Designing Dense Satellite Clusters for Distributed Space-based Datacenters為分散式太空資料中心設計高密度衛星叢集
Circular relative orbits permit denser packing than Suncatcher's elliptical pattern. Three-dimensional packing becomes useful as cluster size grows. A Clos fabric requires satellites dedicated to switching. The analysis separates geometric feasibility from link performance.圓形相對軌道的堆積密度高於 Suncatcher 的橢圓配置，三維配置則在叢集規模增大後取得優勢。Clos 網路需要部分衛星專責交換，因此須把幾何可行性、可用運算量與鏈路性能分開評估。
The main caveat is that links are purely topological: the paper leaves link range, data rate, re-pointing and latency outside its model. Thus, it says which fabrics can be wired with operating speed outside its scope.主要附註是鏈路純屬拓樸：論文將鏈路距離、資料速率、重新指向與延遲排除於模型之外，所以它說明哪些架構接得起來，運作速度則位於範圍之外。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Constellation configuration | Pénot and Balakrishnan model Suncatcher as a packing problem at 650 km and 98° inclination. Satellites fit inside radius R_max with minimum separation R_min. Each must see the Sun and maintain unobstructed links to stable neighbors throughout the orbit. [102, Fig. 2] preprint |
| Constellation configuration | With Suncatcher's own parameters, R_min = 100 m and R_max = 1 km, Google's square grid of 2:1 elliptical relative orbits holds 81 satellites. In comparison, a hexagonal lattice of circular relative orbits in a plane tilted by π/3 holds 367, "more than four times" as many [102, Figs. 4, 6]. |
| Evaluation conditions | Fitted exponents are 1.996 for Suncatcher, 2.00 for optimal planar packing and 2.99 for stacked three-dimensional packing. The three-dimensional design wins when R_max/R_min ≥ 13.5. [102, Tab. 1, Fig. 9] |
| Clos feasibility | An integer-feasibility model maps a VL2-like Clos onto the line-of-sight graph with k = 4–12 ports. Two-layer fabrics are usually infeasible, while L ≥ 3 works across the sweep. Switching satellites replace compute satellites, leaving compute fraction r = k/(k + 4L − 6). [102, Eq. 8, Tab. 4] |
| 傾角與覆蓋 | Pénot 與 Balakrishnan 把 Suncatcher 叢集當成一個堆積問題：在 650 km、傾角 98° 的軌道上，當每顆衛星還必須看得到太陽、並在整圈軌道中與一組穩定的鄰居保持視線暢通的鏈路時，半徑 R_max 的球內、以最小間距 R_min 能放進多少顆衛星[102, Fig. 2]preprint。 |
| 星座配置 | 以 Suncatcher 自己的參數 R_min = 100 m、R_max = 1 km，Google 由 2:1 橢圓相對軌道組成的正方網格容納 81 顆衛星，而在傾斜 π/3 的平面上、由圓形相對軌道組成的六角晶格能容納 367 顆，「超過四倍」[102, Figs. 4, 6]。 |
| 評估條件 | 擬合的尺度律給出 Suncatcher 網格指數 1.996、最佳平面設計 2.00、堆疊三維設計 2.99，因此三維設計在 R_max/R_min ≥ 13.5 時超越平面堆積[102, Tab. 1, Fig. 9]。 |
| Clos 可行性 | 論文接著以整數可行性求解，把具有 k = 4–12 個埠的類 VL2 Clos 網路架構對映到視線鏈路圖上，發現兩層架構通常超出可行條件，而 L ≥ 3 在整個掃描範圍內都可行，代價是交換衛星取代了運算，使運算比例為 r = k/(k + 4L − 6)[102, Eq. 8, Tab. 4]。 |
1. Where this paper sits1. 這篇論文的位置
