VISUALIZING LEO NETWORKS

Since LEO networks are new to us, and likely to most of the networking research community, we found it extremely useful to visualize some aspects of them, and thus build our intuitions on their expected behavior. We discuss some of the visualizations Hypatia provides. While these are best appreciated online in video and interactive Javascript [7], we include here snapshots discussing their utility.

由于低地球轨道（LEO）网络对我们以及大多数网络研究社区来说都是新的，我们发现可视化其某些方面极为有用，从而建立对其预期行为的直观理解。我们讨论了Hypatia提供的一些可视化工具。虽然这些可视化在在线视频和交互式JavaScript中效果最佳，但我们在此包含了一些快照，以讨论它们的实用性。

Satellite trajectories: It is difficult to grasp the role of different satellite trajectory parameters (§2.1) without being able to visually see their outcomes. Visualizing the trajectories of satellites in a constellation also drives intuition about how satellites travel together, the differences between the multiple shells of some constellations, the density of satellites over equatorial and polar regions, etc.

低地球轨道（LEO）网络的卫星轨迹参数的作用难以理解，尤其是在没有可视化结果的情况下。可视化卫星在星座中的轨迹有助于我们直观地理解卫星如何共同移动、某些星座多个轨道层之间的差异、赤道和极地区域的卫星密度等。

Fig. 11 shows snapshots of the first shells of Starlink, Kuiper, and Telesat — S1, K1, and T1 in Table 1. A live 3D version of this figure is available online [7]; it is interactive and allows one to change the camera perspective in order to better see the spatial variations. Telesat covers the polar regions by virtue of the higher inclination of its orbits (98.98°), while Kuiper and Starlink provide denser coverage at lower latitudes. Given that a vast majority of the global population resides at lower latitudes [19], lower inclination allows satellites to spend more time over densely populated areas. These design differences may imply differences in the target markets of the constellation operators.

图11展示了Starlink、Kuiper和Telesat的第一层轨道——分别为S1、K1和T1（见表1）。该图的实时3D版本可在线访问；它是互动式的，允许用户改变摄像机视角，以更好地观察空间变化。由于Telesat的轨道倾角较高（98.98°），它能够覆盖极地区域，而Kuiper和Starlink则在较低纬度提供更密集的覆盖。考虑到全球绝大多数人口居住在较低纬度，较低的倾角使卫星能够在密集人口区域上空停留更长时间。这些设计差异可能暗示了星座运营商目标市场的不同。

Besides coverage, inclination also has other implications for connectivity: Telesat’s almost north-south orbits may offer more direct paths for routes like between Europe and Africa, while the other constellations will do so for east-west routes like between North America and Europe.

除了覆盖范围外，倾角对连接性还有其他影响：Telesat几乎北南向的轨道可能为欧洲和非洲之间的路线提供更直接的路径，而其他星座则在东西向路线（如北美与欧洲之间）上提供类似的优势。

We include satellite trajectory visualizations primarily for completeness: there are a variety of other beautiful visualizations of similar nature online [6, 12, 22, 30, 32]. To the best of our knowledge, no open-source visualization tools are available that focus on network behavior of LEO constellations, aspects of which we describe next.

我们包含卫星轨迹可视化主要是为了完整性：网上有多种其他类似性质的美丽可视化。根据我们所知，目前没有专注于LEO星座网络行为的开源可视化工具，而我们将在接下来的部分中描述这些行为的某些方面。

Ground station view: For any given constellation, and a specified location, Hypatia can show how that constellation appears in the sky to a ground station. This view helps understand the role of the minimum angle of elevation, as well as the inclination of orbits. The visualizations show that close to the horizon, there are many more satellites, but the satellites a GS can communicate with, i.e., above the minimum angle of elevation, are much more limited. From high latitude cities, one can see the limits of low-inclination orbits: few satellites in such orbits are visible, with this visibility often being intermittent. The online version of this visualization [7] provides video of the ground observer’s perspective.

