Chapter 1 of 13 · Part I · The physics
第 1 章（共 13 章）· 第一部 · 物理
Orbits and constellations: altitude, period, passes and the constellations actually flying軌道與星座：高度、週期、過頂，以及真正在飛的星座
Use altitude and an elevation mask to calculate orbital period, speed, visibility and pass duration. Read Walker specifications and trace Starlink, Kuiper, OneWeb and Telesat parameters to filings, observations or models.本章說明如何從高度與仰角遮罩計算週期、速度、可見範圍及過頂時間，並解讀 Walker 星座記法。Starlink、Kuiper、OneWeb 與 Telesat 的參數則依申請文件、實際觀測與模型假設區分。
New terms in this chapter (14)本章新名詞（14）
Each term is defined in the text where it first appears. The link jumps there.
每個名詞都在它第一次出現的段落中定義，點連結可跳過去。
- Low Earth orbit (LEO)低地球軌道（LEO） Orbits below about 2,000 km altitude, where broadband constellations fly. 高度約 2,000 km 以下的軌道，寬頻星座都在這裡飛行。
- Orbital period軌道週期 Time for one revolution, fixed by altitude alone for a circular orbit. 繞行一圈所需的時間，圓軌道時只由高度決定。
- Elevation angle仰角 Angle of the satellite above the user's local horizon. The mask is the minimum the operator allows. 衛星高於使用者地平線的角度。遮罩是營運商允許的最低值。
- Slant range斜距 Straight-line distance from user to satellite, which sets the propagation delay. 使用者到衛星的直線距離，決定傳播延遲。
- Pass過頂 The interval during which one satellite stays above the elevation mask. 一顆衛星停留在仰角遮罩之上的時間區間。
- Orbital plane軌道面 The plane containing one orbit, located by its inclination and ascending node. 包含一條軌道的平面，由傾角與升交點定位。
- Inclination傾角 Tilt of the orbital plane to the equator. It bounds the latitudes a satellite reaches. 軌道面相對赤道的傾斜角，決定衛星能到達的最高緯度。
- Shell殼層 A group of planes sharing one altitude and inclination, filed and operated as a unit. 共享同一高度與傾角的一組軌道面，在申請與營運上視為一個單位。
- Walker notationWalker 記法 i: t/p/f describes a symmetric constellation by inclination, total, planes and phasing. 以 i: t/p/f 描述對稱星座的傾角、總數、面數與相位。
- Phase offset相位偏移 The along-track shift between satellites in neighboring planes, 360·f/t degrees. 相鄰軌道面衛星之間沿軌方向的錯位，等於 360·f/t 度。
- Seam接縫 Where the first and last planes of a Star pattern meet moving in opposite directions. Star 型星座中第一與最後一個軌道面相遇、彼此反向運動的地方。
- Nodal precession升交點進動 Slow drift of the ascending node caused by Earth's oblateness (J₂). 地球扁率（J₂）造成的升交點緩慢漂移。
- Sun-synchronous orbit (SSO)太陽同步軌道（SSO） A retrograde orbit whose nodal precession matches the Sun's apparent motion. 升交點進動速率與太陽視運動相同的逆行軌道。
- Eclipse地影 The part of each orbit spent in Earth's shadow. 每一圈軌道中位於地球陰影內的部分。
1.1Why low orbit: altitude, period and speed為什麼選低軌道：高度、週期與速度
Four textbook relations connect altitude to the quantities used throughout satellite networking. These include the CoNEXT title's "27,000 km/hour" and the four-and-a-half-minute passes that require handovers.衛星網路常用的數值可由高度與四條教科書關係式計算，包含 CoNEXT 論文標題中的「每小時 27,000 公里」，以及促使系統換手的四分半鐘過頂時間。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Orbital altitude | This primer defines low Earth orbit (LEO) as altitudes below about 2,000 km. A satellite follows a nearly circular path with radius \(a = R_E + h\). Kepler’s third law gives the period as \(T = 2\pi\sqrt{a^3/\mu}\). The circular speed is \(v = \sqrt{\mu/a}\). |
| Model configuration | The constants are \(\mu = 398{,}600.4418\) km³/s² and \(R_E = 6{,}378.137\) km. Vallado supplies them in Fundamentals of Astrodynamics and Applications, 4th ed. (2013), Appendix D textbook. The model assumes a spherical Earth and circular orbits, as does the networking literature. |
| Orbital period | At 550 km these give a period of 95.65 min and a speed of 7.585 km/s. This is 27,306 km/h. This calculation explains Bhattacherjee and Singla’s title, "Network topology design at 27,000 km/hour". Section 2.2 gives 27,306 km/h at 550 km [1, §2.2]. Bhattacherjee et al. quote "27,306 km/h, 95 min 39 s" [2, §2]. |
| Orbital altitude | These relations also reproduce Handley’s "≈7.3 km/s" and "≈107 minutes" for the earlier 1,150 km Starlink design [3, §3–4]. At that altitude, the formula gives 7.28 km/s and 108.3 min. |
| 軌道高度 | 一顆位於低地球軌道（LEO）（本教材指高度約 2,000 km 以下）的衛星，沿著半徑 \(a = R_E + h\) 的近圓路徑運動，克卜勒第三定律把它的軌道週期定為 \(T = 2\pi\sqrt{a^3/\mu}\)，圓軌道速度則是 \(v = \sqrt{\mu/a}\)。 |
| 模型配置 | 本教材全程採用 Vallado《Fundamentals of Astrodynamics and Applications》第 4 版（2013）附錄 D 的常數 \(\mu = 398{,}600.4418\) km³/s² 與 \(R_E = 6{,}378.137\) km 教科書，並假設球形地球與圓軌道，這也是網路文獻慣用的模型。 |
| 軌道週期 | 在 550 km，這兩式給出 95.65 分鐘的週期與 7.585 km/s 的速度，換算為 27,306 km/h，而這正是 Bhattacherjee 與 Singla 論文標題「Network topology design at 27,000 km/hour」背後的算術，該論文第 2.2 節也給出 550 km 下同樣的 27,306 km/h[1, §2.2]，也是 Bhattacherjee 等人引用的「27,306 km/h、95 分 39 秒」[2, §2]。 |
| 軌道高度 | 同一組關係式也重現了 Handley 對早期 1,150 km Starlink 設計所寫的「約 7.3 km/s」與「約 107 分鐘」[3, §3–4]，因為公式在該高度給出 7.28 km/s 與 108.3 分鐘。 |
Ground-track speed and propagation delay follow from the same relations. The price is a smaller footprint, shorter passes and more satellites for the same coverage. Constellation design must balance these effects.同一組關係式也給出地面軌跡速度與傳播延遲。相較之下地球赤道自轉速度只有 0.465 km/s，所以許多過頂時間估算乾脆忽略它。代價則是較小的覆蓋足跡、較短的過頂，以及要達到相同覆蓋所需的更多衛星，星座設計必須平衡這些因素。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Ground-track motion | The sub-satellite point sweeps across the ground at \(v_g = v\,R_E/a\), which at 550 km is 6.983 km/s. Thus, a satellite crosses a 24 km-wide user cell in a few seconds and the ground-station or user-terminal geometry changes continuously. Earth's own equatorial rotation of 0.465 km/s is small by comparison. This is why many pass-time estimates ignore it. |
| Propagation delay | Directly overhead, one-way propagation delay equals \(h/c\). It is 1.83 ms at 550 km and 4.00 ms at OneWeb’s 1,200 km. Lower altitude reduces the delay floor and free-space path loss, helping explain broadband operators’ choice of low orbits. Chapters 2 and 3 develop this relation. |
| 星下點移動 | 星下點以 \(v_g = v\,R_E/a\) 掠過地面，在 550 km 為 6.983 km/s，因此一顆衛星幾秒內就會橫越一個直徑 24 km 的使用者格，地面站或使用者終端的幾何關係也隨時在變。 |
| 單程傳播延遲 | 到正上方衛星的單程傳播延遲就是 \(h/c\)，在 550 km 為 1.83 ms，在 OneWeb 的 1,200 km 則為 4.00 ms，這是寬頻營運商選擇低軌道的第一個理由：延遲下限會隨高度下降，而第 2 章與第 3 章會說明自由空間路徑損耗也同樣下降。 |
| Question問題 | Calculation算式 | Result結果 |
|---|---|---|
| Orbital period at 550 km550 km 的軌道週期 | \(2\pi\sqrt{(6{,}928.137\ \text{km})^3/\mu}\) | 95.65 mincomputed. μ, R_E from Vallado App. D計算值。μ、R_E 取自 Vallado 附錄 D |
| Orbital speed at 550 km550 km 的軌道速度 | \(\sqrt{\mu/6{,}928.137\ \text{km}}\) | 7.585 km/s = 27,306 km/hcomputed. The CoNEXT 2019 title number計算值。即 CoNEXT 2019 標題中的數字 |
| Ground-track speed at 550 km550 km 的地面軌跡速度 | \(v\,R_E/a = 7.585 \times 6{,}378.137/6{,}928.137\) | 6.983 km/scomputed. Earth rotation ignored計算值。忽略地球自轉 |
| One-way delay to a satellite at zenith到天頂衛星的單程延遲 | \(h/c = 550\ \text{km} / 299{,}792.458\ \text{km/s}\) | 1.83 mscomputed. 4.00 ms at 1,200 km計算值。1,200 km 時為 4.00 ms |
| Where is GEO, for the scale in Figure 1.1?GEO 在哪裡（供圖 1.1 比例用）？ | \(a = (\mu T^2/4\pi^2)^{1/3},\ T = 86{,}164\ \text{s}\) | a = 42,164 km, h = 35,786 kmcomputed from one sidereal day. A 12 h orbit (MEO) sits at 20,184 km由一個恆星日計算而得。12 小時軌道（MEO）在 20,184 km |
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Orbital altitude | The reference values use the same relations, constants and assumptions. Relevant altitudes include 340 km for Starlink Gen2 very-low shells and 1,200 km for OneWeb. The 500–650 km band includes Starlink Gen1, Kuiper and Google’s Suncatcher proposal. |
| Orbital period | Across LEO, the period changes relatively little, from 91 to 109 min. The pass and slant-range columns show stronger changes in visibility, derived in Section 1.2. |
| 軌道高度 | 下表供後續各章引用，各列皆使用上述關係式、常數與假設，涵蓋以下高度：Starlink Gen2 極低殼層的 340 km、Starlink Gen1、Kuiper 與 Google Suncatcher 提案所在的 500–650 km，以及 OneWeb 的 1,200 km。 |
| 軌道週期 | 沿著週期欄往下看，可以發現整個 LEO 範圍內週期變化很小，只從 91 分鐘到 109 分鐘，而沿著第 1.2 節推導的過頂與斜距欄往下看，則會發現可見性的變化大得多。 |
