# A method for classifying orbits near asteroids

## TL;DR

This paper introduces a classification method for orbits near asteroids affected by complex gravitational fields, providing analytical and simulation-based insights for spacecraft orbit design in asteroid exploration.

## Contribution

It presents a novel classification scheme for asteroid orbits based on gravitational perturbations, with analytical derivations and validation through simulations.

## Key findings

- Nine categories of orbit transitions identified.
- Analytical expressions for orbital energy changes derived.
- Simulations confirm analytical predictions for asteroid 216 Kleopatra.

## Abstract

A method for classifying orbits near asteroids under a polyhedral gravitational field is presented, and may serve as a valuable reference for spacecraft orbit design for asteroid exploration. The orbital dynamics near asteroids are very complex. According to the variation in orbit characteristics after being affected by gravitational perturbation during the periapsis passage, orbits near an asteroid can be classified into 9 categories: (1) surroundingto-surrounding, (2) surrounding-to-surface, (3) surroundingto-infinity, (4) infinity-to-infinity, (5) infinity-to-surface, (6) infinity-to-surrounding, (7) surface-to-surface, (8) surfaceto-surrounding, and (9) surface-to- infinity. Assume that the orbital elements are constant near the periapsis, the gravitation potential is expanded into a harmonic series. Then, the influence of the gravitational perturbation on the orbit is studied analytically. The styles of orbits are dependent on the argument of periapsis, the periapsis radius, and the periapsis velocity. Given the argument of periapsis, the orbital energy before and after perturbation can be derived according to the periapsis radius and the periapsis velocity. Simulations have been performed for orbits in the gravitational field of 216 Kleopatra. The numerical results are well consistent with analytic predictions.

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Source: https://tomesphere.com/paper/1704.03981