We assessed the impact of the uncertainties in the gravity field harmonic coefficients of Mercury on the orbital evolution of the Mercury Planetary Orbiter (MPO), part of the European-Japanese BepiColombo mission. We used in our simulations the most recent estimation of the gravity field model of Mercury determined from radio tracking data of the NASA spacecraft MESSENGER. Thereby we propagated the orbital evolution of MPO by means of plausible gravity fields compatible with the covariance matrix measured gravity field coefficients. We considered two scenarios: 1) the optimistic case, where the formal errors were considered plausible, i.e. scaled by 1; and 2) the conservative case where the formal errors were scaled with a factor of 3. With our simulations we could also demonstrate the importance of the correlation between the errors of the gravity field coefficients for the uncertainty in the trajectory evolution.

As the altitude of the spacecraft above the surface is most important in Mercury's harsh thermal environment, we mostly focused our analysis on the evolution of the periherm altitude. The results of the MPO orbit propagation show a non-linear decrease in the periherm altitude over the simulated timeframe of 1000 days. However, the decrease rate varies significantly among the generated gravity fields. Moreover, the dispersion of the periherm altitude gets larger with increasing scale factor (optimistic to conservative scenario) and over the mission time. While the values of the orbital elements of MPO are still in an acceptable range after the first year, the periherm altitude may fall below a critical value of 200 km after 2 years in orbit about Mercury.

我们评估了水星重力场谐波系数的不确定性对水星行星轨道飞行器（MPO）轨道演变的影响，这是欧洲日本BepiColombo任务的一部分。我们在仿真中使用了根据美国宇航局航天器“信使”的无线电跟踪数据确定的水星重力场模型的最新估计。因此，我们通过与协方差矩阵测得的重力场系数兼容的合理重力场，传播了MPO的轨道演化。我们考虑了两种情况：1）乐观的情况，形式错误被认为是合理的，即以1缩放。2）保守的情况，其中形式错误的比例是3。

由于在水星恶劣的热环境中，航天器的表面高度是最重要的，因此我们主要将分析的重点放在周身高度的演变上。MPO轨道传播的结果表明，在模拟的1000天时间范围内，周缘高度呈非线性下降。但是，减小的速率在所产生的重力场之间变化很大。此外，随着比例因子的增加（对保守情景的乐观），整个任务期间，周围的高度的散布变得更大。虽然第一年后MPO的轨道元素值仍在可接受的范围内，但在绕水星运行2年后，周长高度可能降至200 km的临界值以下。