| h (km) | T (min) | v (km/s) | slant @25° (km)25° 斜距 (km) | 1-way delay @25° (ms)25° 單程延遲 (ms) | max pass @25° (min)25° 最長過頂 (min) | λ @25° | eclipse fraction, β = 0地影比例，β = 0 | SSO inclinationSSO 傾角 |
|---|---|---|---|---|---|---|---|---|
| 340 | 91.33 | 7.703 | 727.7 | 2.43 | 2.86 | 5.63° | 0.398 (36.4 min) | — |
| 500 | 94.62 | 7.613 | 1,031.9 | 3.44 | 4.11 | 7.82° | 0.378 (35.8 min) | 97.40° |
| 550 | 95.65 | 7.585 | 1,123.4 | 3.75 | 4.49 | 8.45° | 0.372 (35.6 min) | 97.59° |
| 570 | 96.06 | 7.574 | 1,159.6 | 3.87 | 4.64 | 8.70° | 0.370 | — |
| 600 | 96.69 | 7.558 | 1,213.4 | 4.05 | 4.87 | 9.07° | 0.367 (35.5 min) | 97.79° |
| 650 | 97.73 | 7.531 | 1,302.0 | 4.34 | 5.25 | 9.67° | 0.362 (35.4 min) | 97.99° |
| 1,200 | 109.42 | 7.252 | 2,204.8 | 7.35 | 9.29 | 15.29° | 0.318 (34.8 min) | 100.42° |
All values computed from the four relations of this chapter with Vallado's constants, spherical Earth and circular orbits. The pass column is the zenith pass for a non-rotating Earth. Maral & Bousquet, Satellite Communications Systems, Ch. 2 textbook.所有數值皆以本章四條關係式與 Vallado 常數計算，假設球形地球與圓軌道。過頂欄為地球自轉速率取零的模型下的天頂過頂時間。Maral 與 Bousquet《Satellite Communications Systems》第 2 章 教科書。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Evaluation conditions | Sources of the formulas: Vallado 2013, Ch. 2, 5, 9 and 11. |
| 評估條件 | 公式來源：Vallado 2013 第 2、5、9、11 章。 |
Original figure note原始圖說出處
Drawn for this primer. Radii and periods computed from Kepler's law with Vallado 2013 App. D constants.Stop and think停下來想一想
Slide from 550 km to 1,200 km. The period grows by only 14%, yet the delay at 25° elevation nearly doubles. Which relation makes delay more sensitive to altitude than orbital period? Explain its implications for an operator lowering a shell to reduce latency.
把高度從 550 km 拉到 1,200 km。週期只增加 14%，但 25° 仰角的延遲幾乎翻倍。是哪一條關係式讓延遲對高度的敏感度遠高於週期？這對想藉由降低殼層來換取延遲的營運商意味著什麼？
1.2Seeing a satellite: elevation mask, slant range, coverage and the pass看見一顆衛星：仰角遮罩、斜距、覆蓋與過頂
Recall
回顧
Section 1.1 gave the period and the mean motion \(n = 2\pi/T\). This section adds the minimum angle for terminal communication. Together, they determine visibility.
第 1.1 節給出了週期與平均運動 \(n = 2\pi/T\)。本節加上終端建立通訊所需的最低角度，再由這兩項條件推導可見範圍。
A user terminal measures a satellite by its elevation angle ε above the local horizon. Each operator sets a minimum elevation, called the mask, for link attempts. Near the horizon, signals cross more atmosphere, antenna gain falls and buildings or trees can block the path. The mask and the triangle between Earth's center, the user and the satellite determine three quantities [4, Ch. 2] [5, Ch. 11] .
The coverage circle’s Earth-central half-angle is \(\lambda(\varepsilon) = \arccos[(R_E/a)\cos\varepsilon] - \varepsilon\). slant range means the straight-line user–satellite distance: \(d(\varepsilon) = R_E[\sqrt{(a/R_E)^2 - \cos^2\varepsilon} - \sin\varepsilon]\). The satellite’s nadir angle is \(\eta(\varepsilon) = \arcsin[(R_E/a)\cos\varepsilon]\). These three angles sum to 90°. Delay depends on the serving satellite’s sky position.
A scheduler switching between zenith and 25° elevation can double propagation delay within one minute.
使用者終端用衛星高於當地地平線的仰角 ε 描述衛星的位置。營運商設定的最低通訊仰角稱為遮罩。接近地平線時，訊號穿越的大氣較多、天線增益下降，建築物與樹木也可能遮擋路徑。給定遮罩後，由地心、使用者與衛星構成的球面三角形可求得三個量[4, Ch. 2][5, Ch. 11]。覆蓋圓的地心半角是 \(\lambda(\varepsilon) = \arccos[(R_E/a)\cos\varepsilon] - \varepsilon\)，斜距也就是使用者到衛星的直線距離是 \(d(\varepsilon) = R_E[\sqrt{(a/R_E)^2 - \cos^2\varepsilon} - \sin\varepsilon]\)，衛星端的天底角則是 \(\eta(\varepsilon) = \arcsin[(R_E/a)\cos\varepsilon]\)，三個角相加為 90°。因此延遲取決於服務衛星恰好在天空中的哪個位置，當排程器把終端在天頂衛星與 25° 衛星之間切換時，傳播延遲會在一分鐘之內變動達兩倍。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Slant range | At 550 km and Starlink’s declared 25° mask [6, §2.2], λ = 8.45° and slant range is 1,123 km. One-way delay is therefore 3.75 ms. |
| Nadir angle | , a nadir angle of 56.6° |
| Ground coverage radius | , and a ground coverage radius \(R_E\lambda\) of 941 km. |
| Horizon range | At the horizon the slant range stretches to 2,705 km |
| 40° elevation mask | , and at a 40° mask it shrinks to 812 km and 2.71 ms. |
| 斜距 | 在 550 km 與 25° 遮罩下（這是 Starlink 宣告的值）[6, §2.2]，可得 λ = 8.45°、斜距 1,123 km、因此單程延遲 3.75 ms、天底角 56.6°，以及 \(R_E\lambda\) = 941 km 的地面覆蓋半徑。 |
| 斜距 | 在地平線上斜距拉長到 2,705 km，而在 40° 遮罩下則縮到 812 km 與 2.71 ms。 |
A pass is the interval during which a satellite stays above the mask. Its maximum over a stationary Earth occurs through the user’s zenith: \(t_{\max} = 2\lambda/n\).過頂是一顆衛星停留在遮罩之上的時間區間，其可能的最長值，對應於一顆在地球自轉速率取零的模型上正好穿過使用者天頂的衛星，是 \(t_{\max} = 2\lambda/n\)。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Inclination and coverage | At 550 km and 25°, the maximum pass is 4.49 min. Including Earth’s rotation at 53° inclination gives 4.67 min through \(\omega_{rel} = \sqrt{n^2 - 2n\omega_E\cos i + \omega_E^2}\). Off-zenith passes are shorter. |
| Orbital altitude | Raising the mask to 40° reduces the maximum pass to 2.74 min. Lowering altitude to 340 km gives 2.86 min. At OneWeb’s 1,200 km, it reaches 9.29 min. |
| Handover and scheduling | These minutes are the budget within which every handover, every route recomputation and every transport-layer adaptation in Chapters 3, 5 and 6 must operate. Hypatia therefore reports path changes "multiple times per minute" [6, §4]. Starlink reassigns terminals every 15 s, several times within a pass ( Section 3.5 ). |
| 過頂時長 | 在 550 km 與 25° 下這是 4.49 分鐘，若透過相對角速率 \(\omega_{rel} = \sqrt{n^2 - 2n\omega_E\cos i + \omega_E^2}\) 把 53° 傾角下的地球自轉納入則是 4.67 分鐘，偏離天頂的過頂時間則更短。 |
| 軌道高度 | 把遮罩提高到 40° 會把最大值砍到 2.74 分鐘，把高度降到 340 km 則砍到 2.86 分鐘，只有在 OneWeb 的 1,200 km 才能達到 9.29 分鐘。 |
| 換手與排程 | 這幾分鐘就是第 3、5、6 章裡每一次換手、每一次路由重算與每一次傳輸層調適必須在其中完成的預算，這也是為什麼 Hypatia 回報路徑「每分鐘變動多次」[6, §4]，以及 Starlink 終端重新指派週期縮短至每 15 秒的原因（第 3.5 節）。 |
Operators disagree on the mask, and the disagreement propagates into every comparison. Hypatia models Kuiper at 30°, which slightly overstates its pass length. The spherical-Earth formula gives 1,412 km for the same inputs. The recorded difference remains an open question.各營運商對遮罩的取值各有差異，而這種差異會滲入每一項比較。Hypatia 以 30° 建模 Kuiper，略微高估了它的過頂長度。球形地球公式對相同輸入給出 1,412 km，記錄中的這項差距仍待釐清。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Evaluation conditions | The November 2018 modification lowered Starlink’s mask from 40° to 25° [7, §2]. The 2021 FCC order permits user terminals and gateways down to 25°, and polar gateways down to 5° [8]. |
| Evaluation conditions | Kuiper supports user beams above 35°. Its filing expresses this as a 48.2° "satellite angle", matching the nadir formula at 630 km. Its gateways work down to 20° [9, Tab. 7] . |
| Evaluation conditions | Telesat filed a 10° minimum [10, p. 15]. Hypatia adopts it and describes feasibility as "is unclear". OneWeb guarantees visibility above 55° and permits pointing above 25° [11, pp. 11–12]. |
| Slant range | The 55° figure explains why del Portillo et al. list OneWeb's slant path as only 1,504 km despite its 1,200 km altitude [12, Tab. 5]. |
| 評估條件 | Starlink 在 2018 年 11 月的修改申請中把遮罩從 40° 降到 25°[7, §2]，2021 年的 FCC 命令允許使用者終端與閘道低至 25°、極區閘道低至 5°[8]。 |
| 星座配置 | Amazon 的 Kuiper 申請文件只在 35° 以上支援 |
| 使用者仰角 | 使用者波束，並把它表示為 48.2° 的「衛星角」，天底角公式在 630 km 正好重現這個值，而閘道則可低至 20°[9, Tab. 7]。 |
| 評估條件 | Telesat 申請 10° 的最低仰角[10, p. 15]，Hypatia 採用此值並將其可行性標為「待確認」，而 OneWeb 保證 55° 以上的可見性、允許 25° 以上的波束指向[11]。 |
| 斜距 | 這個 55° 解釋了為什麼 del Portillo 等人把 OneWeb 的斜距只列為 1,504 km，儘管它的高度有 1,200 km[12, Tab. 5]。 |
How many satellites a terminal can see decides how much choice a scheduler has. The two counts therefore describe separate geometries. Panel 1.2 compares each with the uniform estimate.終端能看見多少顆衛星，決定了排程器有多少選擇。因此兩個數字各自對應一套幾何條件，面板 1.2 則顯示均勻估計與兩者的差距。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Constellation configuration | A first estimate spreads N satellites uniformly over a sphere. The expected count above the mask equals the coverage-cap fraction: \(N(1-\cos\lambda)/2\). At 550 km and 25°, the fraction is 0.54%. The authorized 4,408-satellite Gen1 constellation therefore gives about 24 visible satellites. |
