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Knowing the performance parameters of a given rocket, is there a methodology to figure out what flightpath the rocket must follow to reach a particular orbit? In other words, is there a direct way to determine the timing of each launch phase and the rate of change for the flight path angle during the gravity turn, -or- does the methodology consists of running a series of trial and error simulations using different parameter values until a satisfactory flight profile is found?

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    $\begingroup$ Space Shuttle Powered Explicit Guidance: ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19740024190.pdf $\endgroup$ – Organic Marble Jun 24 '20 at 19:58
  • $\begingroup$ I've edited the title because the answer to "Is there a method to reach a specific orbit?" is of course "Yes", because if it were "No" then we wouldn't be able to reach a specific orbit! $\endgroup$ – uhoh Jun 28 '20 at 1:05
  • $\begingroup$ for what I was able to find so far, determining the flightpath comes down to an optimization problem, where given a set of parameters (time, altitude, speed, FP angle ...), their initial values, and constraints they must follow (altitude <= orbit, t < t_burnout ...), the optimizer converges to the best parameter values to reach the objective. Based on these results, a sequence of events is determined to reflect this ideal trajectory. When the rocket is launched, the onboard computer follows that sequence and makes adjustments if there are any deviations from the "nominal" trajectory. $\endgroup$ – ChuckM Jul 5 '20 at 3:29

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