The Suncatcher paper fixes a link rate and a lattice but leaves the network inside the cluster unspecified. This preprint addresses both satellite arrangement and network wiring for the proposed cluster. The Part III companion is van Berkel's analysis of torus and Clos bisection and latency at 8,000 nodes. That analysis leaves orbital geometry open. In comparison, this paper has the geometry and rates outside the model. Read together, the two bracket what is known about an orbital cluster fabric.Suncatcher 論文確定了鏈路速率與晶格，叢集內部網路則保留為待定，而這篇預印本是唯一處理這個缺口所引出兩個問題的學術著作：衛星該怎麼排列、該怎麼連線。它在第三部分的搭檔是 van Berkel 的分析，後者提供了 8,000 個節點規模下環面與 Clos 架構的對分頻寬與延遲數字，軌道幾何則位於模型範圍之外。本文則處理幾何，速率則位於範圍之外，兩者合讀，正好框出目前對軌道叢集網路架構所知的範圍。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Evaluation conditions | It reads Suncatcher as one point in a design space rather than as a design, contrasting it in the introduction with Starcloud's monolithic structure. The solar argument assumes dawn–dusk panels are "approximately five times as productive as equivalent panels on Earth". Google instead states up to 8×. The fact base records this assumption difference (Part C, item 33). |
| Evaluation conditions | The current version is v2, dated 28 September 2026, with a venue still pending as of October 2026. |
| 評估條件 | 它把 Suncatcher 看成設計空間中的一個具體配置，在引言中把它與 Starcloud 的單體結構對比，並以太陽能論證作為在軌運算的動機，說晨昏軌道的太陽能板「約為地面同等太陽能板的五倍產能」，而 Google 說最多 8 倍，這是一個假設上的差異，事實庫有所記錄（Part C 第 33 項）。 |
| 評估條件 | 目前版本是 2026 年 9 月 28 日的 v2，截至 2026 年 10 月發表場合仍待確認。 |
2. The problem, measured2. 問題，用量測說話
Four constraints hold throughout the orbit. Pairwise separation stays at least R_min to avoid collision. All satellites remain inside radius R_max, limiting maximum separation to 2R_max. Each satellite keeps an unobstructed solar view.
The fourth constraint preserves unobstructed links to stable nearest neighbors. The objective maximizes count for (R_min, R_max). Analysis uses a Hill frame around a reference orbit with a_c = 7,028 km. [102, Fig. 2] Mean relative orbital elements have zero relative semi-major axis. All satellites therefore share the cluster center's period.
Suncatcher loses packing space in three ways. The usable ellipse occupies only part of the full disc. Its 2:1 shape requires 2R_min spacing along one axis. The lattice is square rather than hexagonal [102, Fig. 4] .
問題被表述為一個最佳化，每顆衛星在整圈軌道中都必須滿足四個限制：與其他每顆衛星至少相距 R_min 以免碰撞。留在半徑 R_max 的球內，使最大間距為 2R_max。對太陽有視線暢通的視野。並與一組穩定的最近鄰居保持視線暢通的鏈路。
目標是在給定 (R_min, R_max) 下使衛星數最大[102, Fig. 2]。分析在叢集中心的 Hill 座標系中進行，參考軌道 a_c = 7,028 km，使用平均相對軌道根數，相對半長軸為零，使每顆衛星與中心有相同週期。以這些條件衡量，Suncatcher 的基準在三方面浪費空間：可用區域是內接於球的橢圓，可用面積小於完整圓盤。因為橢圓長是高的兩倍，沿一軸的間距必須是 2R_min。
而且晶格是正方配置，相較六角配置有較大空隙[102, Fig. 4]。