| Visibility and selection | The real sky is more crowded than this at mid-latitudes. A 53° shell concentrates satellites near its inclination latitude and has fewer near the equator. Tanveer et al. measured 35–44 visible satellites per 15-second slot at 25° in Western Europe and the United States [13, §3–6]. The scheduler chose satellites a median 22.9° higher than rejected candidates. Satellites at 45–90° accounted for 30% of candidates and 80% of selections (§5.1, Fig. 4). |
| Constellation configuration | Handley's "approximately 30 satellites overhead" was computed for the proposed 1,150 km design, which remained a proposal with a 40° nadir-angle rule [3, §2]. |
| 評估條件 | 最初步的估計把星座視為均勻分布在一個球面上，此時遮罩之上的期望數量是總數 N 乘以覆蓋帽占球面的比例 \(N(1-\cos\lambda)/2\)，在 550 km 與 25° 下為 N 的 0.54%，對已核准的 4,408 顆 Gen1 來說大約是 24 顆。 |
| 星座配置 | 真實的天空在中緯度比這更擁擠，因為 53° 殼層會把衛星集中在接近其傾角的緯度附近、在赤道附近則變稀疏，而唯一的實測數字證實了這個誤差的方向：Tanveer 等人從西歐與美國的終端數得每個 15 秒時槽內在 25° 之上可見 35–44 顆 Starlink 衛星[13, §3–6]，而他們觀察到的排程器所選的衛星比被略過的衛星仰角中位數高 22.9°，45–90° 的衛星占候選者 30% 卻占選擇結果 80%（§5.1，Fig. 4）。 |
| 星座配置 | Handley 的「大約 30 顆衛星在頭頂」是針對停留在提案階段的 1,150 km 設計、以 40° 天底角規則算出的[3, §2]。 |
| Question問題 | Calculation算式 | Result結果 |
|---|---|---|
| Coverage half-angle at 550 km, 25° mask550 km、25° 遮罩的覆蓋半角 | \(\arccos[(6{,}378.137/6{,}928.137)\cos 25^\circ] - 25^\circ\) | 8.45°computed. Ground radius R_E·λ = 941 km計算值。地面半徑 R_E·λ = 941 km |
| Slant range at 25°25° 的斜距 | \(R_E[\sqrt{(a/R_E)^2 - \cos^2 25^\circ} - \sin 25^\circ]\) | 1,123 km → 3.75 mscomputed. 812 km / 2.71 ms at 40°. 2,705 km at the horizon計算值。40° 時 812 km / 2.71 ms。地平線 2,705 km |
| Maximum zenith pass at 25°25° 的最長天頂過頂 | \(2\lambda/n = 2 \times 0.1475\ \text{rad} \times 95.65\ \text{min}/2\pi\) | 4.49 mincomputed. 4.67 min with Earth rotation at i = 53°計算值。納入 53° 傾角下的地球自轉為 4.67 分鐘 |
| Kuiper's 35° mask as a satellite angle at 630 kmKuiper 的 35° 遮罩換成 630 km 的衛星角 | \(\arcsin[(6{,}378.137/7{,}008.137)\cos 35^\circ]\) | 48.2°computed. Matches Kuiper Technical Appendix Table 7. Maximum zenith pass 3.67 min計算值。與 Kuiper 技術附錄 Table 7 相符。最長天頂過頂 3.67 分鐘 |
| Satellites in view, uniform-sphere estimate, N = 4,408可見衛星數，均勻球面估計，N = 4,408 | \(N(1-\cos 8.45^\circ)/2\) | ≈ 24computed. Tanveer et al. measured 35–44 at mid-latitudes計算值。Tanveer 等人在中緯度實測為 35–44 |
Original figure note原始圖說出處
Drawn for this primer from the spherical-Earth geometry of Maral & Bousquet Ch. 2 and Vallado Ch. 11. Values computed with Vallado App. D constants.Stop and think停下來想一想
OneWeb is twice as high yet its longest pass is barely longer.OneWeb 高度是兩倍，但最長過頂只略長一點。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Evaluation conditions | Set 630 km and 35°, Kuiper's filed geometry, then 1,200 km and 55°, OneWeb's guaranteed geometry. |
| Constellation configuration | Trace how the 55° mask changes λ(ε). Identify OneWeb’s benefit and the extra satellite count needed to obtain similar service at 25°. |
| 評估條件 | 先設定 630 km 與 35°（Kuiper 的申請幾何），再設定 1,200 km 與 55°（OneWeb 保證的幾何）。 |
| 星座配置 | 追蹤一下 55° 遮罩吃掉了 λ(ε) 裡的哪一項，並想想 OneWeb 用高遮罩換到了什麼，而那是 25° 的營運商必須用更多衛星才能買到的。 |
1.3Shells, planes and Walker patterns殼層、軌道面與 Walker 星座
One satellite gives a few minutes of service per pass, so coverage comes from arrangement. An orbital plane contains a circular orbit. Inclination i measures its tilt from the equator. RAAN locates the ascending node, where the orbit crosses the equator northward. Inclination i bounds the latitudes a satellite reaches. Two families exist.一顆衛星每次過頂只能提供幾分鐘的服務，所以覆蓋來自於排列。軌道面是包含一條圓軌道的平面，由它的傾角 i（相對赤道的傾斜）以及升交點經度（RAAN，軌道向北穿越赤道的那一點）來定位。傾角 i 決定衛星可到達的緯度範圍。它分成兩個家族。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Evaluation conditions | Starlink therefore uses its 53° shells for lower latitudes and its 97.6° shell for polar coverage. |
| Plane configuration | A shell groups planes with a shared altitude and inclination. It is the FCC authorization unit and the unit used in simulations. Walker notation i: t/p/f spreads t satellites evenly across p equally spaced planes. The integer f ranges from 0 to p−1 and sets a phase offset of 360·f/t degrees. This is the along-track shift between corresponding satellites in neighboring planes (Walker, J. Brit. Interplanetary Soc. 37, 1984. Ballard, IEEE Trans. AES 16(5), 1980 textbook). |
| Plane configuration | Walker Delta spreads p ascending nodes across 360° of RAAN, keeping neighboring planes co-rotating. Starlink’s 53° and 43° shells, all Kuiper shells and their Hypatia models use this pattern. Hypatia describes satellites as "uniformly spaced out" within orbits, with orbits "uniformly spread across the Equator" [6, §3.1]. |
| Plane configuration | Walker Star spreads near-polar planes across about 180° of RAAN. Iridium, OneWeb Gen1, Telesat’s polar shell and Starlink’s 97.6° shell use this pattern. Satellites move northward on one half of Earth and southward on the other. The first and last planes meet at a seam where neighbors counter-rotate at twice orbital speed. Links across that seam last seconds, while other links can last an orbit. |
| 評估條件 | Starlink 的 53° 殼層服務較低緯度，97.6° 殼層則提供極區覆蓋。 |
| 軌道高度 | 營運商把共享同一高度與傾角的軌道面歸為一個殼層，這是 FCC 核准的單位、也是論文模擬的單位，而大多數殼層都用 Walker 記法 i: t/p/f 來描述，其中 t 顆衛星均勻分布在 p 個等距的軌道面上，而介於 0 到 p−1 之間的整數 f 設定相位偏移，也就是相鄰軌道面中對應衛星沿軌方向的錯位，等於 360·f/t 度[14][15]。 |
| 軌道面配置 | 在 Walker Delta 中，p 個軌道面的升交點散布在完整的 360° RAAN 上，所以相鄰軌道面永遠同向運行，Starlink 的每個 53° 與 43° 殼層、Kuiper 的每個殼層，以及 Hypatia 對它們全部的建模都屬於這一類，Hypatia 明言衛星在軌道內「均勻間隔」且軌道「均勻分布在赤道上」[6, §3.1]。 |
| 軌道面配置 | 在 Walker Star 中，也就是 Iridium、OneWeb Gen1、Telesat 極軌殼層與 Starlink 97.6° 殼層採用的型式，近極軌的軌道面只散布在約 180° 的 RAAN 上，衛星在地球的一半向北飛、另一半向南飛，而在第一與最後一個軌道面相遇之處有一道接縫，兩側的鄰居以兩倍軌道速度的相對速度反向運動，使得任何跨越它的星間鏈路維持時間縮短為數秒，與其他位置的一整圈形成差距。 |
The phase offset changes the geometry of inter-plane links.相位偏移會改變跨面鏈路的幾何關係。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Plane configuration | Handley found optimal f values of 5 for the 32-plane 2016 Phase 1 and 17 for the 32-plane 53.8° shell. Ascending and descending satellites cross within an inclined Delta pattern. His fifth laser bridges "the NE-bound and SE-bound meshes" and must "rapidly switch to a new satellite" [3, §2–3]. This resembles the polar seam and explains inter-plane link fragility in Section 2.5. |
| Constellation configuration | Public ephemerides reveal the flown geometry. Ali et al. describe Shell 1 as Walker Delta 53°: 1296/72/45, with an inter-plane phase step about 12.5°. Regular satellites have 20° along-track spacing. This is 18 per plane rather than the 22 the FCC authorized [16, §3.2.2–3.2.4, Tab. 2] . |
| Constellation configuration | The spacing of satellites within a plane also sets the intra-plane ISL length. This is why Chapter 2 cares whether a 1,584-satellite shell is cut into 24 planes of 66 or 72 planes of 22. |
| 軌道面配置 | Handley 算出 2016 年 Starlink 第一期的最佳值是 32 個軌道面中取 f = 5，53.8° 殼層則是 32 中取 17，他並觀察到在傾斜的 Delta 星座中上升段與下降段的衛星會彼此交錯，因此他的第五具雷射，也就是銜接「東北向與東南向網格」的那一具，必須「快速切換到新的衛星」[3, §2–3]，這正是極軌接縫在傾斜星座裡的對應物，也是第 2.5 節把跨面鏈路視為脆弱鏈路的原因。 |
| 星座配置 | 今天實際在飛的配置已從公開星曆中讀出：Ali 等人把 Starlink Shell 1 描述為 Walker Delta 53°: 1296/72/45，跨面相位步進約 12.5°，「正規」衛星沿軌道面每 20° 一顆，也就是觀測值每面 18 顆，對照 FCC 核准的每面 22 顆[16, §3.2.2–3.2.4, Tab. 2]。 |
| 軌道面配置 | 軌道面內衛星的間距也決定了面內 ISL 的長度，這就是第 2 章在意一個 1,584 顆的殼層究竟切成 24 面各 66 顆還是 72 面各 22 顆的原因。 |
Orbital planes drift after launch. Precession rate depends on altitude. Operators can place a launch batch into one parking plane and let it drift relative to the target shell. Once the desired RAAN separation accumulates, they raise each subgroup.
