The dwarf planet Haumea is one of the most compelling trans-Neptunian objects to study, hosting two small, dynamically interacting satellites, a family of nearby spectrally unique objects, and a ring system. Haumea itself is extremely oblate due to its 3.9 hr rotation period. Understanding the orbits of Haumea’s satellites, named Hi’iaka and Namaka, requires detailed modeling of both satellite–satellite gravitational interactions and satellite interactions with Haumea’s nonspherical gravitational field (parameterized here as J ₂). Understanding both of these effects allows for a detailed probe of the satellites’ masses and Haumea’s J ₂ and spin pole. Measuring Haumea’s J ₂ provides information about Haumea’s interior, possibly determining the extent of past differentation. In an effort to understand the Haumea system, we have performed detailed non-Keplerian orbit fitting of Haumea’s satellites using a decade of new, ultra-precise observations. Our fits detect Haumea’s J ₂ and spin pole at ≳2.5σ confidence. Degeneracies present in the dynamics prevent us from precisely measuring Haumea’s J ₂ with the current data, but future observations should enable a precise measurement. Our dynamically determined spin pole shows excellent agreement with past results, illustrating the strength of non-Keplerian orbit fitting. We also explore the spin–orbit dynamics of Haumea and its satellites, showing that axial precession of Hi’iaka may be detectable over decadal timescales. Finally, we present an ephemeris of the Haumea system over the coming decade, enabling high-quality observations of Haumea and its satellites for years to come.

中文翻译：

---

超越点质量。三．探测 Haumea 的非球形引力场

矮行星豪美亚是最引人注目的海王星外天体之一，它拥有两颗动态相互作用的小型卫星、附近一系列光谱独特的天体和一个环系统。豪美亚星本身由于其 3.9 小时的自转周期而呈极其扁圆形。要了解 Haumea 卫星（名为 Hi'iaka 和 Namaka）的轨道，需要对卫星间引力相互作用以及卫星与 Haumea 非球形引力场的相互作用进行详细建模（此处参数化为J ₂）。了解这两种效应可以对卫星的质量和 Haumea 的质量进行详细的探测J ₂、旋转极。测量 Haumea 的J _图2提供了有关豪美亚内部的信息，可能确定过去分化的程度。为了了解 Haumea 系统，我们利用十年来的新的超精确观测结果对 Haumea 卫星进行了详细的非开普勒轨道拟合。我们的配合可检测 Haumea 的J ₂且旋转极点≳2.5σ信心。动力学中存在的简并性使我们无法精确测量 HaumeaJ ₂使用当前数据，但未来的观察应该能够实现精确的测量。我们动态确定的自旋极与过去的结果非常吻合，说明了非开普勒轨道拟合的强度。我们还探索了 Haumea 及其卫星的自旋轨道动力学，表明 Hi'iaka 的轴向进动可能在十年的时间尺度上是可检测到的。最后，我们提出了未来十年豪美亚系统的星历表，以便在未来几年对豪美亚及其卫星进行高质量的观测。