One major different between high thrust and low thrust trajectories are the thrust profiles for each of their propulsion systems.
For example in an orbit transfer using a solid rocket, the thrust profile is almost fixed and known with a predefined variation (neutral, progressive or regressive) and it is impossible to change the magnitude of the thrust during the burn time.
However, according to the literatures, it is possible to have variable thrust magnitude during the transfer in low thrust propulsion system.
I have read so many papers about low thrust trajectory design and optimization in different journals. Most of them contain profiles of thrust vector and its magnitude. The authors claim that they have found an “optimal” thrust variation that makes a trajectory which transfers the spacecraft from one orbit to another. We can find so many papers in which the transfer trajectory is modeled using Fourier series, Chebyshev polynomials or different kind of mathematical functions.
My question is:
“Are these thrust variations truly achievable in a real space mission?”
“Are low thrust propulsion systems nowadays capable of providing such thrust profiles?”
If yes then:
“How much thrust variation (Newton per second) is allowed in a low thrust trajectory?”
I already know that the limit of thrust magnitude can be up to 1 Newton typically in low thrust transfers. Please note that my question is about “the variation (the rate of increment or reduction)”, not the limit of the thrust profile.
I would appreciate if you answer with references.
Thanks in advance
Hi, I am not a specialist in propulsion but generally, the optimal profile for thrust magnitude is constant and maximum for minimum-time transfers and on-off for minimum-fuel problems. It is possible to modulate the value of the maximum thrust magnitude but only by modifying the specific impulse when possible.
we need at final injection velocity which is called delta v .. or injection velocity require to escape from the orbit as an orbital escape velocity . then we need something called -dell v ..where we have to captor the terrestrial planets ..orbit where we reduce to an velocity and the trajectory of flight must be tangent to the host orbit around that planet so we need to change in velocity one is escape and another is capture
I agree with Dr. Epenoy's answers. Actually, for the bounded-thrust minimum-time transfer problem, the thrust magnitude is always the maximum in the whole period, then we need to optimize the thrust angles. For the bounded-thrust minimum-fuel rendezvous problem, the thrust is on-off constant (Bang-Bang), thus we need to optimize the thrust angles and the switching points.
Richard and Gang are right, if specific impulse is variable. In electric propulsion, available power is constant (at constant distance from the sun, in case of solar power). In minimum fuel problems, it may be convenient to reduce specic impulse in order to get more thrust or viceversa. In general it would be convenient to gradually increase specific impulse. In a very academic problem, one can show that a greater DV can be obtained than Tsiolkowsky or rocket equation (that assumes constant specific impulse); see J. Propulsion & Power, Vol. 16 No.4, 2000, pp. 705-708. For a practical application see J. Guidance, Control & Dynamics, Vol. 27 No. 4, 2004, pp. 678-684,
I can confirm that for a minimum-time transfer the thrust magnitude is constant and maximal. For a minimum-fuel transfer, the thrust magnitude alternates from maximal-thrust and zero-thrust.
Back to your question, I can only speak for electric propulsion, which is usually referred as low-thrust propulsion. In general, the thrust of an electric propulsion thruster can be throttled. Depending on the thruster type (arcjets, RITs, HET etc.), the throttle characteristic is very specific. The operation region varies from type to type. The power and/or the specific impulse shift from the initial operation point to one direction or the other. Every thruster type has its very own specific throttle characteristic. The challenge is modeling this characteristic in your optimization problem to find your optimal steering law.
Another aspect is the benefit-cost ratio. A thrust variation might save a fraction of fuel mass, but the downside is a more complex control of the propulsion system and a much more complex qualification process of such a thrust profile. Sometimes different operation points are given by the suppliers, see link.
http://www.space-propulsion.com/brochures/electric-propulsion/electric-propulsion-thrusters.pdf
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