Ali et al. document this plane-formation behavior from TLEs [16] . This drift keeps a +Grid geometrically fixed relative to its constellation. The constellation slowly rotates relative to the ground network.
軌道面在發射後會持續漂移。因為速率取決於高度，營運商可以把一整批發射的衛星放進停泊高度的同一個軌道面，讓這批衛星以相對目標殼層有差異的速率進動，直到累積出所需的 RAAN 間隔，再分批把各子群抬升。Ali 等人從 TLE 記錄了這種建面行為[16]。同樣的漂移也說明了為什麼 +Grid 拓樸相對於星座維持固定幾何關係，而整個星座卻在地面網路之下緩慢旋轉。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Nodal precession | Earth’s equatorial bulge has coefficient J₂ = 1.08262668×10⁻³ [5, App. D]. It shifts prograde ascending nodes westward at \(\dot\Omega = -\tfrac{3}{2}\,n\,J_2\,(R_E/a)^2\cos i\). This drift is nodal precession [5, Ch. 9]. |
| Evaluation conditions | The formula gives −4.49°/day at 550 km and 53°. It gives −4.42°/day for Kuiper’s 630 km and 51.9°, and −0.20°/day for OneWeb’s 1,200 km and 87.9°. |
| 升交點進動 | 地球赤道隆起[5]會以長期速率 \(\dot\Omega = -\tfrac{3}{2}\,n\,J_2\,(R_E/a)^2\cos i\) 把順行軌道的升交點向西拖動，這種漂移稱為升交點進動[5, Ch. 9]。 |
| 評估條件 | 在 550 km 與 53° 下它是每天 −4.49°，在 Kuiper 的 630 km 與 51.9° 下是每天 −4.42°，而在 OneWeb 的 1,200 km 與 87.9° 下只有每天 −0.20°，皆由公式計算而得。 |
Wertz 與 Larson《SMAD》教科書）。
| 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 sun-synchronous orbit (SSO) precesses with the Sun’s apparent eastward motion of 0.9856°/day. This requires retrograde inclination. The formula gives 97.59° at 550 km and 97.99° at 650 km [5, Ch. 11]. |
| Inclination and coverage | Starlink’s 560 km/97.6° Gen1 and 360 km/96.9° Gen2 shells match the computed sun-synchronous inclinations. This is an inference from geometry. A SpaceX statement would establish the operator’s intended purpose. |
| Eclipse and sunlight | The dawn–dusk variant. Its plane stays roughly perpendicular to the Sun line, with ascending-node local time near 06:00 or 18:00. Solar beta angle stays about 66.6–90° throughout the year. These angles determine eclipse, the orbital segment within Earth’s shadow. |
| Eclipse and sunlight | For a cylindrical shadow with the Sun in the orbital plane the eclipse fraction is \(f = \arcsin(R_E/a)/\pi\). This is 0.372 at 550 km, or 35.6 of every 95.65 minutes, and 0.398 at 340 km. The orbit is eclipse-free whenever |β| exceeds arccos(R_E/a), 23.0° at 550 km and 24.8° at 650 km (Vallado, Ch. 5. Wertz & Larson, SMAD textbook). |
| Evaluation conditions | A dawn–dusk SSO at 650 km therefore stays sunlit all year. Google’s Suncatcher proposal therefore places its 81-satellite cluster in a 650 km dawn–dusk SSO (Agüera y Arcas et al., Joule 2026. Google Research blog, 4 Nov 2025 company), a choice Section 8.2 turns into a power budget and Chapter 11 into a network. |
| 太陽同步條件 | 把進動速率設為等於太陽每天 0.9856° 的視東移，軌道就成為太陽同步軌道（SSO），這需要逆行的傾角，公式在 550 km 定為 97.59°、在 650 km 定為 97.99°[5, Ch. 11]。 |
| 軌道高度 | Starlink 的 560 km/97.6° Gen1 殼層與 Gen2 的 360 km/96.9° 殼層都位於各自高度的太陽同步傾角上，此判斷來自計算值，歸屬於本教材的推論。 |
| 軌道面配置 | 晨昏型 SSO 的軌道面與太陽方向大致垂直，升交點地方時接近 06:00 或 18:00，使太陽 β 角全年維持在約 66.6° 到 90° 之間，而這之所以重要，是因為地影，也就是每一圈軌道中位於地球陰影內的部分。 |
| 軌道面配置 | 在圓柱形陰影且太陽位於軌道面內的情況下，地影比例為 \(f = \arcsin(R_E/a)/\pi\)，在 550 km 為 0.372，即每 95.65 分鐘有 35.6 分鐘，在 340 km 為 0.398，而只要 |β| 超過 arccos(R_E/a)（550 km 為 23.0°，650 km 為 24.8°）軌道全程受到日照（Vallado 第 5 章。 |
| 星座配置 | 因此 650 km 的晨昏 SSO 全年都在陽光下，這正是 Google 的 Suncatcher 提案把 81 顆衛星的叢集放在 650 km 晨昏 SSO 的原因（Agüera y Arcas 等人，《Joule》2026。 |
| 評估條件 | Google Research 部落格，2025 年 11 月 4 日 公司），第 8.2 節會把這個選擇變成電力預算，第 11 章則把它變成一個網路。 |
| Question問題 | Calculation算式 | Result結果 |
|---|---|---|
| Phase step of the observed Shell 1, 53°: 1296/72/45觀測到的 Shell 1（53°: 1296/72/45）的相位步進 | \(\Delta\phi = 360 f/t = 360 \times 45/1296\) | 12.5°computed from [16, Tab. 2] descriptor由 [16, Tab. 2] 的描述子計算 |
| Nodal precession at 550 km, 53°550 km、53° 的升交點進動 | \(-\tfrac{3}{2}\,n J_2 (R_E/a)^2 \cos 53^\circ\) | −4.49°/daycomputed. N = 2π/95.65 min, J₂ from Vallado App. D計算值。n = 2π/95.65 分，J₂ 取自 Vallado 附錄 D |
| Sun-synchronous inclination at 650 km650 km 的太陽同步傾角 | \(\cos i = -\dfrac{0.9856^\circ/\text{day}}{\tfrac{3}{2}\,n J_2 (R_E/a)^2}\) | 97.99°computed. 97.59° at 550 km, 100.42° at 1,200 km計算值。550 km 為 97.59°，1,200 km 為 100.42° |
| Eclipse fraction at 550 km, β = 0550 km、β = 0 的地影比例 | \(\arcsin(6{,}378.137/6{,}928.137)/\pi\) | 0.372 → 35.6 mincomputed. Cylindrical shadow. Eclipse-free if |β| > 23.0°計算值。圓柱形陰影。|β| > 23.0° 時全程受日照 |
| Eclipse-free threshold at 650 km650 km 的全程受日照門檻 | \(\arccos(6{,}378.137/7{,}028.137)\) | 24.8°computed. A dawn–dusk plane keeps |β| ≈ 66.6–90°計算值。晨昏軌道面使 |β| 維持約 66.6–90° |
Original figure note原始圖說出處
Drawn for this primer from the Walker (1984) and Ballard (1980) definitions and Handley, HotNets 2018, §2–3.1.4Starlink as filed and as flownStarlink：申請文件上的與實際在飛的
Recall
回顧
Section 1.3 defined shells and Walker patterns. Every "Starlink" geometry below is a set of shells, each a Delta or Star pattern. The only question is which document or which TLE census it comes from.