3. The design3. 設計
The planar improvement rests on one property of relative motion. The three-dimensional design stacks inclined grids along-track. Staggering keeps adjacent planes R_min apart. Satellites leaving the R_max sphere at any time are removed.平面設計的改進建立在相對運動的一個性質上。當每顆衛星的相對傾角與相對離心率比值相同、節點也相同時，衛星會共用一個平面。三維設計把這種傾斜網格沿軌堆疊，彼此錯開以讓相鄰平面保持 R_min 間距，並刪去任何時刻離開 R_max 球的衛星。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Inclination and coverage | A shared relative inclination/eccentricity ratio and node place all satellites in a common plane. Choosing i_d = √3·e_d tilts it by π/3. Relative orbits then become circles. [102, Fig. 6] |
| Constellation configuration | Hill–Clohessy–Wiltshire theory gives this general-circular-orbit condition. Cross-track amplitude √3 times radial amplitude turns a 2:1 ellipse into a circle. The cluster rotates rigidly, keeping pairwise distances fixed throughout the orbit. An R_min-spaced hexagonal lattice fills the R_max disc, accommodating 367 satellites versus 81. |
| Inclination and coverage | At R_max/R_min = 10 it reaches 264 at a local inclination of 39°, below the planar 367. This is why the fitted crossover lies at a ratio of 13.5 [102, Figs. 7–9, Tab. 1]. |
| Constellation configuration | Disc-shaped satellites retain full solar exposure below a 50 m radius in Suncatcher. Self-shadowing starts at 19 m in optimal planar packing and 3 m in 3-D packing. [102, Fig. 10, Tab. 5] |
| 評估條件 | 選擇 i_d = √3·e_d 會使該平面傾斜 π/3，並讓每條相對軌道成為圓[102, Fig. 6]。 |
| 評估條件 | 這是 Hill–Clohessy–Wiltshire 理論中的一般圓形軌道條件：橫軌振幅為徑向振幅的 √3 倍，就把 2:1 橢圓變成圓。 |
| 星座配置 | 其結果是叢集像剛體一樣旋轉，每對衛星的距離在整圈軌道中保持固定，於是一個間距 R_min 的六角晶格能放進 R_max 圓盤內，得到 367 顆，對比 81 顆。 |
| 傾角與覆蓋 | 在 R_max/R_min = 10、局部傾角 39° 時它達到 264 顆，低於平面的 367 顆，這就是擬合交叉點落在比值 13.5 的原因[102, Figs. 7–9, Tab. 1]。 |
| 星座配置 | 接著是日照限制了衛星大小：把衛星建模為圓盤時，Suncatcher 網格在半徑 50 m 以下保持完全日照，最佳平面設計在 19 m 開始自我遮蔽，三維設計則在 3 m[102, Fig. 10, Tab. 5]。 |
Network mapping requires each link to remain unobstructed throughout the orbit. Small planar satellites satisfy this by construction relative to R_min. 3-D clusters require numerical verification ("Integer Programming Formulation"). The alternative is a VL2-like Clos of L layers in which each switching satellite has at most k simultaneous links. A Gurobi feasibility problem assigns one virtual Clos node to each satellite. Virtual edges require line of sight between their mapped pairs. [102, Eq. 7]網路的部分問的是哪些架構能放進視線圖：兩顆衛星之間的鏈路只有在整圈軌道中皆維持暢通視線時才算數。當衛星相對 R_min 很小時，平面叢集依構造即滿足此性質，三維叢集則必須數值驗證（"Integer Programming Formulation"）。替代方案是 L 層的類 VL2 Clos，每顆交換衛星最多有 k 條同時鏈路。每顆衛星透過一個僅求可行解的 Gurobi 問題被指派一個虛擬 Clos 節點，唯一的限制是僅能把虛擬邊放在具備視線的衛星對上[102, Eq. 7]。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Constellation configuration | The nearest-neighbor mesh has planar diameter, mean path length and bisection scaling as N^{1/2}. Three-dimensional bisection scales as N^{2/3}. The authors judge mesh scaling poor beyond a few dozen satellites. [102, Tab. 2] |
