16.522, Space Propulsion Prof. manuel martinez-sanchez Lecture 2: Mission Analysis for Low Thrust 1. Constant power and thrust Prescribed mission time Starting with a mass Mo, and operating for a time t an electric thruster of jet speed C, such as to accomplish an equivalent(force-free) velocity change of Av the final nass Is if c=constant(consistent with constant power and thrust), then V=CIn M4=M。e and the propellant mass used M=Mol-e c The structural mass is comprised of a part Mso which is independent of power level, plus a part a p proportional to rated power p, where a is the specific mass of the powerplant and thruster system In turn the power can be expressed as the rate of expenditure of jet kinetic energy divided by the propulsive efficiency (3) and since m is also a constant in this case m=M/t Altogether, then Ms (4) The payload mass is M=M Combining the above expressions, 16.522, Space Propulsion ecture 2 Prof. manuel martinez-Sanchez Page 1 of 1916.522, Space Propulsion Lecture 2 Prof. Manuel Martinez-Sanchez Page 1 of 19 16.522, Space Propulsion Prof. Manuel Martinez-Sanchez Lecture 2: Mission Analysis for Low Thrust 1. Constant Power and Thrust: Prescribed Mission Time Starting with a mass M0 , and operating for a time t an electric thruster of jet speed c, such as to accomplish an equivalent (force-free) velocity change of ∆V , the final mass is dv dM M = - c dt dt dM dv = -c M if c=constant (consistent with constant power and thrust), then f M v = c ln M 0 - Vc M =M e f 0 ∆ (1) and the propellant mass used V - c M =M 1-e P 0 ∆ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ (2) The structural mass is comprised of a part Mso which is independent of power level, plus a part α P proportional to rated power P, where α is the specific mass of the powerplant and thruster system. In turn, the power can be expressed as the rate of expenditure of jet kinetic energy, divided by the propulsive efficiency: 1 2 P= mc 2η i (3) and, since m i is also a constant in this case, m=M t. p i Altogether, then, P 2 s so M M =M + c 2 t α η (4) The payload mass is M =M -M L fs . Combining the above expressions