Impossible moons - transit timing effects that cannot be due to exomoon

Transit Timing Effects due to an Exomoon

As the number of known exoplanets continues to grow, the question as to whether such bodies harbour satellite systems has become one of increasing interest. In this paper, we explore the transit timing effects that should be detectable due to an exomoon and predict a new observable. We first consider transit time variation (TTV), where we update the model to include the effects of orbital eccen...

Transit timing effects due to an exomoon II

In our previous paper, we evaluated the transit duration variation (TDV) effect for a co-aligned planet-moon system at an orbital inclination of i = 90◦. Here, we will consider the effect for the more general case of i 6 90◦ and an exomoon inclined from the planet-star plane by Euler rotation angles α, β and γ. We find that the TDV signal has two major components, one due to the velocity variat...

Measurement of Planet Masses with Transit Timing Variations Due to Synodic “chopping” Effects

Gravitational interactions between planets in transiting exoplanetary systems lead to variations in the times of transit that are diagnostic of the planetary masses and the dynamical state of the system. Here we show that synodic “chopping” contributions to these transit timing variations (TTVs) can be used to uniquely measure the masses of planets without full dynamical analyses involving dire...

Aspherical manifolds that cannot be triangulated

Although Kirby and Siebenmann [13] showed that there are manifolds which do not admit PL structures, the possibility remained that all manifolds could be triangulated. In the late seventies Galewski and Stern [10] constructed a closed 5–manifold M 5 so that every n–manifold, with n 5, can be triangulated if and only if M 5 can be triangulated. Moreover, M 5 admits a triangulation if and only if...

Needle Variations that Cannot be Summed