Thamiris de Santana

Daphnis is a small moon (around 4 km in radius) of Saturn, orbiting in the middle of the A ring. It was discovered in 2005 by Cassini Spacecraft inside the Keeler Gap. Its existence was inferred due to the waves caused by the gravitational disturbance in the edges of the gap. With all data from Cassini mission combined, it was not possible to find a unique orbit to describe Daphnis’ motion. It seems like the moon was jumping among different orbits.

We performed the astrometry of Daphnis, i.e. measured its location in space, and made corrections on all useful images took during the Cassini Mission from 2005 to 2017. For each image that Daphnis can be seen and also some stars in the background sky, we converted the moon position from the image into spatial coordinates.

To analyse the results, we plot an angular quantity and if the motion is regular, all points should lie in a straight line, what would imply that the moon follows a well behaved circular orbit. In Daphnis case, the behaviour changes twice, indicated that it changed its orbit twice during the mission period. To understand why Daphnis was changing orbits, we did a dynamical study of its motion. Performed numerical simulations allowed us to discovered that two other Saturn moons, Prometheus and Atlas are related with Daphnis, through mean motion resonances. A mean motion resonance is a gravitational mechanism among two or more bodies that can intensify their interaction in a way that sometimes it can result in large effects such as orbits changes. The resonance angles are indicators for this relation. When an angle circulates between 0o and 360o, the resonance is not active. The resonance signature is when the angle oscillates within limited ranges. We found a mixed behaviour between the two cases (the structures like waves in the plots), what suggests that the resonances are relevant and also that Daphnis could be in a chaotic orbit.

Chaos can be explained as a behaviour of a dynamical system that evolves over time and is governed by equations whose solutions are extremely sensitive to the initial conditions. This way, small differences at the beginning will result in extremely different later states.
The Fast Lyapunov Indicator (FLI) is a tool used in this study that allows measuring if a system is chaotic or not. If its grows in a logarithm way, the system is regular. If it grows linearly, it is chaotic. We tested Daphnis orbit with and without the gravitational influence of Prometheus and Atlas. When these satellites are not considered, Daphnis orbit is regular. If we include the other moons, the FLI increases quickly over time. It shows that both satellites are responsible for Daphnis chaotic orbit. Inspired by @astrokatie: ”Daphnis is only 8 km wide, and orbits in a ring gap of 42 km. It uses its tiny gravity to disrupt Saturn’s mighty rings and make waves. Its relation with others moons resulted in an incredible high chaotic orbit. Daphnis doesn’t let being a tiny insignificant speck in a vast uncaring universe stop it. -Be like Daphnis.”

All the arts presented on slides were made by the author. The author thanks the co-authors: Radwan Tajeddine, Maryame El Moutamid, Philip D. Nicholson and Othon C. Winter and the financial support from CAPES.