Solar-powered space flight

3d. Power required to reach earth orbit ignoring atmospheric drag: Assuming that we launch approximately ‘horizontally’, with capped variable exhaust velocity

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3.10        More plausible, for reasons set out later, would be to place an upper limit on the propellant ejection velocity of circa  = 10,000 ms^-1. The optimal approach is as above until this ejection speed is reached. Thereafter you would again choose  to maximise , so:

Flight metrics for various ratios of  using this approach are in Table 4. In such a trajectory,   is the effective thrust acceleration experienced by the vehicle. This acceleration is relatively modest in relation to that typically applicable to chemical powered rocketry (although much higher than for previously suggested solar-powered vehicles). If  = 10 kW/kg then  starts at , falls to approximately  somewhat after half-way through the flight into orbit, and then increases again to about  when orbital velocity is reached, see Figure 4. Once the propellant ejection speed reaches its upper limit, the optimal ejection angle ceases to be 45° to the vertical and changes (seemingly uniformly through time) until it becomes horizontal when orbit is reached. In practice, it may be preferable to continue to eject propellant in a direction opposite to that of the sun, see later. Given the relatively short flight time involved this would imply an approximately constant ejection angle throughout flight, which if adopted would increase modestly the required power per unit lifted mass, but would also result in a somewhat higher initial orbit.

Table 4. Flight characteristics to reach orbit for a range of , if propellant is ejected at optimal speeds (subject to an upper limit of 10,000 ms^-1) and the vehicle travels horizontally

Figure 4. Plot of vehicle velocity and mass as a function of time, if propellant ejected at optimal speeds (subject to an upper limit of 10,000ms^-1) and angles to the vertical, if  = 10 kW/kg

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