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It would appear that gravity drag has a exact formulation for an instantaneous moment in a rocket launch.

I'm tempted to think that some calculus could get you an exact number for Delta-v of an entire launch to orbit knowing only the starting and ending values. For any given launch, we have know things like:

  • altitude at the launch site
  • altitude of the orbit (assuming circular)
  • the time and position when it reached full orbit

It seems non-obvious whether this information is sufficient to get an expression for the gravity drag or not. Given the same initial/final location and timing, do all approaches to orbits have the same gravity drag?

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It's definitely not--Counterexample:

Mission #1:

The spacecraft is fired from a supergun. At apogee a little booster fires to lift perigee out of the atmosphere. It then deploys solar cells and uses a ion engine to complete the job of orbital insertion.

Mission #2, designed by a lunatic that hates g forces:

It lifts at 1.00001g until it's on the transfer orbit, then relights the same booster to circularize.

Obviously mission #2 suffers an awful lot more gravity drag. (That is, if you could built it at all. I doubt anything less than antimatter has the Δv for the mission.)

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