Obviously, with the international space station you need to do some station keeping when you're falling into the atmosphere. However, I saw the following image showing the Halo orbit that the [Deep Space Climate Observatory](https://en.wikipedia.org/wiki/Deep_Space_Climate_Observatory) is in:

[![Orbit of DSCOVR...][1]][1]

It seems like once it hits its [<s>stable</s> exponentially unstable halo orbit][2], that the speed is between 0.15km/s and 0.05km/s. At what point would there be a red flag? Is there an easily calculable escape velocity for an orbit around a Lagrangian? What would scientists be looking for to alert them that they need to do corrections for such an orbit?


  [1]: https://i.sstatic.net/9mv63.gif
  [2]: https://en.wikipedia.org/wiki/Lissajous_curve