The KOI-94 system is a closely-packed , multi-transiting planetary system discovered by the Kepler space telescope .
It is known as the first system that exhibited a rare event called a “ planet-planet eclipse ( PPE ) , ” in which two planets partially overlap with each other in their double-transit phase .
In this paper , we constrain the parameters of the KOI-94 system with an analysis of the transit timing variations ( TTVs ) .
Such constraints are independent of the radial velocity ( RV ) analysis recently performed by Weiss and coworkers , and valuable in examining the reliability of the parameter estimate using TTVs .
We numerically fit the observed TTVs of KOI-94c , KOI-94d , and KOI-94e for their masses , eccentricities , and longitudes of periastrons , and obtain the best-fit parameters including m _ { c } = 9.4 _ { -2.1 } ^ { +2.4 } M _ { \oplus } , m _ { d } = 52.1 _ { -7.1 } ^ { +6.9 } M _ { \oplus } , m _ { e } = 13.0 _ { -2.1 } ^ { +2.5 } M _ { \oplus } , and e \lesssim 0.1 for all the three planets .
While these values are mostly in agreement with the RV result , the mass of KOI-94d estimated from the TTV is significantly smaller than the RV value m _ { d } = 106 \pm 11 M _ { \oplus } .
In addition , we find that the TTV of the outermost planet KOI-94e is not well reproduced in the current modeling .
We also present analytic modeling of the PPE and derive a simple formula to reconstruct the mutual inclination of the two planets from the observed height , central time , and duration of the brightening caused by the PPE .
Based on this model , the implication of the results of TTV analysis for the time of the next PPE is discussed .