低地球轨道（LEO）网络的地面站视图：对于任何给定的星座和指定位置，Hypatia可以显示该星座在地面站的天空中呈现的样子。这种视图有助于理解最低仰角的作用以及轨道的倾角。可视化显示，靠近地平线时，有更多的卫星可见，但地面站能够与之通信的卫星（即在最低仰角之上的卫星）则要少得多。从高纬度城市可以看到低倾角轨道的局限性：在这种轨道中的卫星可见性很少，并且这种可见性往往是间歇性的。该可视化的在线版本提供了地面观察者视角的视频。

Fig. 12 shows two snapshots of Kuiper’s K1 seen from St. Petersburg. The azimuth along the 𝑥-axis is the panoramic view of the sky (0°is due North, 90°is due East). The 𝑦 -axis is the angle of elevation, 0°for the horizon, and 90°for directly overhead. Satellites in the shaded region are above the horizon, but still at an angle of elevation lower than the minimum needed for connectivity. Over certain periods, a GS at this location can connect to Kuiper, as in Fig. 12(a), while at other times, it looses connectivity, as in Fig. 12(b). This explains the results for Rio de Janeiro to St. Petersburg between 155-165 s in Fig. 3(a), Fig. 4(a), and Fig. 5.

图12展示了从圣彼得堡看到的Kuiper K1的两个快照。 \(x\) 轴上的方位角是天空的全景视图（0°为正北，90°为正东）。\(y\) 轴是仰角，0°表示地平线，90°表示正上方。阴影区域内的卫星在地平线上方，但仍然低于连接所需的最低仰角。在某些时间段内，位于此位置的地面站可以连接到Kuiper，如图12(a)所示，而在其他时间则失去连接，如图12(b)所示。这解释了图3(a)、图4(a)和图5中155到165秒之间从里约热内卢到圣彼得堡的结果。

End-end paths: In §4.1, we discuss RTT variations due to the LEO dynamism. To better understand these, it is useful to visualize the end-end paths at different points in time. Fig. 13 shows an example path on Starlink, Paris-Luanda, which experiences one of the highest RTT variations. The longest (117 ms) and shortest (85 ms) RTT paths during our 200 s simulation are shown. It is typical of such north-south paths to pick an orbit and stick to it as long as possible in order to reduce latency. But in the former case, exiting this orbit (at the north end of the illustrations) towards the destination takes 9 zig-zag hops, while in the latter case only 6 are needed.

在第4.1节中，我们讨论了由于低地球轨道（LEO）网络的动态性导致的往返时间（RTT）变化。为了更好地理解这些变化，可视化不同时间点的端到端路径是非常有用的。图13展示了Starlink网络中巴黎到罗安达的一个示例路径，该路径经历了最高的RTT变化之一。在我们200秒的模拟过程中，最长的RTT为117毫秒，最短的RTT为85毫秒。对于这样的南北向路径，通常会选择一个轨道并尽可能保持在该轨道上，以减少延迟。然而，在前一种情况下，从图示的北端退出该轨道前往目的地需要9次锯齿形跳跃，而在后一种情况下仅需6次。

Link utilization: In §5.4, we discuss how even for a static traffic matrix, LEO dynamics cause links and paths to vary in utilization over time. This is shown for one example path in Fig. 14, for the same experiment across Kuiper described in §5.4. The thicker / warmer-colored ISLs are more congested.

We can also visualize network-wide bottlenecks as shown in Fig. 15. For the particular traffic matrix we use, the ISLs over the Atlantic, connecting the US to Europe and parts of Asia, are highly congested. This indicates that there will be substantial value in using non-shortest path and multi-path routing across such busy regions.

在第5.4节中，我们讨论了即使在静态流量矩阵下，低地球轨道（LEO）网络的动态性也会导致链路和路径的利用率随时间变化。图14展示了同一实验中Kuiper网络的一个示例路径。较粗的/较暖色的星间链路（ISL）表示更拥挤。

我们还可以可视化网络范围内的瓶颈，如图15所示。对于我们使用的特定流量矩阵，连接美国与欧洲及部分亚洲的跨大西洋星间链路高度拥挤。这表明在这些繁忙区域使用非最短路径和多路径路由将具有显著价值。