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Hohmann's orbital transfer is explained in theory in terms of instantaneous impulses, but in real life instantaneous impulses do not exist. Finite burn is used instead. How is the burn duration calculated?

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    $\begingroup$ Comment instead of answer as I'm only an armchair orbital mechanic: Since, in reality, an orbital transfer always has to contend with non-circular orbits at different inclinations, nonuniform gravitational fields, external perturbations, and so forth, I assume there's no general closed-form solution. The solution has to be iteratively approximated: start with a guess (which might be the burn magnitude of the theoretical Hohmann), simulate the resulting trajectory, apply a correction based on the destination error, and repeat until you get within a few thousand km of where you want to be. $\endgroup$ – Russell Borogove Aug 21 at 16:28
  • $\begingroup$ The initial guess for the burn may be largely based on the required change in velocity multiplied by the mass of the spacecraft, divided by thrust of the engine, with tweaking of mass based on the fuel used for the burn (in turn calculated from the required change in velocity, and engine thrust and ISP) $\endgroup$ – JCRM Aug 21 at 16:50
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It's technically no longer a proper Hohmann orbital transfer if you add any realism to the problem, but it's still usually called that if it's close.

How is the burn duration calculated?

There may be some approximations available in texts on spaceflight, but these days people simply use a computer simulation.

In addition to burn duration, you may also want to slightly tweak the direction of thrust and exact time of burn initiation as "tweaking parameters".

If the burn is relatively short you can keep a fixed attitude with the thrust parallel to the original orbit at the anticipated midpoint of the burn where you'd normally do the instantaneous impulse (e.g. periapsis or apoapsis), and extend the burn start and stop times equally on either side in order to get the same impulse.

Then you run a simple numerical integrator and propagate the orbit past the destination and see how close you get, and iteratively adjust the details of the burn until you converge on an acceptable solution.

A good example of when even approximations break down and you need a numerical calculation is the low-thrust available from electric propulsion. In this case you may burn for days or months or even years, and it's strictly numerical orbit propagation and iterative convergence based on criteria.

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