Abstract: Upstart space companies are actively developing massive constellations of lowflying satellites to provide global Internet service. We examine the problem of designing the intersatellite network for low latency and high capacity. We posit that the high density of these new constellations and the highvelocity nature of such systems render traditional approaches for network design ineffective, motivating new methods specialized for this problem setting.
We propose one such method, explicitly aimed at tackling the high temporal dynamism inherent to lowEarth orbit satellites. We exploit repetitive patterns in the network topology such that we avoid expensive link changes over time, while still providing nearminimal latencies at nearly 2x the throughput of standard past methods. Further, we observe that the geometry of satellite constellations admits more efficient designs, if a small, controlled amount of dynamism in links is permissible. For the leading Starlink constellation, our approach enables an efficiency improvement of 54%. 

A uniform 40x40 (40^{2}) 53° inclined constellation: This is a uniform 2π constellation consisting of 40 orbits each with 40 satellites. The inclination is 53° and operating height is ∼550 km. The (theoretical) maximum ISL length at this operating height is 5,014 km.

SpaceX Starlink Phase 1: Starlink's first phase will have 1,584 satellites, in 24 orbits (53°, 550 km), each with 66 satellites. We evaluate our motifbased approach using both (a) the maximum ISL range, with only the visibility constraint, which is 5,014 km; and (b) the minimum range necessitated by +Grid, 2,006 km. The latter represents worstcase powerlimited ISLs.

Amazon Kuiper Phase 1: : Kuiperâ€™s first phase will be a 34^{2} constellation (51.9°, 630 km). In this case, the maximum and minimum ISL ranges are 5,440 km and 1,761 km respectively.

Traffic matrix: 1,000 most populous cities (2025 population estimates) as ground sites, with citycity traffic volume scaled ∈ [0, 1] in proportion to the population products of the city pairs. (We also examine a different workload based on economic activity in the paper.)

Hardware dependencies: The experiments will run on any general purpose computer. However, more cores would make the motif routines run faster.

Software dependencies: Experiments in this paper were run on Ubuntu 16.04 with Python 3.6.8. The Python packages used are ephem and networkx. The scripts use gnuplot 5.0 or higher (for the pdfcairo/pngcairo terminal). But if you don't have it, you can still get the result files and plot them using other software.

A can connect to any satellites within its view (circle). If A chooses B and C, repeating this pattern across all satellites fully specifies the constellation's ISLs. Then any satellite A′ has the same local view of its connectivity, as shown. We call such local views motifs.
How can we generate a satellite constellation with satellite positions varying over time? Here are the steps:

For the 40^{2} constellation, the above figure shows the topology's average stretch and hopcount for each motif at one arbitrarily chosen system snapshot in time. The metrics are computed using the populationproduct traffic matrix across popular cities. For clarity, we trim the plot to leave out motifs with overly large stretch or hop count. Key takeaways: (a) Different motifs differ widely in their performance; (b) motifs expose a tradeoff between stretch and hop count, with several motifs at the Pareto frontier.
+Grid provides low stretch (1.25), but with very high hop count (10.57). 
Regenerate single motif metric plot from data (Fast). Steps:

The above table shows improvements in the M_{1} (median of sum of average weighted stretch and hop count across citypairs) and Φ_{1} (weighted M_{1} sum) for Starlink, Kuiper, and a 40^{2} constellation. The largest reductions in the metrics are for Starlink, where even with worstcase assumptions about ISL range, improvements of 37% (median M_{1}) and 40% (Φ_{1}) are achievable. This is due to Starlink's structure with fewer orbits and more satellites in each orbit. Fewer orbits imply that satellites in adjacent orbits are farther from each other, necessitating a higher minimum ISL range for +Grid, while a larger number of satellites per orbit imply an increased number of candidates for longer ISLs.

Regenerate data using scripts (Slow). Steps:
