A continuation approach for computing periodic orbits around irregular-shaped asteroids. An application to 433 Eros

Bifurcations of Periodic Orbits in the Gravitational Field of Irregular Bodies: Applications to Bennu and Steins

“…Based on the above discussions, we can obtain three critical curves in the parameter (A, B) plane: Furthermore, the distribution of characteristic multipliers in different regions of the parameter plane (A, B) is plotted in Figure 1. It is noteworthy that a similar picture can be seen in Scheeres [29] and Karydis et al [34]. However, the parameters plotted in the figures are different.…”

“…Based on this method, many studies about the three-body problem have been conducted, see, for example, Zagouras and Markellos [31], Papadakis and Zagouras [32], Kalantonis [33], etc. Recently, Karydis et al [34] proposed the shape continuation method to find periodic orbits around irregular small bodies. Furthermore, the bifurcations of periodic orbits during continuation were also studied.…”

Families of periodic orbits around asteroids: From shape symmetry to asymmetry

“…In Karydis et al (2021), which will be referred in the following as 'Paper I', we approach the potential of an irregular body by starting from the symmetric potential of a simplified model (an ellipsoid), where the families of periodic orbits can be easily computed and show particular structures and types. Then, asymmetric terms are gradually introduced in the potential and periodic orbits are continued along this procedure, which is called shape continuation and ends when the 'real' potential of the target asteroid is adequately approximated.…”

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In Karydis et al (2021) we have introduced the method of shape continuation in order to obtain periodic orbits in the complex gravitational field of an irregularly-shaped asteroid starting from a symmetric simple model. What's more, we map the families of periodic orbits of the simple model to families of the real asteroid model.

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