1. .1 100 0107 .0 (55) When compared to truth data, this equation has an overall worst average accuracy of 3.7 percent based on percent error after excluding the first 100 points. The accuracy decreases as altitude increases further away from 100 km. Therefore, the 1,500-km case (largest altitude) has the worst accuracy of 3.7 percent for the altitude range. The average error for points 200-300 is 5.6 percent and drops below 1.6 percent after the first 300 minutes and stays below this error for the remainder of time. The ΔV inclusion for this equation becomes problematic as discussed in the nextparagraph.
2. The problem setup of varying the length of time the EP system is firing to achieve a specific level of ΔV does not allow for a simple scaling factor as before. Figure 18 shows the distance curves for three values of ΔV, 0.01, 0.05, and 0.1 km/s. Since the acceleration of the thruster is set to 1e-6 km/s2, the only way to vary ΔV is by the amount of time the thruster fires. There is no simple expression that can account for the different levels of ΔV since the relationship is very complex. If we use the same ratio method as the previous Section, it will not yield a constant ratio that is suitable as a scaling factor. Figure 18 demonstrates the behavior of distance versus time. The slope continues to increase as long as the thrusters are firing. Once we reach the desired ΔV, the distance continues to grow at the rate of change at the time of thruster shut-off. Instead of finding an equation that accounts for time, altitude, and ΔVforthisproblemsetup, wesimplyleavetheexpressionsasafunctionoftime and altitude forseveral ΔV values. It would be straightforward to develop more equations using the same method as before and code them into an algorithm to determine an approximate ground trackdifference.
3. When compared to truth data, the average accuracy for points 100-200 is 1.1 percent and drops below 1 percent after that. Excluding the first 100 points, this equation has an average accuracy of 1.1 percent. There is no need account for different values of ΔV here since the thrusting period, hence fuel consumption, remains constant between cases. Using this equation, we can very accurately predict the achievable terrestrialdistancesusingEP.
4. ΔV (km/s) 0.01 0.05 0.1 ΔV (km/s) 0.01 0.05 0.1 ΔV (km/s) 0.047 0.107 0.146 Distance (km) 2365 12105 24196 Distance (km) 1735 6540 7945 Distance (km) 2365 12105 24196