第 1.3 節定義了殼層與 Walker 星座。下面每一組「Starlink」幾何都是一組殼層，各自是 Delta 或 Star 型，唯一的問題是它來自哪份文件或哪一次 TLE 普查。
Most quantitative Starlink results use a frozen regulatory snapshot. Three versions of the first 1,584-satellite shell explain much of the conflicting geometry. Figure 1.4 maps the papers to the snapshots they froze.網路文獻中幾乎每一個量化的 Starlink 數字都是凍結下來的監管快照，而第一個 1,584 顆殼層的三份快照造成了大部分的混淆。圖 1.4 把各論文對應到它們所凍結的快照。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Plane configuration | SpaceX’s November 2016 application (SAT-LOA-20161115-00118) placed Phase 1 at 1,150 km, with 32 planes of 50. Phase 2 added 2,825 satellites at 1,100–1,325 km, totaling 4,425. That is the constellation Handley simulated with five lasers per satellite [3, §2–3] . |
| Constellation configuration | The November 2018 modification (SAT-MOD-20181108-00083) brought the 1,584 satellites down to 550 km in 24 planes of 66. This is the geometry of Bhattacherjee and Singla [1, §2.1, §6], of Handley's ground-relay paper [7] and of Chaudhry and Yanikomeroglu's laser-ISL studies [17]. |
| Constellation configuration | The August 2019 modification [18] redistributed the same 1,584 satellites across 72 planes of 22. Hypatia adopted this geometry [6, Tab. 1], followed by later simulators, emulators and topology studies. |
| Path length and hops | The last two filings share a physical shell. Changing plane count changes intra-plane neighbor distance from 659 km to 1,969 km. Section 2.1 shows how this changes +Grid hop lengths and latency. |
| 軌道面配置 | SpaceX 2016 年 11 月的申請（SAT-LOA-20161115-00118）把第一期放在 1,150 km、32 個軌道面各 50 顆，第二期再加 2,825 顆介於 1,100 與 1,325 km 之間，總計 4,425 顆，這就是 Handley 以每顆衛星五具雷射模擬的星座[3, §2–3]。 |
| 軌道面配置 | 2018 年 11 月的修改申請（SAT-MOD-20181108-00083）把這 1,584 顆降到 550 km、24 個軌道面各 66 顆，這是 Bhattacherjee 與 Singla[1, §2.1, §6]、Handley 的地面中繼論文[7]以及 Chaudhry 與 Yanikomeroglu 的雷射 ISL 研究[17]所用的幾何。 |
| 軌道面配置 | 2019 年 8 月的修改申請[18]把同樣的 1,584 顆重新排成 72 個軌道面各 22 顆，這是 Hypatia 採用的幾何[6, Tab. 1]，之後所有模擬器、模擬平台與拓樸論文都繼承了它。 |
| 星座配置 | 後兩種情況的實體殼層相同，但面內相鄰衛星距離從 659 km 變成 1,969 km，第 2.1 節會說明這改變了每一個 +Grid 跳距與延遲結果。 |
This primer uses indirect evidence for the order. Specific paragraph references remain to be established. Gen2 arrived in two tranches of 7,500.命令的具體段落編號仍待核對。Gen2 分兩批各 7,500 顆到來。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Constellation configuration | The authorized Gen1 constellation is FCC 21-48, adopted 27 April 2021, which fixes 4,408 satellites in five shells: |
| Gen1: 550 km shell | 550 km/53.0° in 72 × 22 |
| Gen1: 540 km shell | and 540 km/53.2° in 72 × 22 (1,584 each) |
| Gen1: 570 km shell | 570 km/70.0° in 36 × 20 (720) |
| Gen1: polar shells | and two 560 km/97.6° Star shells of 6 × 58 and 4 × 43 (348 and 172) |
| Gen1: elevation limits | with terminals and gateways permitted down to 25° and polar gateways to 5°. |
| Evaluation conditions | Sources include McDowell’s filing transcription secondary and ISPreview’s order report FCC filing. Zhang, Xu and Abdu Jyothi give identical parameters in Table 1 (arXiv 2402.08988 preprint). Their 570 km shell has 20 × 36 satellites. |
| Inclination and coverage | FCC 22-91 authorized shells at 525, 530 and 535 km with inclinations 53°, 43° and 33°. It is dated 1 December 2022 (Via Satellite, 2 Dec 2022 FCC filing). |
| Constellation configuration | FCC DA 26-36, dated 9 January 2026, authorized another 7,500 satellites. Paragraph 5 states this brings authorized Gen2 size to 15,000. |
| Gen2: deferred satellites | deferred the remaining 14,988 including everything above 600 km (¶5) |
| Gen2: lower shells | authorized up to 144 satellites in up to 72 planes in each of the 340, 345, 350, 355 and 365 km shells |
| Gen2: 480–485 km shells | and up to 120 satellites in up to 56 planes at 480 and 485 km (¶6) |
| Gen2: altitude changes | permitted the 525/530/535 km shells to be lowered to 480/485/475 km (¶13(c)) |
| Gen2: deployment milestones | and set milestones of half the constellation by 1 December 2028 and the remainder by 1 December 2031 (¶14(a)) [19]. |
| 評估條件 | 已核准的 Gen1 星座是 2021 年 4 月 27 日通過的 FCC 21-48，它定下五個殼層共 4,408 顆： |
| Gen1：550 km 殼層 | 550 km/53.0° 的 72 × 22 與 |
| Gen1：540 km 殼層 | 540 km/53.2° 的 72 × 22（各 1,584 顆）、 |
| Gen1：570 km 殼層 | 570 km/70.0° 的 36 × 20（720 顆），以及 |
| Gen1：極軌殼層 | 兩個 560 km/97.6° 的 Star 型殼層 6 × 58 與 4 × 43（348 與 172 顆） |
| Gen1：仰角限制 | 終端與閘道允許低至 25°、極區閘道低至 5°。 |
| 評估條件 | 本教材以間接證據說明這份命令，參數依據為 McDowell 對申請文件的轉錄 二手來源、Zhang、Xu 與 Abdu Jyothi 內容相同的 Table 1（arXiv 2402.08988 預印本，他們把 570 km 殼層寫成 20 × 36），以及 ISPreview 對該命令的報導 FCC 文件。 |
| 傾角與覆蓋 | 2022 年 12 月 1 日的 FCC 22-91 核准了 525、530 與 535 km、傾角 53°、43° 與 33° 的殼層（Via Satellite，2022 年 12 月 2 日 FCC 文件），申請的幾何是 2021 年 8 月修正案（SAT-AMD-20210818-00105，九個殼層共 29,988 顆）中每殼層 28 面 × 120 顆，但核准的面數仍待一手來源確認。 |
| 星座配置 | 2026 年 1 月 9 日的 FCC DA 26-36 接著核准第二批 7,500 顆，「使已核准的 Gen2 Starlink 星座總規模達到 15,000 顆」（¶5） |
| Gen2：延後審理範圍 | 延後其餘 14,988 顆包括所有 600 km 以上的衛星（¶5） |
| Gen2：低軌殼層 | 授權在 340、345、350、355 與 365 km 各殼層部署至多 72 個軌道面各至多 144 顆、 |
| Gen2：480–485 km 殼層 | 在 480 與 485 km 部署至多 56 個軌道面各至多 120 顆（¶6） |
| Gen2：高度調整 | 允許把 525/530/535 km 殼層降至 480/485/475 km（¶13(c)） |
| Gen2：部署里程碑 | 並設定 2028 年 12 月 1 日前部署一半、2031 年 12 月 1 日前完成其餘的里程碑（¶14(a)）[19]。 |
| System / shell系統 / 殼層 | Altitude / inclination高度 / 傾角 | Planes × satellites軌道面 × 衛星 | Total總數 | User mask使用者遮罩 | ISL | Source and status來源與狀態 |
|---|---|---|---|---|---|---|
| Starlink Gen1 S1 | 550 km / 53.0° | 72 × 22 | 1,584 | 25° | optical, from v1.5光學，v1.5 起 | [8] (27 Apr 2021) FCC filing secondary[8] （2021-04-27） FCC 文件 二手 |
| Starlink Gen1 S2 | 540 km / 53.2° | 72 × 22 | 1,584 | 25° | optical光學 | same order同一命令 |
| Starlink Gen1 S3 | 570 km / 70.0° | 36 × 20 | 720 | 25° | optical光學 | same order. Zhang et al. write 20 × 36同一命令。Zhang 等人寫成 20 × 36 |
| Starlink Gen1 S4, S5 | 560 km / 97.6° | 6 × 58, 4 × 43 | 348, 172 | 25° (polar gateways 5°)25°（極區閘道 5°） | optical光學 | same order. Star pattern at the SSO inclination同一命令。位於 SSO 傾角的 Star 型 |
