Thermal rockets can theoretically give high performance, depending on the fuel used and design specifications, and a great deal of research has gone into a variety of types.
However, aside from the simple cold gas thruster and steam rocket, none have proceeded past the testing stage.
For reaction mass which is not monatomic, some of the thermal energy may be retained as internal energy of the exhaust, and this equation will be modified depending on the degree of dissociation in the exhaust, frozen-flow losses, and other internal losses, but the overall square-root proportionality will remain.
A more detailed equation for the maximum performance of a thermal rocket can be found under de Laval nozzle or in Chung.
Originally "drop-in" replacements were considered for higher performance, but a larger replacement for the S-IVB stage was later studied for missions to Mars and other high-load profiles, known as the S-N. Nuclear thermal translunar or interplanetary space "shuttles" were planned as part of the Space Transportation System to take payloads from a propellant depot in low Earth orbit to the Moon and other planets.
Robert Bussard proposed the Single-Stage-To-Orbit "Aspen" vehicle using a nuclear thermal rocket for propulsion and liquid hydrogen propellant for partial shielding against neutron back scattering in the lower atmosphere.
To date, no nuclear thermal rocket has flown, although the NERVA NRX/EST and NRX/XE were built and tested with flight design components.
The NERVA NRX/XE, judged by SNPO to be the last "technology development" reactor necessary before proceeding to flight prototypes, accumulated over 2 hours of run time, including 28 minutes at full power.
Current (2010) 25,000 pound-thrust reference designs (NERVA-Derivative Rockets, or NDRs) are based on the Pewee, and have specific impulses of 925 seconds.
[citation needed] In the shorter term, solar thermal propulsion has been proposed both for longer-life, lower-cost and more-flexible cryogenic upper stage launch vehicles and for orbiting propellant depots.
Solar thermal propulsion is also a good candidate for use in reusable inter-orbital tugs, as it is a high-efficiency low-thrust system that can be refueled with relative ease.
Relative to lasers, the main advantage of using microwaves is that sources currently cost 1 to 3 orders of magnitude less per Watt.