N-body simulations of exoplanets and their moons

Abstract: The planet-planet interactions in a many-planet system cannot be analytically calculated. Instead, they have to be investigated by using an N-body simulation. I discuss three questions about the N-body interactions in planetary systems: The first two are on the system 55 Cnc, a system with five known planets around a K-type star. I will first simulate the influence, that the other planets have on the transit timing variations of planet e. The second goal is to understand the behaviour of dust in the environment of 55 Cnc e and to estimate if it can be responsible for the variations in the secondary eclipses which have been observed using visible and infrared photometry with CHEOPS and Spitzer. The third goal is to ascertain if the presence of a moon around a planet of the pulsar PSR B1257+12 could be detectable in the pulse arrival timing of its pulses. I have done simulations on the variation in transit timings of 55 Cnc e to find the influence of the inclination of the orbits of the other planets in the system. The result is that the orbits would have to be at nearly a right angle to have a measurable effect on planet e’s TTVs. Simulations of dust, which planet e might emit, show that the dust can live for several hundred hours. It distributes itself around the star in such a way that it probably does not cause the observed differences in occultation depth. I also simulated the effect a moon around one of the planets of the pulsar PSR B1257+12 would have on the movement of this pulsar. The effect is a measurable signal with an as-yet unidentified hyperperiod. The signal of a moon is different from the signal other sources could produce, such as a fourth planet or the uncertainty of the known planets’ masses. This means that it is feasible that with more sustained observations of PSR B1257+12, exomoons may be detectable in the future.