# Possibilities of Electrical Space Ship Propulsion

## Abstract

A study on feasibility and performance of an electrical propulsion system for interplanetary space ships is presented. A propulsion system is proposed in which a suitable propellant (cesium or rubidium) is vaporized and ionized at incandescent platinum surfaces. Ions and electrons are accelerated and expelled at equal rates; they recombine immediately after leaving the thrust chambers. The power for the accelerating fields is obtained from turbo-electric generators. Heat source is the sun. A thermo-electric pile would be about ten times less efficient than a turbo-electric plant with the same total mass. The acceleration of a space ship equipped with an electrical propulsion system is of the order of 4 × 10^{-5} G. A space ship with a pay load of 50 tons, a total initial mass of 270 tons, and a total flight time of one year would cover a distance of about 183 • 10^{6} km if it started with the velocity zero and traveled through space without gravity fields. Application of the results to a ship travelling from an earth satellite orbit to a mars satellite orbit and back will be presented in a later paper.

## List of Symbols

*Note:*CGS — units are to be used in all formulae of this paper with the following exceptions:

- Voltages (
*U, E, e*) volts

- Currents (
*I, j*) amperes

- Resistances
*(R)* ohms

- Resistivities
*(ϱ)* ohm cm

- Temperatures (
*T*) : degrees Kelvin

*A*_{mir}= area of mirror, cm

^{2}*A*_{con}= area of condenser, cm

^{2}*a*_{i}= initial acceleration of ship, cm sec

^{-2}*a*= specific power of powerplant, erg sec

^{-1}g-^{1}*D*_{τ}= distance covered by ship after the time

*τ*, cm*δ*_{a}= density of thermocouple component

*a*, g cm^{-3}*δ*_{b}= density of thermocouple component

*b*, g cm^{-3}*E*= total emf of thermocouple, volts

*e*_{12}= differential thermo-electric force of thermocouple, volts degr

^{-1}*ε*= electric charge of ion, amp sec

*η*= efficiency of ideal steam engine

*ηc*= efficiency of thermocouple

*F*_{a}= cross-section of thermocouple component

*a*, cm^{2}*F*_{b}= cross-section of thermocouple component

*b*, cm^{2}*F*_{1}= input area of thermocouple, cm

^{2}*F*_{2}= output area of thermocouple, cm

^{2}*G*= earth’s acceleration, cm sec

^{-2}*γ*= efficiency reduction factor for steam engine

*γ*_{c}= efficiency reduction factor for thermocouple

*i*= current density, amp cm

^{-2}*I*= total ion current, amp

*j*= current through thermocouple, amp

*x*_{a}= heat conduction coefficient for thermocouple component

*a*, erg sec^{-1}cm^{-1}degr^{-1}*x*_{b}= heat conduction coefficient for thermocouple component

*b*, erg sec^{-1}cm^{-1}degr^{-1}*L*= total power for acceleration of ions, erg sec

^{-1}*1*= length of thermocouple, cm

*M*_{F}propellant mass, g

*M*_{i}= total mass of ions, g

*M*_{e}= total mass of electrons, g

*M*_{D}= dry mass of ship, g

*M*_{O}= total initial mass of ship, g

*m*_{p}= mass of power plant without condenser and working fluid, g

*m*_{c}= mass of condenser and working fluid, g

*m*_{mir}= mass of mirror, g

*m*_{s}= mass of ion source, g

*m*_{0}= mass of payload, g

*m*_{th}= mass of thermocouple pile, g

*M*_{F}= rate of propellant consumption, g sec

^{-1}*μ*= mass of one ion, g

*v*= efficiency of ideal thermodynamic cycle

*p*_{r}= specific radiation loss, erg sec

^{-1}amp^{-1}*P*_{rad}= radiation loss, erg sec

^{-1}*P*_{12}= Peltier coefficient at hot junction, erg sec

^{-1}amp^{-1}*P*_{21}= Peltier coefficient at cold junction, erg sec

^{-1}amp^{-1}*Q*_{1}= input power, erg sec

^{-1}*Q*_{2}= heat power leaving cold junction of thermocouple, erg sec

^{-1}*Qc*= heat power conducted through thermocouple, erg sec

^{-1}*Q*_{p1}= Peltier heat at hot junction, erg sec

^{-1}*Q*_{p2}= Peltier heat at cold junction, erg sec

^{-1}*q*_{c}= specific mass of condenser and working fluid, g cm-

^{2}*q*_{m}= specific mass of mirror, g sec erg

^{-1}*qp*= specific mass of power plant, g sec erg-

^{1}*q*_{s}= specific mass of ion source, g amp

^{-1}*R*_{a}= Resistance of component

*a*of thermocouple, ohm*R*_{b}= Resistance of component

*b*of thermocouple, ohm*R*_{L}= Resistance of load, ohm

*r*= reflectivity of mirror

*Q*_{a}= resistivity of component

*a*of thermocouple, ohm cm*Q*_{b}= resistivity of component

*b*of thermocouple, ohm cm*S*= solar constant, erg sec

^{-1}cm^{-2}*σ*= STEFAN-BOLTZMANN constant, erg sec

^{-1}cm^{-2}degr-^{4}*T*_{1}= boiler temperature

*or*hot junction temperature, degr K*T*_{2}= condenser temperature

*or*cold junction temperature, degr K*Th*= total thrust developed by thrust chamber, g cm sec

^{-2}*Th*_{i}= thrust developed by ions, g cm sec

^{-2}*Th*_{e}= thrust developed

*b*electrons, g cm sec^{-2}*τ*= total time of propulsion, sec

*U*=*U*_{i}=voltage to accelerate ions, volts

*U*_{e}= voltage to accelerate electrons, volts

*v*_{0}= end velocity of ship, cm sec

^{-1}*V*^{ex}=*vi*= exhaust velocity of ions, cm sec

^{-1}*x*= distance, cm

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## References

- 1.See e. g. H. Oberth, Wege zur Raumschiffahrt. München and Berlin: R. Oldenbourg, 1929.Google Scholar
- H. Preston-Thomas, Bristol (England), Private communication; also: J. Brit. Interplan. Soc.
**11**, 173 (1952).Google Scholar - 2.