Figure B.23. Spacecraft velocity increment, acceleration time, and propellant consumed as a function of Isp for a 1001 spacecraft.
To show the potential, and limitations, posed by these powered trajectories, let us consider propulsion solutions for a nominal Earth to Mars mission (Earth to Mars distance, d, is assumed here about 1.5 x 108 km); for the purpose of illustration, distance d chosen is doubled to 3 x 1011.
The matrix of input data is M = 102t and 1031; Isp = 105m/s, 106m/s, and 107 m/s, and thrust power P = 1 GW, 10 GW, and 100 GW. The results are in Figures B.23 and B.24, plotting on log-log scales the propellant mass m, the acceleration time (tacc) and the A V as a function of Isp (in m/s) for the two spacecraft cases, M = 1001 and M = 1,0001. Generally speaking, these results show again the positive effect of Isp on propellant mass consumption, and its negative effect on time to accelerate (trip time) and AV: in fact, at fixed power, increasing thrust comes at the expense of decreasing Isp, so it takes longer and longer to reach smaller and smaller AV.
The curves show the sharp increase in consumed propellant at the lowest Isp. However, with a modest Isp = 105 m/s and for the higher spacecraft mass, the mission is doable and practical using a thrust power P = 1 GW. The M = 1001 case is not doable under the assumptions made, because m is of the same order of M.
At the intermediate Isp = 106 m/s, both spacecraft masses can perform the mission in reasonable times, the best being the case M = 1001 and P = 10 GW. Achieving the highest Isp (107 m/s) poses quite a propulsion challenge; however, once met and successfully overcome, such an Isp enables fast missions, albeit only at the highest power (100 GW). Scaling of open magnetic fusion reactors/thrusters is not established with the same level of confidence as tokamaks, so such power would imply solving a host of problems related to how to design, build, and operate such reactors.
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