| Compute and switch roles | ToR satellites compute, while aggregation and intermediate satellites switch. The compute fraction is r(k, L) = k/(k + 4L − 6). Figure A uses k = 8 and L = 3. [102, Eq. 8, Tab. 3] |
| 拓樸擴展性 | 最近鄰網格是基準，在平面中它的直徑、平均路徑長與對分頻寬都隨 N^{1/2} 增長，三維中對分頻寬隨 N^{2/3}，作者判斷它在超過幾十顆衛星後擴展性很差[102, Tab. 2]。 |
| 運算與交換分工 | 因為 ToR 節點承載運算，而匯聚層與中介層是只做交換的衛星，運算比例為 r(k, L) = k/(k + 4L − 6)[102, Eq. 8, Tab. 3]，圖 A 以 k = 8、L = 3 為例呈現。 |
Original figure note原始圖說出處
Drawn for this primer from Pénot & Balakrishnan, arXiv 2605.15335 v2, Table 1, Table 3, Eq. 8 and Figs. 4, 6, 7, 9, 12. Curve values computed from the fitted coefficients.4. Evaluation setup4. 實驗設定
The whole evaluation is analysis and numerical simulation, with bench and flight components outside its scope. Orbits are propagated as Keplerian motion by advancing each satellite's mean anomaly linearly in time from mean relative orbital elements. Thus, the propagation model excludes J₂ and drag. The worst-case solar model uses a circular disc of radius R_sat. Its Sun vector rotates once per orbit, about 8° from the Hill-frame z axis. [102, Eqs. 1–5]
ISL rate lies outside the model. A link is a binary line-of-sight entry that must hold over the whole orbit, with maximum range and link budget outside the model. Latency lies outside the model, only scaling exponents for mesh diameter and mean path length. Failure modeling lies outside the study.
Hardware enters through the disc approximation and port count k.
整個評估都是分析與數值模擬，實驗台與飛行部分皆位於範圍之外。軌道以克卜勒運動傳播，從平均相對軌道根數出發、讓每顆衛星的平近點角隨時間線性前進，所以傳播模型排除 J₂ 與大氣阻力。日照模型是半徑 R_sat 的最壞情況圓盤，太陽向量每圈繞一條偏離 Hill 座標系 z 軸約 8° 的軸旋轉一次[102, Eqs. 1–5]。ISL 速率位於模型範圍之外：一條鏈路就是一個必須在整圈軌道中成立的二元視線項，最大距離與鏈路預算皆位於模型範圍之外。
延遲位於模型範圍之外，只有網格直徑與平均路徑長的尺度指數。拓樸包括平面中的六角最近鄰網格、三維中的 8 最近鄰晶格，以及 L 層的類 VL2 Clos 架構，而胖樹與環面位於比較範圍之外。失效位於模型範圍之外，硬體描述則限於圓盤近似與埠數 k。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Evaluation conditions | Topologies include a planar hexagonal mesh, an 8-nearest-neighbor 3-D lattice and VL2-like L-layer Clos fabrics. Fat-trees and tori lie outside the comparison. |
| Evaluation conditions | The Gurobi integer-feasibility sweep uses R_max = 500–2,000 m in 100 m steps. It uses k = 4–12 in steps of 2. Satellite radius R_sat = 0–15 m varies in 5 m steps. [102, Tab. 4] |
| 評估條件 | 網路掃描範圍為 R_max = 500–2,000 m（每步 100 m）、k = 4–12（每步 2）、R_sat = 0–15 m（每步 5 m），以 Gurobi 作為整數可行性問題求解[102, Tab. 4]。 |
