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Interplanetary mission trajectories are frequently likened in popular media to hitting a small target with a dart from vast distances, but in reality, spacecraft don't need absurdly high precision, because they can execute midcourse correction maneuvers if they find they're off target.

How precisely known, in practice, are spacecraft trajectories and planetary positions?

More specifically, I'd like to know:

  • Shortly after a spacecraft performs a translunar or interplanetary injection burn to leave Earth orbit, what is the typical order-of-magnitude uncertainty in the spacecraft's position and velocity?
  • How does this uncertainty evolve over a translunar or interplanetary flight?
  • What is the order-of-magnitude uncertainty in the Moon's position and velocity relative to the Earth? How about other planets?
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  • $\begingroup$ potentially helpful 1 (search for "residuals" or "km"). Also 2, 3 $\endgroup$ – uhoh Sep 17 '18 at 20:13
  • $\begingroup$ Related: How is the trajectory of spacecraft monitored? $\endgroup$ – Russell Borogove Sep 17 '18 at 20:13
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    $\begingroup$ @uhoh Nice, millimeter positioning for the moon, sub-kilometer positioning for the inner planets and tens of km for Jupiter and Saturn! $\endgroup$ – Russell Borogove Sep 17 '18 at 20:22
  • $\begingroup$ some limited insight into errors in the radial component of velocity can be found in references here: space.stackexchange.com/q/23791/12102 and in the answer there as well. $\endgroup$ – uhoh Sep 18 '18 at 5:36
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The injection accuracy of the launch vehicle is typically measured in m/s, as the velocity change required to get the spacecraft exactly on the desired trajectory. This wraps up all the dimensions of the error (the energy, the trajectory plane, your time of arrival, etc.) into one number.

From my recollection, that number is on the order of 1 to 10 m/s. Pretty damned good. The larger end is for solid-motor upper stages that you don't get to cut off when you like. (E.g. Delta II.) You should be able to find this number in the payload planners guide for the respective vehicle.

As for the propagation of the error, just add 1 m/s in random directions to a trajectory and see how far off it gets by the end. The $\Delta V$ to get back on track grows quite a bit over time, so the first trajectory correction maneuver is done about ten days after launch to limit that growth, but still provide some time to become acquainted with the spacecraft before jerking it around.

As for tracking uncertainty, this is represented as an ellipse on the B-plane of the target (e.g. Mars), and the uncertainty in the time of flight, i.e. the exact second the B-plane would be crossed. (Note that the B-plane numbers assume that the target is not there gravitationally.) For the MER maneuvers at launch plus ten days, the orbit determination uncertainties were on the order of 3500 x 1300 km, with a time-of-flight uncertainty of about 1000 seconds. Those are all $3\sigma$. I don't recall when the data cutoff was, but those would have been the result of about eight days of tracking.

We know where the center of Mars is to about 100 m, due to tracking many orbiters there over a long period of time. The Moon we know far better due to laser tracking of retroreflectors left there by Apollo. I don't know the number, but better than a meter.

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  • $\begingroup$ To clarify, that 1-10 m/s figure is error in the injection maneuver, and tracking precision is significantly better? Does the "time to become acquainted with the spacecraft" correspond to refining the tracking data? This is interesting information but I'm more curious about the uncertainty than the error itself; I want to know if ~10ppm clock drift would be lost in the noise of other uncertainties or not. $\endgroup$ – Russell Borogove Sep 18 '18 at 16:38
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    $\begingroup$ Yes, the ten days provides a good arc for tracking. Though I think you could do a good maneuver after maybe three days of tracking. The ten days is really to provide time to checkout the spacecraft, respond to small anomalies, e.g. fault limits set too tight. $\endgroup$ – Mark Adler Sep 18 '18 at 17:03
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    $\begingroup$ The answer to your question depends on the interpretation of "shortly". I took it to mean minutes after injection, in which case your knowledge is your control. If you mean days after, then the uncertainty is far lower. $\endgroup$ – Mark Adler Sep 18 '18 at 17:07

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