| Starlink Gen2, tranche 1 | 525 / 530 / 535 km at 53° / 43° / 33° | applied 28 × 120 each. Authorized count unconfirmed申請每殼 28 × 120。核准面數待確認 | 7,500 | 25° | optical光學 | [27] (1 Dec 2022) FCC filing[27] （2022-12-01） FCC 文件 |
| Starlink Gen2, tranche 2 | 340–365 km shells (53°, 48°, 38°, 43°, 96.9°, 28°/32°). 475–485 km (28°/32°, 53°, 43°) | ≤ 72 planes × ≤ 144 (340–365 km). ≤ 56 × ≤ 120 (480/485 km)≤ 72 面 × ≤ 144（340–365 km）。≤ 56 × ≤ 120（480/485 km） | 7,500 (15,000 Gen2 total)7,500（Gen2 共 15,000） | 25° | optical光學 | FCC DA 26-36 (9 Jan 2026) ¶5, ¶6, ¶13(c) FCC filingFCC DA 26-36（2026-01-09）¶5、¶6、¶13(c) FCC 文件 |
| Amazon Kuiper (Amazon Leo) | 630 / 51.9°. 610 / 42°. 590 / 33° | 34 × 34. 36 × 36. 28 × 28 | 3,236 | 35° user, 20° gateway使用者 35°，閘道 20° | optical, 100 Gbps demo company光學，100 Gbps 示範 公司 | [28] (30 Jul 2020) . Technical Appendix Tables 1, 2, 7 FCC filing . ~392 in orbit Oct 2026 secondary FCC filing secondary[28] （2020-07-30） 。 技術附錄 Tables 1、2、7 FCC 文件 。 2026 年 10 月約 392 顆在軌 二手 FCC 文件 二手 |
| OneWeb Gen1 | 1,200 km / 86.4° or 87.9° (unresolved)1,200 km / 86.4° 或 87.9°（待釐清） | 12 × 49 | 588 + spares (648 planned)588 + 備用（規劃 648） | 55° guaranteed. Beams above 25°保證 55°。波束 25° 以上 | none排除 | [11, pp. 11–12] . 654 in space Aug 2026 company FCC filing companyOneWeb 附件 B 第 11–12 頁 FCC 文件。2026 年 8 月 654 顆在軌 公司 |
| Telesat Lightspeed | filed 1,015 km / 98.98° + 1,325 km / 50.88°. 2025: 1,335 km and 1,325 km申請 1,015 km / 98.98° + 1,325 km / 50.88°。2025 年：1,335 km 與 1,325 km | 27 × 13 + 40 × 33 as filed. 2025 plane count awaits source evidence申請 27 × 13 + 40 × 33。2025 年面數仍待來源證據 | 1,671 filed → 156 + 108申請 1,671 → 156 + 108 | 10° | optical, four per satellite company光學，每顆四具 公司 | [10, Tab. A.2-1] . First launch NET Dec 2026 secondary FCC filing secondary[10, Tab. A.2-1] 。 首次發射安排於 2026 年 12 月或之後 二手 FCC 文件 二手 |
| Guowang (China SatNet) | ITU: 508–600 km and 1,145 km. Flown 1,175 km / 86.5° and 1,156 km / 50°ITU：508–600 km 與 1,145 km。實飛 1,175 km / 86.5° 與 1,156 km / 50° | seven sub-shells filed申請七個子殼層 | 12,992 filed. ~204 LEO by Sep 2026申請 12,992。2026 年 9 月約 204 顆 LEO | — | undocumented文件待補 | ITU filing via McDowell, Wikipedia secondaryITU 文件，經 McDowell、Wikipedia 二手 |
| Qianfan (SSST) | 1,160 km reported報導 1,160 km | — | 1,296 Phase 1. 200 launched by Jun 2026第一期 1,296。2026 年 6 月已發射 200 | — | undocumented文件待補 | CircleID, Wikipedia secondaryCircleID、Wikipedia 二手 |
What flies is a different object from what is authorized.實際在軌配置與核准內容各有差異。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Constellation configuration | Jonathan McDowell’s TLE tally dated 28 October 2026 lists 13,069 launches and 11,190 satellites in orbit. Of these, 11,176 were working and 10,022 occupied operational orbits. |
| Gen1 status | split into Gen1 4,714 launched / 3,127 in orbit / 3,116 working / 2,379 operational |
| Gen2 status | Gen2 8,309 / 8,037 / 8,034 / 7,643 |
| V3 status | and 46 V3 satellites launched of which 20 failed to reach orbit and 26 are in orbit [20]. |
| PoP coverage | The table below reproduces Ali et al.’s end-2025 TLE census. The canonical 53.0°/552 km research shell holds about 575 satellites. The 53.2° population includes 1,376 at 540 km, 1,848 at 484 km and 315 at 354 km. The 43° shells are flown at 559, 489 and 355 km rather than the authorized 530 km [16, Tab. 1] . |
| Flown shell geometry | The 525–535 km Gen2 shells operate near 484–489 km and 354–355 km. These altitudes agree with the lowering authority in DA 26-36. Observed along-track spacing exceeds filed spacing in every shell. Examples are 20.0° against 16.4° at 552 km and 10.0° against 8.4° at 557 km (Table 2). |
| Orbital altitude | Use roughly 340–570 km for Starlink’s altitude range. Treat 550 km/53° as the canonical modeling shell, and report median satellite altitude separately. |
| 評估條件 | Jonathan McDowell 以 TLE 為基礎、日期為 2026 年 10 月 28 日的統計列出 13,069 顆 Starlink 已發射、11,190 顆在軌、11,176 顆運作中、10,022 顆位於工作軌道 |
| Gen1 狀態 | 其中 Gen1 為 4,714 發射 / 3,127 在軌 / 3,116 運作 / 2,379 工作軌道 |
| Gen2 狀態 | Gen2 為 8,309 / 8,037 / 8,034 / 7,643 |
| V3 狀態 | 而 V3 發射 46 顆、20 顆入軌失敗、26 顆在軌[20]。 |
| 星座配置 | Ali 等人對 2025 年底 TLE 的普查顯示各殼層實際的填充情形，下表重現了它：典型的 53.0°/552 km 研究殼層只有大約 575 顆衛星，53.2° 殼層在 540 km 有 1,376 顆、但在 484 km 有 1,848 顆、354 km 有 315 顆，而 43° 殼層飛在 559、489 與 355 km，與核准值 530 km 形成差異[16, Tab. 1]。 |
| 評估條件 | 因此 525–535 km 的 Gen2 殼層實務上是在約 484–489 km 與 354–355 km 運作，與 DA 26-36 的降軌授權一致，而每個殼層觀測到的面內間距都比申請值寬，552 km 為 20.0° 對 16.4°，557 km 為 10.0° 對 8.4°（Table 2）。 |
| 軌道高度 | 教材應把「Starlink 高度」寫成大約 340–570 km 的範圍，並把 550 km/53° 當作典型的建模殼層，中位數衛星高度則須另行統計。 |
| Observed shell ([16, Tab. 1])觀測殼層（[16, Tab. 1]） | Inclination傾角 | Altitude高度 | Satellites, end-2025衛星數，2025 年底 | Authorized counterpart對應的核准殼層 |
|---|---|---|---|---|
| Shell 1, the "research shell"Shell 1，「研究殼層」 | 53.0° | 552 km | 575 | 550 km, 1,584 (Gen1)550 km，1,584（Gen1） |
| Shell 2 at altitudeShell 2 於設計高度 | 53.2° | 540 km | 1,376 | 540 km, 1,584 (Gen1)540 km，1,584（Gen1） |
| 53.2° lowered53.2° 降軌 | 53.2° | 484 km | 1,848 | 525 km (Gen2) → 480 km per DA 26-36525 km（Gen2）→ 依 DA 26-36 降至 480 km |
| 53.2° very low53.2° 極低軌 | 53.2° | 354 km | 315 | 340–355 km shells (Gen2)340–355 km 殼層（Gen2） |
| 43° at altitude43° 於設計高度 | 43.0° | 559 km | 1,220 | 530 km authorized. Filed vs flown disagree核准 530 km。申請與實飛差異 |
| 43° lowered43° 降軌 | 43.0° | 489 km | 1,380 | 530 km → 485 km per DA 26-36530 km → 依 DA 26-36 降至 485 km |
| 43° very low43° 極低軌 | 43.0° | 355 km | 321 | 355 km shell (Gen2)355 km 殼層（Gen2） |
| 70° shell70° 殼層 | 70.0° | 570 km | 590 | 570 km, 720 (Gen1)570 km，720（Gen1） |
| Polar Star shell極軌 Star 殼層 | 97.6° | 557 km | 511 | 560 km, 348 + 172 (Gen1)560 km，348 + 172（Gen1） |
TLE census from Ali et al., arXiv 2603.25835 (March 2026) preprint. "authorized counterpart" is this primer's mapping to the FCC shells above.
