The minimum time control problem of Kepler equation was appointed by Jean-Baptiste Caillau, Joseph Gergaud, and Joseph Noailles, as one of the unsolved problems in the book "Unsolved Problems in Mathematical Systems and Control Theory", edited by Vincent D. Blondel and Alexandre Megretski. The description of the problem can be seen in the figure. The authors indicated that the problem have raised three questions:

. Question 1: Is the optimal control unique?

. Question 2: Are there continuous optimal controls?

. Question 3: Does the product T(Γ) · Γ have a limit when Γ tends to zero?

As the publication of the book is from the year 2004, I think important we indicate if the problem remains open or someone had proposed solution.