5. What was measured5. 量到了什麼
| Claim宣稱 | Setup and caveat設定與附註 |
|---|---|
| At R_min = 100 m and R_max = 1 km, optimal planar packing holds 367 satellites. Suncatcher holds 81, making the increase "more than four times" [102, Figs. 4, 6].在 R_min = 100 m、R_max = 1 km 下，最佳平面設計 367 顆，對比 Suncatcher 網格 81 顆，「超過四倍」[102, Figs. 4, 6]。 | Claimed maximal for planar packing. Assumes satellites small relative to R_min and Keplerian motion.宣稱為平面堆積的最大值。假設衛星相對 R_min 很小，並採克卜勒運動。 |
| The ratio is x = R_max/R_min. Fits are N = 0.80·x^1.996, 3.63·x^2.00 and 0.27·x^2.99. At x ≥ 13.5, 3-D packing overtakes planar packing. [102, Tab. 1, Fig. 9]擬合 N = 0.80·x^1.996、3.63·x^2.00 與 0.27·x^2.99，x = R_max/R_min。x ≥ 13.5 時三維超越平面[102, Tab. 1, Fig. 9]。 | RMSE 4.65, 8.99 and 16.40. At Suncatcher's x = 10 the planar design still wins, with the 3-D design at 264.RMSE 各自為 4.65、8.99、16.40。在 Suncatcher 的 x = 10 時平面設計仍勝出，三維設計為 264 顆。 |
| Full solar exposure below R_sat = 50 m for the Suncatcher grid. Self-shadowing from 19 m (planar) and 3 m (3-D) [102, Fig. 10, Tab. 5].Suncatcher 網格在 R_sat = 50 m 以下完全日照。平面從 19 m、三維從 3 m 開始自我遮蔽[102, Fig. 10, Tab. 5]。 | Disc model, worst case. Denser packings pay in permissible satellite size.圓盤模型、最壞情況。越密的堆積以可容許的衛星尺寸為代價。 |
| Clos mapping usually infeasible for L ≤ 2 and feasible for L ≥ 3 across the whole sweep, planar and 3-D [102, Tab. 4]. Examples of 37 planar and 30 3-D satellites at k = 10, L = 3 [102, Figs. 13–14].Clos 對映在 L ≤ 2 時通常超出可行條件，L ≥ 3 時在整個掃描範圍內（平面與三維）都可行[102, Tab. 4]。k = 10、L = 3 的例子有平面 37 顆與三維 30 顆[102, Figs. 13–14]。 | Feasibility only, line of sight only. Rate, range, re-pointing and bisection values lie outside its scope.僅為可行性、僅考慮視線。速率、距離、重新指向及對分頻寬數字皆位於範圍之外。 |
| Compute fraction r(k, L) = k/(k + 4L − 6). Mesh bisection ∝ N^{1/2} planar and ∝ N^{2/3} 3-D [102, Eq. 8, Tabs. 2–3].運算比例 r(k, L) = k/(k + 4L − 6)。網格對分頻寬平面 ∝ N^{1/2}、三維 ∝ N^{2/3}[102, Eq. 8, Tabs. 2–3]。 | Exponents only, with absolute values outside its reported results. Agrees in scaling with van Berkel's torus formulas.只有指數，絕對值位於報告範圍之外。在尺度上與 van Berkel 的環面公式一致。 |
| Question問題 | Formula公式 | Result結果 |
|---|---|---|
| How much denser is the planar design?平面設計密多少？ | \( 367 / 81 \) | ≈ 4.5×computed from Figs. 4 and 6由 Figs. 4、6 計算 |
| Where do the planar and 3-D fits cross?平面與三維擬合在哪裡交叉？ | \( 3.63\,x^{2.00} = 0.27\,x^{2.99} \Rightarrow x = (3.63/0.27)^{1/0.99} \) | x ≈ 13.8computed from Table 1 coefficients. The paper reports 13.5 from the data由 Table 1 係數計算。論文依資料報告 13.5 |
| How many layers does the 367-satellite cluster need at k = 12?k = 12 時 367 顆的叢集需要幾層？ | \( (k/2)^{L-1} + (2L-3)(k/2)^{L-2}:\ L{=}3 \to 54,\ L{=}4 \to 396 \) | L = 4computed from Table 3 node capacity and Eq. 9由 Table 3 節點容量與 Eq. 9 計算 |
