Thegeometry of transiting planets as implemented in KOBE. Left: Transit geometry for a single star–planet system. The dashed red arrow represents the initial location of an observer O_i(θ, ϕ), and the solidred arrow gives the rotated location of same observer O_i(f, α) (see text for details). Right: Example of transit shadow bands for a 24-planet system (star and planets are not shown). KOBE-Shadows calculates whether an observer is present inside the fulltransit shadow band of any planet in this system. The innermost planet has P_tra =12% and is detectable by observers marked in blue. The second (P_tra = 6%) and the third innermost planet (P_tra = 2%) are detectable by observers (in orange and green, respectively). The probability to potentially detect any four planets simultaneously via transit for this system is ~ 8%, which is halved for simultaneously detecting any nine planets.