TLE 普查取自 Ali 等人，arXiv 2603.25835（2026 年 3 月）預印本。「對應的核准殼層」是本教材對上表 FCC 殼層的對應。
Satellites also wear out. A network model that runs for years must say so. These reliability figures carry preprint and tracker tags. Their status awaits confirmation through a peer-reviewed Starlink reliability study.衛星也會老化，一個要運行多年的網路模型必須說明這一點。這些可靠度數字標記為預印本與追蹤者資料，其結論仍待經同儕審查的 Starlink 可靠度研究確認。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Satellite design life | The same preprint reports a nominal five-year design life with most satellites operating for four to six years |
| Operational phase | an operational phase of median 864 days between a 64-day ascent and a 107-day descent |
| Daily failure probability | a mean daily failure probability of 0.0128% over the first 1,000 days |
| Survival probability | a survival probability of about 0.83 at day 1,395 |
| Wear-out timing | a wear-out peak near day 1,850 |
| Orbital maneuvers | and roughly 264 manoeuvres per day across the five shells of which 74.6% are collision avoidance [16, §3.3–3.4, Figs. 16, 21]. |
| Constellation configuration | McDowell lists 20 failures to orbit, 181 early deorbits, 1,525 completed disposals and 153 reentries after failure, among 13,069 launches secondary. Thus, roughly 1.3% failed in orbit and about 13% underwent deliberate retirement. |
| 衛星設計壽命 | 同一份預印本報告了名目五年的設計壽命、大多數衛星運作四到六年、 |
| 工作階段 | 介於 64 天上升段與 107 天下降段之間中位數 864 天的工作階段、 |
| 每日故障機率 | 前 1,000 天平均每日 0.0128% 的故障機率、 |
| 存活機率 | 第 1,395 天約 0.83 的存活機率、 |
| 磨損高峰 | 約第 1,850 天的磨損高峰 |
| 軌道機動 | 以及五個殼層每天約 264 次機動、其中 74.6% 是碰撞避讓[16, §3.3–3.4, Figs. 16, 21]。 |
| 星座配置 | McDowell 的獨立統計則給出 13,069 顆已發射中 20 顆入軌失敗、181 顆提前離軌、1,525 顆完成處置、153 顆故障後再入 二手來源，因此約 1.3% 的已發射衛星在軌道上故障，而約 13% 已被有意退役。 |
Original figure note原始圖說出處
Drawn for this primer from the filing records SAT-LOA-20161115-00118, SAT-MOD-20181108-00083, SAT-MOD-20190830-00087 and the fact base's register of frozen snapshots.1.5The other constellations: Kuiper, OneWeb, Telesat, Guowang and Qianfan其他星座：Kuiper、OneWeb、Telesat、國網與千帆
Deployment has lagged the licence. Every Kuiper number therefore needs a date beside it.部署進度落後於許可。因此每一個 Kuiper 數字旁邊都需要標上日期。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Constellation configuration | Amazon's Kuiper, rebranded Amazon Leo, is authorized by FCC 20-102 of 30 July 2020 for 3,236 satellites in three Delta shells |
| Amazon Leo: 630 km shell | 630 km/51.9° in 34 planes of 34 |
| Amazon Leo: 610 km shell | 610 km/42° in 36 of 36 |
| Amazon Leo: 590 km shell | and 590 km/33° in 28 of 28 |
| Amazon Leo: ascending-node spacing | with the 610 km planes "equally spaced 10° apart in ascending node" |
| Amazon Leo: gateway elevation | gateways down to 20° |
| Amazon Leo: user elevation | user beams only above 35° |
| Amazon Leo: initial service | and a Phase 1 of 578 satellites in 17 planes at 630 km after which service begins between 39° and 56° of latitude [9, Tabs. 1, 2, 7]. |
| Constellation configuration | Amazon reports 100 Gbps optical links over about 1,000 km between KuiperSat-1 and -2. Production satellites carry "multiple optical terminals" [21]. The terminal count requires disclosure. |
| Constellation configuration | Secondary trackers list 270 production satellites after 11 launches on 27 April 2026. Counts reached 396 or 398 after the final Atlas V launch on 2 July. October 2026 tracking lists 392 objects, all in the 630 km shell [22]. Payload reported "only 331" on 9 June 2026 secondary. |
| Constellation configuration | Each count falls below the 1,616-satellite, 50% milestone due 30 July 2026. Amazon received a conditional FCC waiver in June 2026. Later satellites lose Ka/Ku priority until 30 March 2028 or milestone completion FCC filing. |
| 星座配置 | Amazon 的 Kuiper（已更名為 Amazon Leo）依 2020 年 7 月 30 日的 FCC 20-102 獲准部署 3,236 顆衛星，分成三個 Delta 殼層： |
| Amazon Leo：630 km 殼層 | 630 km/51.9° 的 34 面各 34 顆、 |
| Amazon Leo：610 km 殼層 | 610 km/42° 的 36 面各 36 顆 |
| Amazon Leo：590 km 殼層 | 以及 590 km/33° 的 28 面各 28 顆 |
| 升交點間距 | 其中 610 km 的軌道面「升交點等距相隔 10°」 |
| 閘道仰角 | 閘道低至 20°、 |
| 使用者仰角 | 使用者波束只在 35° 以上 |
| 初期服務 | 第一期為 630 km 的 17 個軌道面共 578 顆，之後在南北緯 39° 到 56° 之間開始服務[9, Tabs. 1, 2, 7]。 |
| 星座配置 | 它的星間鏈路屬於公司聲明：Amazon 報告 KuiperSat-1 與 -2 之間跨約 1,000 km 的 100 Gbps 光學鏈路，並表示量產衛星搭載「多具光學終端」（Amazon，2023 年 12 月 14 日 公司），終端數量仍待公開資料。 |
| 星座配置 | 二手追蹤者統計 2026 年 4 月 27 日 11 次發射後有 270 顆量產衛星、2026 年 7 月 2 日最後一次 Atlas V 飛行後為 396 或 398 顆、2026 年 10 月有 392 個物體在軌，全部位於 630 km 殼層[22]，而 Payload 在 2026 年 6 月 9 日報導「只有 331 顆」二手來源。 |
| 星座配置 | 上述各項統計皆顯示，Amazon 都錯過了 2026 年 7 月 30 日到期、1,616 顆的 50% 里程碑，並在 2026 年 6 月獲得 FCC 的條件式豁免，之後發射的衛星在 2028 年 3 月 30 日前或達成里程碑前失去 Ka/Ku 優先權 FCC 文件。 |
Because every OneWeb packet must come down at a gateway within the same satellite's footprint, both del Portillo and Pachler find it gateway-limited. This is the clearest demonstration in the literature of what ISLs buy.因為每一個 OneWeb 封包都必須在同一顆衛星足跡內的閘道落地，del Portillo 與 Pachler 都發現它受閘道數量限制，這是文獻中關於 ISL 能換到什麼最清楚的示範。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Plane configuration | OneWeb Gen1 uses ground relays for its inter-satellite connectivity. Its 1,200 km near-polar Star pattern has 12 planes of 49 satellites. This gives 588 satellites plus spares, against 648 planned. Reported OneWeb inclinations differ: Wikipedia gives 86.4°, while McDowell’s transcription and del Portillo’s Table 1 give 87.9°. Del Portillo’s text gives 87°. Resolving this requires further primary-source evidence secondary. |
| Constellation configuration | The filing guarantees visibility above 55° and permits beams above 25° [11, pp. 11–12]. In August 2026, Eutelsat reported 654 Gen1 satellites in space at about 150 kg each [23]. Roughly 600 provide coverage, and the remainder provide redundancy. Useful life is about five years. |
| OneWeb 星座 | OneWeb Gen1 是唯一以地面中繼取代星間鏈路的寬頻星座，是 1,200 km 的近極軌 Star 型，12 個軌道面各 49 顆，即 588 顆加上備用、規劃 648 顆，其傾角 Wikipedia 寫 86.4°、McDowell 的轉錄與 del Portillo 的 Table 1 寫 87.9°、del Portillo 的內文寫 87°，這項分歧仍待進一步一手證據釐清 二手來源。 |
| 星座配置 | 它的申請文件保證 55° 以上的可見性、允許 25° 以上的波束（OneWeb 附件 B，第 11–12 頁 FCC 文件），Eutelsat 則報告 2026 年 8 月有 654 顆約 150 kg 的 Gen1 衛星在軌，其中約 600 顆用於覆蓋、其餘為冗餘，使用壽命約五年[23]。 |
Telesat Lightspeed has been redesigned twice. The Chinese systems rely on secondary documentation. Primary documents and published ISL details require further evidence. This primer therefore reports altitudes and counts.Telesat Lightspeed 已經重新設計了兩次。中國的系統只有二手文件。這兩個系統的一手文件與公開星間鏈路資訊仍待補充，因此本教材的描述範圍限於高度及數量。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Constellation configuration | The May 2020 filing specified 1,671 satellites. Its polar shell had 27 planes of 13 at 1,015 km and 98.98°. Its inclined shell had 40 planes of 33 at 1,325 km and 50.88°. The model used a 10° mask and optical ISLs [10, Tab. A.2-1, pp. 2, 15, 25]. Hypatia simulates this filing and finds half as many path changes as Starlink. |
| Constellation configuration | The 2025 modification reduced the fleet to 156 satellites at 1,335 km and 108 at 1,325 km. MDA builds them with four optical terminals each (eoPortal company). First launch was scheduled for December 2026 or later [24] [25]. The new inclinations and plane counts require source evidence. |
| Constellation configuration | Guowang’s ITU filings total 12,992 satellites: 6,080 in GW-A59 and 6,912 in GW-2. Seven subshells span 508–600 km and 1,145 km. Roughly 204 operational satellites launched by September 2026 occupy 1,175 km/86.5° and 1,156 km/50°, outside those filed altitudes (Wikipedia, McDowell secondary). Qianfan had launched 200 satellites by June 2026 at a reported 1,160 km. Phase 1 targets 1,296 satellites (CircleID, Wikipedia secondary). |
| 星座配置 | 2020 年 5 月的申請文件載明 1,671 顆衛星：1,015 km、98.98° 的極軌殼層 27 面各 13 顆，以及 1,325 km、50.88° 的傾斜殼層 40 面各 33 顆，最低仰角 10°，並配備光學星間鏈路[10, Tab. A.2-1]，這就是 Hypatia 模擬的對象，也是它發現 Telesat 路徑變動頻率只有 Starlink 一半的原因。 |
| 傾角與覆蓋 | 2025 年的修改把機隊縮減為 1,335 km 的 156 顆加上 1,325 km 的 108 顆，由 MDA 製造、每顆四具光學終端（eoPortal 公司），首次發射安排於 2026 年 12 月或之後[24][25]，新殼層的傾角與面數仍待來源證據。 |