| What compute fraction does that leave?這留下多少運算比例？ | \( r = \dfrac{12}{12 + 4\cdot4 - 6} \) | ≈ 0.55computed from Eq. 8. About 45% of satellites only switch由 Eq. 8 計算。約 45% 的衛星只做交換 |
6. Limits and open questions6. 限制與待解的問題
- Geometric feasibility with link performance outside its scope. The authors state that link range, data rate, acquisition and re-pointing are outside the model. Thus, a Clos edge between the two farthest satellites counts the same as one between neighbors. The Clos results are upper bounds on topological feasibility rather than designs with a bisection bandwidth.評估聚焦於幾何可行性，鏈路性能則位於範圍之外。作者說明鏈路距離、資料速率、擷取與重新指向都在模型之外，所以最遠兩顆衛星之間的 Clos 邊與相鄰衛星之間的邊算法相同，Clos 的結果是拓樸可行性的上限，對分頻寬則須另行計算。
- Port counts far above today's terminals. The sweep allows k = 4–12 simultaneous links per switching satellite. Current Starlink satellites carry 3 laser terminals, while Suncatcher leaves terminal count unspecified. Hardware limits are therefore likely to make k the binding constraint.埠數遠高於現今的終端。掃描允許每顆交換衛星 k = 4–12 條同時鏈路，而目前的 Starlink 衛星只搭載 3 具雷射終端，Suncatcher 則終端數仍待說明，所以一旦把硬體放進模型，k 很可能就成為束縛條件。
- Keplerian propagation. The propagation model excludes J₂ and drag. Suncatcher uses a 2:1.0037 correction to keep J₂ drift below 3 m/s/yr per km. Its Joule version budgets formation-maintenance ΔV under 30 m/s per year. Circular-lattice and 3-D-stack ΔV estimates are still needed for a propellant comparison. [36, p. 5]克卜勒傳播。傳播模型排除 J₂ 與大氣阻力，雖然 Suncatcher 需要 2:1.0037 的修正才能把 J₂ 漂移壓在每公里每年 3 m/s 以下，其 Joule 版本並把編隊維持的 ΔV 預算定為每年低於 30 m/s[36, p. 5]，而圓形軌道晶格與三維堆疊的 ΔV 皆仍待估計，所以比較兩者推進劑需求時仍須這些估計。
- Switch satellites displace compute. At k = 12 and 367 satellites, about 45% become Clos switches (calculation table). This compute loss should accompany the reported 4.5× packing gain.交換衛星取代運算。Clos 之所以可行，是因為把叢集中相當大的比例變成交換節點，367 顆在 k = 12 時約 45%（計算表），一篇以排進更多運算為目的的論文應該把這一點與 4.5 倍的密度增益放在一起權衡。
- Baselines and comparisons left out. Fat-tree and torus fabrics remain outside the comparison, the mesh is characterized only by exponents. The 3-D line-of-sight property must be checked numerically, so absolute hop count, diameter and bisection remain unreported for any design.遺漏的基準與比較。胖樹與環面架構位於比較範圍之外，網格只以指數描述，三維的視線性質必須數值檢查，所以各設計的絕對跳數、直徑與對分頻寬皆仍待補充。
- What the static geometry does well. Circular relative orbits keep pairwise distances and formation-relative partner directions fixed. This avoids the 2–30 s reacquisition delay emphasized in constellation studies. The 15-second Starlink schedule is irrelevant inside such a formation. The status remains an unreviewed v2 preprint with a venue still pending.固定幾何做得好的地方。因為圓形相對軌道讓每個距離保持固定，平面叢集的鏈路在編隊內維持固定對象方向，避開了現代終端 2–30 秒的擷取延遲，這是星座文獻大多忽略的。Starlink 的 15 秒排程在這種編隊內部位於此編隊的模型範圍之外，而本文目前仍是審查狀態待確認、發表場合仍待確認的 v2 預印本。
