1. Samara State Aerospace University (SSAU) Samara 2015 SELECTION OF DESIGN PARAMETERS AND OPTIMIZATION TRAJECTORY OF MOTION OF ELECTRIC PROPULSION SPACECRAFT WITH LOW THRUST Prof. O.L. Starinova

2. Optimization of low thrust Earth-to-Mars transfer Samara State Aerospace University 2 - All the spacecraft maneuvers (acceleration and transfer to the departure trajectory, heliocentric transfer and the braking maneuver to ascent the orbit of the artificial satellite of Mars) are supposed to be held by the electric propulsion system; - The minimum initial mass of the spacecraft on the parking orbit is used as the optimization criteria. The statement of the design and ballistic optimization of the Earth-Mars transportation mission problem: Figure 1 – The ballistic scheme of Earth – Mars mission

3. The design model of the space tug Initial mass of the space tug can be represented as the sum of the masses of it’s general systems, fuel and payload. (1) In a first approximation, the system masses depend on velocity exhaust of propellant and nominal thrust as follows: - the power plant mass;(2) - the propulsion system mass;(3) - the tank mass, including the propellant system;(4) - the construction mass.(5) Samara State Aerospace University 3

4. N Engine name, the mode of use Exhaust velocity, m/sek Engine efficiency Thrust of one engine, N 1HiPEP mode 1960000,800,670 2HiPEP mode 2827000,780,460 3HiPEP mode 3800000,740,780 4NEXIS DM 1750000,750,475 5ID-500 (Russia)700000,780,780 6NASA-457M mode 1275000,632,200 7PPS-20kML275000,651,050 8NASA-457M mode 2200000,582,400 The characteristics of the high power propulsions Figure 2 – The general view of engines HiPEP, NEXIS DM1, NASA-457M Samara State Aerospace University 4

5. The fuel mass estimated For electric propulsion space tug, the output power and the thrust depend on the phase coordinates (a distance from spacecraft to the Sun, a power decreasing due to the Earth radiation belts, and possible shading of solar arrays, work duration of a nuclear reactor, etc.). To estimate the design parameters of the spacecraft we can find with low accuracy the fuel consumption on segments using the Tsiolkovsky rocket equation:,(6) Samara State Aerospace University 5 where is a reference velocity needed to make a parabolic velocity increase maneuver in the sphere of influence of the Earth, the heliocentric Earth-Mars transfer and the braking maneuver in the sphere of influence of Mars.

6. The algorithm of optimization 1.The required reference velocity is defined for all segments of the trajectory: The parabolic velocity increase and the Earth escape maneuvers: (7) The heliocentric Earth-Mars transfer: (8) The braking maneuver in the sphere of influence of Mars: (9) 2. The type and quantity (n) of the electric rocket engines for the power interplanetary spacecraft unit is chosen. Their parameters are defined according to the table on slide 3: - exhaust velocity of the engine; - thrust of the engine. Samara State Aerospace University 6

7. The algorithm of optimization 3. The total thrust and the power plant mass are calculated by the formulas: (10) (11) 4. The required power of the energy unit and the energy unit mass can be found as follows: (12) (13) 5. The mass of the spacecraft construction is calculated: (14) Samara State Aerospace University 7

8. The algorithm of optimization 6. The Tzyolkovsky numbers are defined for all segments of the trajectory: The increase of the velocity in the sphere of influence of the Earth: (15) The Earth-Mars transfer: (16) The braking maneuver in the sphere of influence of Mars: (17) 7. The first approximation for the spacecraft initial mass without the fuel and tank mass is calculated: (18) Samara State Aerospace University 8

9. The algorithm of optimization 8. The working body mass is calculated for segments in i approximation: The increase of the velocity in the sphere of influence of the Earth: (19) The Earth-Mars transfer: (20) The braking maneuver in the sphere of influence of Mars: (21) To prove the results the total working body mass is calculated: (22) VERY IMPORTANT ! THE RESULTS RECEIVED BY (21) AND (22) SHOULD FULLY AGREE ! Samara State Aerospace University 9

10. The algorithm of optimization 9. The storage system and the fuel-feed system masses are calculated: (23) and the adjusted initial mass of the spacecraft is defined as follows: (24) 10. The initial masses received within the i and i –1 approximations are compared. IF THE ERROR OF THE INITIAL MASS CALCULATION DOES NOT EXCEED 5% THEN IT IS POSSIBLE TO GO TO STEP 11. IF THE ERROR EXCEEDS 5% THEN IT IS NECESSARY TO MAKE ONE MORE APPROXIMATION I=I+1. TO DO THIS ONE SHOULD REPEAT STEPS 8-10 USING THE FORMULAE (19 - 24). Samara State Aerospace University 10

11. Samara State Aerospace University 11 The initial data The initial data are: m 3 /s 2 – gravitational parameter of the Earth, m 3 /s 2 – gravitational parameter of the Sun, m 3 /s 2 – gravitational parameter of Mars, m – average radius of the Earth, m – average radius of Mars, m – altitude of the initial geocentric orbit, m – altitude of the final areocentric orbit, m – average radius of the Earth orbit, m – average radius of the Mars orbit.

12. Conclusion Samara State Aerospace University 12 IN YOUR TRAINING CASE CONTAINS AN EXAMPLE OF THIS CALCULATION. EXAMINE IT CAREFULLY AND REPEAT FOR THEIR VERSION OF THE ORIGINAL DATA. ANALYZE THE REZULTS. Get and analyze the results Repeat the calculation for your option Examine carefully the example