the major limiting factors in space exploration is fuel efficiency. The fuel efficiency of a spacecraft's propulsion system is usually referred to as specific impulse, which describes the thrust provided per unit weight of a fuel. Higher specific impulse propulsion systems enable faster travel to other planets and heavier equipment loads. Nuclear propulsion can provide high specific impulse and may be the key to commonplace interplanetary travel, as shown in Fig. 1.
All space propulsion systems rely on Newton's third law of motion, every force exerted creates an equal and opposite force. [1] The propulsion system takes a small particle and accelerates it out of the spacecraft very quickly. The acceleration of the low-mass particle out of the spacecraft at high speeds generates a force that pushes the high-mass spacecraft forward a small amount. This process is multiplied on a large scale to push a spacecraft to a new orbit or another planet.
There are a few ways that a spacecraft propulsion system can be made more efficient, and these are largely dependent on the type of propulsion system used. The most prominent methods of space propulsion fall into two categories: thermal and electric. For the highest specific impulse thermal propulsion system, a high temperature low molecular weight particle is desired. This desire for a high temperature low molecular weight particle is derived from an understanding of the relationship between specific impulse and the momentum of a particle. Specific impulse, Isp, is defined as the change in momentum of a spacecraft Δp per unit weight of fuel mfuel used with standard acceleration of gravity g:
| Isp | = | Δp mfuel g |
The momentum p is given in terms of the mass m and velocity by
From this, it is clear that to maximize specific impulse, the velocity of a particle must be maximized.
The traditional method used for thermal propulsion is the burning of fuel, also known as chemical propulsion. As the fuel burns, it heats up to temperature T (units of Kelvin) and is accelerated out of a nozzle to provide thrust, a force used to accelerate the spacecraft. If the molecules of the gas being ejected have mass M then their exit velocity is
| v | = | [ | 3 kB T M |
]1/2 |
where kB is the Boltzmann constant. [2] Therefore in thermal propulsion the the specific impulse is increased by increasing the temperature and/or reducing mass M.
Chemical propulsion is prominent due to its tried-and-tested nature and high thrust-to-weight ratio, a ratio that describes the amount of force a system can provide relative to its weight. A high thrust-to-weight ratio is a requirement for achieving planetary orbit and quick orbital transfer. But despite its high thrust-to-weight ratio, the specific impulse of chemical propulsion is limited by the molecular weight M of the combustion products and the combustion temperature T of the fuel to about 450 seconds. [3]
Nuclear thermal propulsion seeks to maintain the high thrust-to-weight ratio of chemical propulsion but provides significantly higher specific impulse using higher particle temperatures and a lower molecular weight gas. The working concept of nuclear thermal propulsion is like that of chemical propulsion, but instead of burning fuel to generate hot particles, a nuclear reactor is used to heat a low molecular weight gas such as hydrogen.
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| Fig. 2: Artistic rendering of a proposed spacecraft with nuclear propulsion. (Courtesy of NASA) |
There are two types of thermal nuclear propulsion concepts: solid-core and non-solid-core. Solid-core thermal nuclear propulsion systems are relatively simple and contain a solid nuclear core. Their maximum temperature is limited by the melting point of the solid core. Solid-core melting temperatures could theoretically reach as high as 3,950°K using 4TaCZrC, but more realistic temperatures are closer to 2,700°K using a uranium carbide-carbon composite fuel. [4] This more realistic maximum temperature results in a specific impulse of about 925 seconds, as theorized by through the NERVA reactor concept. [4] Non-solid-core reactors contain a liquid or gaseous nuclear core. They can achieve much higher core temperatures up to 55,000°K, resulting in a specific impulse up to about 6,500 seconds. [5,6] The use of a solid core is avoided by containing a gaseous nuclear fuel inside the flow of the propellant or with the use of a buffer gas. The propellant is heated by radiation from the gaseous nuclear fuel and the only major temperature limit is the ability of the spacecraft to expel any heat absorbed from the fuel. [3]
While thermal spacecraft propulsion systems are dominant for interplanetary travel, electric propulsion systems can provide much higher specific impulse at the cost of thrust-to-weight ratio. The dominant electric propulsion systems use an electric field to accelerate particles and provide thrust; the quantity and mass of the particles are low, resulting in low thrust, but their velocity is extremely high, resulting in specific impulse as high as 10,000 seconds. [3] While nuclear electric propulsion system have not yet practically achieved a specific impulse of 10,000 seconds, one modern design currently in development is targeting 7,000 seconds. [7] The high specific impulse but low thrust-to-weight ratio of nuclear electric propulsion systems makes them ideal for satellites that only require limited thrust to maintain orbit and can wait months for a transition between orbits. [8] Nuclear reactors can be installed in spacecraft with electric propulsion systems to eliminate the need for batteries and reliance on solar power.
As of today, space nuclear propulsion has never been deployed, but many designs have been proposed. On July 26, 2023, NASA announced that Lockheed Martin was selected to engineer and test a thermal propulsion system to expedite travel to Mars as part of the DRACO program. [9] Fig. 2 provides a rendering of a proposed nuclear propulsion design.
© Zev Granowitz. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute, and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] P. P. Urone and R. Hinrichs, College Physics (OpenStax, 2020).
[2] S. J. Ling, J. Sanny, and W. Moebs, University Physics, Vol. 2 (OpenStax, 2016).
[3] D. L. Black and S. V. Gunn, "Space Nuclear Propulsion," in Encyclopedia of Physical Science and Technology, ed. by R. A. Meyers (Elsevier, 2003), p. 555.
[4] J. S. Clark, "A Comparison of Nuclear Thermal Propulsion Concepts: Results of a Workshop," AIP Conf. Proc. 217, 740 (1991).
[5] R. G. Ragsdale and E. A. Willis Jr., "Gas-Core Rocket Reactors - A New Look," U.S. National Aeronautics and Space Administration, NASA TM X-67823, June 1971.
[6] R. G. Ragsdale, "High Specific Impulse Gas-Core Reactors," U.S. National Aeronautics and Space Administration, NASA TM X-2243, March 1971.
[7] W. H. Loeb et al., "A Realistic Concept of a Manned Mars Mission with Nuclear-Electric Propulsion," Acta Astronaut. 116, 299 (2015).
[8] I. Levchenko, D. M. Goebel and K. Bazaka, "Electric Propulsion of Spacecraft," Physics Today 75, No. 9, 3844 (September 2022).
[9] K. Chang, "NASA Seeks a Nuclear-Powered Rocket to Get to Mars in Half the Time," New York Times, 26 Jul 23.