7. How it connects7. 與其他內容的關聯
- Section 11.2: the circular relative orbit is the HCW general-circular-orbit case of the 2:1 ellipse introduced there.第 11.2 節：圓形相對軌道是該節介紹的 2:1 橢圓在 HCW 理論中的一般圓形軌道情形。
- Section 11.5 uses Figure 11.2 to compare square packing, hexagonal packing and Clos mapping. It uses this paper's 81, 367 and r(k, L).第 11.5 節：圖 11.2 以本文的 81、367 與 r(k, L) 對比正方晶格、六角晶格與 Clos 對映。
- Section 11.4 and Section 11.6: the topology gap this paper begins to fill and the redesign list it feeds.第 11.4 節與第 11.6 節：本文開始填補的拓樸缺口，以及它所餵入的重新設計清單。
- Section 10.4: Clos feasibility at L ≥ 3 and r = k/(k + 4L − 6) sit beside van Berkel's torus-versus-Clos bisection numbers.第 10.4 節：L ≥ 3 的 Clos 可行性與 r = k/(k + 4L − 6) 與 van Berkel 的環面對 Clos 對分頻寬數字並列。
- Section 13.3: research direction B adds range, rate, terminal count and setup delay to this paper's feasibility model. Section 13.2 asks what collectives run on the resulting fabric.第 13.3 節：研究方向 B 在本文的可行性模型上加入距離、速率、終端數與建鏈延遲。第 13.2 節則問在所得架構上執行什麼集合通訊。
- Suncatcher [36] is the baseline it repacks. van Berkel [101] supplies the rates and latencies it omits. SpaceMoE shows the constellation-scale alternative with sparse, slow links.Suncatcher[36]是它重新堆積的基準。van Berkel[101]提供它省略的速率與延遲。SpaceMoE 展示了以稀疏、慢速鏈路構成的星座規模替代方案。
Key numbers關鍵數字
| Number | 數字 | Meaning (setup) | 意義（設定） |
|---|---|---|---|
| 650 km · 98° · a_c = 7,028 km | Reference orbit of the cluster center ("Methodology") | 叢集中心的參考軌道（"Methodology"） | |
| 81 vs 367 | Suncatcher grid vs optimal planar lattice at R_min = 100 m, R_max = 1 km [102, Figs. 4, 6] | R_min = 100 m、R_max = 1 km 下 Suncatcher 網格對最佳平面晶格[102, Figs. 4, 6] | |
| i_d = √3·e_d · π/3 | Condition for circular relative orbits and the resulting plane tilt | 圓形相對軌道的條件與所得的平面傾角 | |
| 1.996 · 2.00 · 2.99 | Scaling exponents: Suncatcher, optimal planar, 3-D [102, Tab. 1] | 尺度指數：Suncatcher、最佳平面、三維[102, Tab. 1] | |
| ≥ 13.5 | R_max/R_min beyond which 3-D packs more than planar [102, Fig. 9] | 超過此 R_max/R_min 比值時三維比平面排得更多[102, Fig. 9] | |
| k = 4–12 · L ≥ 3 | Ports per switching satellite swept. Clos layers feasible across the sweep [102, Tab. 4] | 掃描的每顆交換衛星埠數。在整個掃描範圍內可行的 Clos 層數[102, Tab. 4] | |
| r = k/(k + 4L − 6) | Fraction of satellites that compute rather than switch [102, Eq. 8] | 負責運算的衛星比例[102, Eq. 8] | |
| N^{1/2} · N^{2/3} | Mesh bisection scaling, planar and 3-D [102, Tab. 2] | 網格對分頻寬的尺度，平面與三維[102, Tab. 2] | |
| none | Link range, data rate, re-pointing, latency, ΔV: outside the model | 鏈路距離、資料速率、重新指向、延遲、ΔV：模型範圍以外 |