The space shuttle used a state propagation algorithm to estimate the current state vector when new data weren't yet available from the navigation system (which would come at a rate of only 0.25 or 0.5 Hz).

The state propagation equations integrated the inertial acceleration once to update the velocity vector and twice to update the position vector.

But what about acceleration? Was it updated at all over the course of a navigation cycle, before new data were available? Or was it assumed to be constant?

I know they had equations to update the gravitational acceleration, so it seems strange that they might neglect changes to inertial acceleration by treating it as a constant.

If the inertial acceleration was updated, how was the estimate calculated?


Found a paper describing the super-G state propagation algorithm used in the space shuttle.

And it's clear from it that various acceleration terms were updated and propagated in the minor loop cycles before new data was available from the IMU.

But while those terms include gravity and drag plus a correction for earth's oblateness, they do not seem to include thrust, which would seem the most important term during launch, nor do they seem to capture the change in mass due to fuel consumption (which I can't imagine being less significant in its impact than earth's oblateness).

From the very last page of the linked document:

enter image description here

A_CFi is the gravitational central force term, A_J2i is the correction term for earth's oblateness, and A_Di is the drag term. No thrust term anywhere to be found...

The Super-G algorithm is described in detail in appendix A pp. A3--A5.

Maybe the paper above considered only the case of a space shuttle already in orbit with thrusters off so that no thrust acceleration would be produced? The equations would be accurate then even without the thrust term...

  • $\begingroup$ Why are you asking all of these questions about minutia of an outdated and obsolete technology? To be blunt, these questions are getting a bit old (pun intended). $\endgroup$ Feb 7, 2021 at 11:04
  • $\begingroup$ You know what they say: the devil is in the minutiae. The minutiae get repetitive and old fast. Sorry. $\endgroup$
    – user36480
    Feb 7, 2021 at 20:20

2 Answers 2


Assuming that the state propagation is only the orbital state, then you don't propagate the accelerations of the vehicle. The only accelerations which matter are the attitude accelerations and those are measured from the IMUs.

The accelerations which affect the spacecraft orbital state are only due to external forces, i.e. celestial objects (typically Earth, Moon, and Sun in LEO), atmospheric drag, solar radiation pressure, and thruster activations.

Source: I write and publish high-fidelity orbit propagators for mission design and orbit determination, for fun and for my job.

  • $\begingroup$ Thanks, @ChrisR! I can see how acceleration would be a nonissue for stable orbits. It probably would matter more for orbital transfers. I'm dealing strictly with rocket launches at this point, so none of that fun just yet for me---but I do need to factor in the very significant net acceleration due to thrust, drag, and gravity... though the super-G algorithm they've used on the space shuttle seems to cover gravity and drag but not thrust, which has me a bit perplexed. I'm clearly missing something but I don't know what that something is just yet... $\endgroup$
    – user36480
    Feb 8, 2021 at 6:05
  • $\begingroup$ Super-G was only for orbit IIRC. $\endgroup$ Feb 8, 2021 at 14:00

It's right there in the abstract you linked. Read it closely again, with my emphasis:

Three types of navigation onorbit numerical integrators were evaluated: (1) power integrators with no delta-V incorporation, just coasting (using Taylor series expansion integrators); (2) coasting integrators using the Cowell method of special perturbations; and (3) coasting integrator using the Pines variation of parameter perturbation method. Results show that the super G integrator is a very simple and effective for 2 and 4 second time steps. Since IMU delta-V data can be easily incorporated in the integration scheme, its use as the standard onorbit navigation propagator for the maintenance of the current state was implemented in the onboard navigation software.

It's designed from the start to ignore thrust, because it's only supposed to be used on orbit while coasting. Thrust appears to have been something else's job.


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