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If you are planning a mission to an outer planet with multiple gravity assists included, do you need to do some burns for corrections, between the slingshots, or the ideal trajectory is already inserted and you have to only burn some fuel at the destination?

Yes, Trajectory Correction Maneuvers (TCMs) are always performed during cruise phases, whether before or after gravity assist flybys. This NASA tutorial serves as a good general reference.

One source of error resulting in an imperfect trajectory (one that would miss its aimpoint at the next destination, whether the ultimate destination or an intermediate gravity-assist destination) is the imperfect results of launch and/or previous TCMs. There's always some "residual", slight deviations of the actual velocity vector resulting from a maneuver from the intended velocity vector. There are many aspects of a maneuver that can lead to those imperfections: burning the engine a bit too long, or not long enough; engine performance is not exactly what was modeled before the burn; spacecraft pointing is not perfect; if timing the burn by accelerometers, the accelerometer data aren't perfect; etc. At JPL we used a rule of thumb to estimate the size of residuals expected after a maneuver that didn't use accelerometers: about 1% of the delta-V.

Another source of error is navigation error: errors in knowing exactly where the spacecraft is, and what its velocity vector is, both direction and magnitude. Such errors can cause the delta-V calculated for an upcoming TCM, again both direction and magnitude, to be slightly off, and that compounds errors in executing the TCM.

The impact of such errors usually grows with time: the longer after the TCM, the farther the spacecraft strays from the intended trajectory. When those errors grow to a threshold level another TCM is called for. Usually even before launch a project will schedule TCMs at several points along a trajectory; if the trajectory turns out to be sufficiently accurate when a scheduled TCM approaches, that TCM is cancelled.

There is yet another potential source of error, especially during the gravity assist flybys: imperfect knowledge of the assisting body's gravity field. Real solar system bodies are never the perfect spheres used in introductory orbital mechanics. They rotate, so they are oblate, the solid bodies have topographical features and mass concentrations or deficits, the giant planets have deep zonal winds that redistribute mass — lots of things can contribute to gravity fields that are rather complex and impossible to measure and characterize exactly. Given such imperfect knowledge of the gravity field, even if the spacecraft hits its inbound aimpoint perfectly, it will miss its outbound aimpoint (probably just a little), which will require a post-flyby TCM or two.

TCMs are performed after a flyby very often, but not always (Tom's detailed answer mentions this in passing). Without a flyby, TCMs are more likely to be skipped. Examples:

• The no-flyby Mars Reconnaissance Orbiter's last three TCM's were skipped.




• The no-flyby OSIRIS-REx skipped its first one.




• Dawn, after a Mars flyby en route to Vesta, skipped its second one,
  and greatly reduced its first to a $Delta V$ of just 60 cm/s.