Going back to basics: accelerating exoplanet transit modelling using Taylor-series expansion of the orbital motion
A significant fraction of an exoplanet transit model evaluation time is spent calculating projected distances between the planet and its host star. This is a relatively fast operation for a circular orbit, but slower for an eccentric one. However, because the planet's position and its time derivatives are constant for any specific point in orbital
Parviainen, H. et al.
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2020