Eccentric Planets & Transit Time Variation

For an extrasolar planet on an eccentric orbit, the orbital velocity is constantly changing, even during a planetary transit. This changing orbital velocity will, in general, cause lightcurve assymetry. The asymmetry causes the mid-transit time to be slightly off-centre from the halfway point between transit ingress and egress. For GJ436b, we estimate that the mid-transit time is shifted by 20 seconds. In the case of a system experiencing secular changes, this difference will lead to a long period transit time variation (L-TTV) signal, under the typical definition of the mid-transit time. In this work, we describe the origins of the effect and evaluate it in the case of GJ436b experiencing hypothetical secular changes. We predict L-TTV could be used to map secular changes in such systems.