| 星座配置 | 國網的 ITU 申請合計 12,992 顆，GW-A59 有 6,080 顆、GW-2 有 6,912 顆，分成 508–600 km 與 1,145 km 的七個子殼層，但到 2026 年 9 月已發射的約 204 顆運作中 LEO 衛星位於 1,175 km/86.5° 與 1,156 km/50°，均位於各申請高度之外（Wikipedia、 |
| 軌道高度 | McDowell 二手來源），而千帆到 2026 年 6 月已發射 200 顆、報導高度 1,160 km，第一期目標為 1,296 顆（CircleID、Wikipedia 二手來源）。 |
1.6How the classic papers model the constellation經典論文如何建模星座
The modeling papers that defined the field each froze one filing. The table below is the key to reading them side by side. All three assume four static ISLs in a +Grid. Section 5.7 treats this as a modeling baseline. Current Starlink satellites carry three terminals, with topology awaiting disclosure.定義了這個領域的建模論文各自凍結了一份申請文件，下表是把它們並排閱讀的鑰匙。三者都假設四條靜態 ISL 的 +Grid，第 5.7 節會說明它已成為建模基準。目前 Starlink 衛星搭載三具終端，其實際拓樸仍待公開資料。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Constellation configuration | Handley simulated the 2016 design: 1,600 satellites at 1,150 km in 32 planes of 50, plus 2,825 higher satellites. Each satellite had five lasers. Dijkstra recomputed routes every 10 ms in a propagation-only model. Capacity remained outside scope. Satellite paths beat fiber beyond about 3,000 km [3, §2–5]. |
| Constellation configuration | Bhattacherjee and Singla used the November 2018 Starlink shell: 1,584 satellites at 550 km in 24 planes of 66. Kuiper’s first shell had 34² satellites at 630 km. Each satellite had four ISLs. Visibility limited Starlink and Kuiper links to 5,014 km and 5,440 km. Minimum +Grid connectivity ranges were 2,006 km and 1,761 km. Repeated local "motifs" varied across three latitude zones and improved a traffic-weighted stretch-plus-hops objective. Their 40² reference +Grid had mean stretch 1.25 and 10.57 hops. Starlink improvement was 54% at 5,014 km and 40% at 2,006 km [1, §2.3, §4.3, §6, Tab. 1]. |
| Plane configuration | Hypatia adopted the August 2019 Starlink geometry, 72 planes of 22, plus four higher shells at 1,110–1,325 km. It included Kuiper’s three shells at a 30° mask and Telesat’s two at 10°. Filed Keplerian elements became TLEs, and forwarding state updated every 100 ms. Median path changes per 200 s were four for Starlink and Kuiper, against two for Telesat. Manila–Dalian RTT ranged from 25 to 48 ms [6, Tabs. 1–2, §4]. |
| 星座配置 | Handley 模擬的是 2016 年的設計，1,150 km、32 面各 50 顆的 1,600 顆衛星加上 2,825 顆較高的衛星，每顆五具雷射，以 Dijkstra 每 10 ms 重算路由，只計傳播延遲、計算範圍排除容量模型，並發現在距離超過約 3,000 km 時衛星路徑勝過光纖[3, §2–5]。 |
| 星座配置 | Bhattacherjee 與 Singla 採用 2018 年 11 月的殼層，550 km、24 面各 66 顆的 1,584 顆衛星，以及 Kuiper 在 630 km 的第一個 34² 殼層，給每顆衛星四條 ISL，以視線可見性把 ISL 長度限制在 Starlink 5,014 km、Kuiper 5,440 km，並以 +Grid 仍能連通的最短距離 2,006 km 與 1,761 km 為下限，證明在三個緯度區各自重複的局部「motif」在流量加權的「延伸比加跳數」目標上優於 +Grid（他們在 40² 參考星座上量得 +Grid 的平均延伸比 1.25 與 10.57 跳），Starlink 在 5,014 km 時改善 54%、在 2,006 km 時改善 40%[1, §2.3, §4.3, §6, Tab. 1]。 |
| 往返時間 | Hypatia 採用 2019 年 8 月的 72 面各 22 顆幾何，加上第一次核准中四個 1,110–1,325 km 的殼層、以 30° 遮罩建模的 Kuiper 三個殼層以及以 10° 建模的 Telesat 兩個殼層，把申請文件中的克卜勒根數轉成 TLE，每 100 ms 重算轉送狀態，並報告 Starlink 或 Kuiper 的路徑每 200 秒變動中位數四次、Telesat 為兩次，馬尼拉到大連的 RTT 在 25 到 48 ms 之間擺盪[6, Tabs. 1–2, §4]。 |
The venue is ICC Workshops. References that name IEEE Aerospace require correction.容量比較的論文凍結了另外幾份快照，得出的結論至今仍被引用。會議是 ICC Workshops，常見的 IEEE Aerospace 引用標示需要修正）。
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Capacity comparison | The capacity-comparison papers froze other snapshots and reached conclusions that are still quoted. |
| Comparison source | del Portillo, Cameron and Crawley modeled OneWeb as 720 satellites in 18 planes of 40 at 55° with ISLs excluded |
| SpaceX configuration | SpaceX as 4,425 satellites at 1,110–1,325 km with a 40° mask and optical ISLs |
| Telesat configuration | and Telesat as 117 satellites |
| Throughput comparison | and found maximum total throughputs of 1.56 Tbps for OneWeb with 71 ground stations |
| Telesat throughput | 2.66 Tbps for Telesat with 42 |
| SpaceX throughput | and 23.7 Tbps for SpaceX with 123 [12, Tabs. 1, 5, 9]. |
| Filing comparison | Pachler, del Portillo, Crawley and Cameron updated the comparison to the 2020–21 filings |
| SpaceX configuration | SpaceX 4,408 satellites in 190 planes at 25° |
| Kuiper configuration | Kuiper 3,236 in 98 planes at 35° |
| Telesat configuration | Telesat 1,671 in 67 planes at 10° |
| OneWeb configuration | and OneWeb 6,372 in 100 planes at 25° |
| Initial-constellation throughput | and obtained initial-constellation throughputs of 10.3, 12.5, 7.52 and 1.44 Tbps |
| Per-satellite throughput | Per-satellite capacity is 6.50 Gbps for SpaceX, 15.5–19.6 for Kuiper, 25.2 for Telesat and 2.01 for OneWeb. These values appear in the authors’ April 2022 slides [31]. |
| Model configuration | That 6.5 Gbps is a model output for a V1 satellite. A competing preprint derives 24 Gbps for V1.5 and 96 Gbps for V2 Mini [26] [23]. It uses SpaceX’s "more than 10×" V3 statement. |
| Evaluation conditions | Section 3.2 and Chapter 4 carry both values with their tags rather than choosing between them. |
| 星座配置 | del Portillo、Cameron 與 Crawley 把 OneWeb 建模為 55° 遮罩、ISL 排除、18 面各 40 顆的 720 顆衛星 |
| SpaceX 配置 | 把 SpaceX 建模為 1,110–1,325 km、40° 遮罩、具光學 ISL 的 4,425 顆衛星 |
| Telesat 配置 | 把 Telesat 建模為 117 顆 |
| 總吞吐量比較 | 發現最大總吞吐量各自是 OneWeb 搭配 71 座地面站 1.56 Tbps、 |
| Telesat 吞吐量 | Telesat 搭配 42 座 2.66 Tbps、 |
| SpaceX 吞吐量 | SpaceX 搭配 123 座 23.7 Tbps[12, Tabs. 1, 5, 9]。 |
| 申請文件比較 | Pachler、del Portillo、Crawley 與 Cameron 把比較更新到 2020–21 年的申請文件： |
| SpaceX 配置 | SpaceX 190 個軌道面、25° 的 4,408 顆 |
| Kuiper 配置 | Kuiper 98 面、35° 的 3,236 顆 |
| Telesat 配置 | Telesat 67 面、10° 的 1,671 顆 |
| OneWeb 配置 | OneWeb 100 面、25° 的 6,372 顆 |
| 初始星座吞吐量 | 得到初始星座的吞吐量 10.3、12.5、7.52 與 1.44 Tbps |
| 單星吞吐量 | 換算成每顆衛星是 SpaceX 6.50 Gbps、Kuiper 15.5–19.6、Telesat 25.2、OneWeb 2.01（[31]，依作者 2022 年 4 月的投影片。 |
| 容量比較 | 那個 6.5 Gbps 是針對 V1 衛星的模型輸出，而一份預印本從 SpaceX 關於 V3「超過 10 倍」的聲明推導出 V1.5 為 24 Gbps、V2 Mini 為 96 Gbps，對此提出質疑[26][23]。 |
| 評估條件 | 第 3.2 節與第 4 章會同時保留兩個值及其標記，並各自說明各自的依據。 |
| Paper論文 | Filing frozen凍結的申請文件 | Starlink geometry used所用的 Starlink 幾何 | ISLs / maskISL / 遮罩 | What is modeled建模內容 |
|---|---|---|---|---|
| [3] | Nov 2016 application2016 年 11 月申請 | 1,150 km · 32 × 50 (+2,825) | 5 lasers · 40° nadir rule5 具雷射 · 40° 天底角規則 | propagation only. Dijkstra every 10 ms. Fiber beaten beyond ~3,000 km只計傳播。每 10 ms 跑 Dijkstra。超過約 3,000 km 勝過光纖 |
| [1, §6, Tab. 1] | Nov 2018 modification2018 年 11 月修改 | 550 km · 24 × 66 | 4 ISLs · ranges 2,006–5,014 km4 條 ISL · 距離 2,006–5,014 km | stretch and hops. Multi-motif Φ1 +54% / +40%延伸比與跳數。多 motif Φ1 +54% / +40% |
| del Portillo et al., Acta Astronautica 2019 | 2016–17 filings2016–17 年申請 | 4,425 at 1,110–1,325 km | optical ISLs · 40°光學 ISL · 40° | capacity: 23.7 Tbps with 123 ground stations容量：123 座地面站下 23.7 Tbps |
| Kassing et al. (Hypatia), IMC 2020 | Aug 2019 modification2019 年 8 月修改 | 550 km · 72 × 22 (+4 shells) | 4 ISLs (+Grid) · 25°4 條 ISL（+Grid）· 25° | packet simulation. Routes every 100 ms. 4 path changes / 200 s封包模擬。每 100 ms 更新路由。每 200 秒 4 次路徑變動 |
| [31] | 2020–21 filings [8]2020–21 年申請[8] | 540–570 km · 190 planes · 4,408 | ISL yes · 25°有 ISL · 25° | capacity: 10.3 Tbps initial, 6.50 Gbps per satellite容量：初始 10.3 Tbps，每顆 6.50 Gbps |
State the source filing and date when quoting a Starlink geometry. Identify each parameter as authorized, observed in TLEs or modeled, then attach its evidence tag. Section 4.5 turns this into a checklist. The physical relations in Sections 1.1–1.3 remain fixed. FCC orders and launches change the constellation parameters, so comparisons require the correct dated configuration.
引用 Starlink 幾何時，先列出申請文件及日期，再註明數字屬於核准值、TLE 觀測值或模型值，並附上證據標記。第 4.5 節會把這個做法變成一份檢查清單。第 1.1–1.3 節的物理關係式維持固定，星座參數則隨 FCC 命令與發射而更新，因此比較研究結果時須核對配置日期。
Chapter summary
本章摘要
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Orbital altitude | Altitude fixes a circular LEO orbit. At 550 km, period is 95.65 min and speed is 7.585 km/s, or the CoNEXT 2019 title’s 27,306 km/h. Ground-track speed is 6.983 km/s. A satellite at zenith is 1.83 ms away. |
| Orbital altitude | Visibility is where altitude really bites. This occurs because the elevation mask fixes the coverage half-angle λ, the slant range and the longest pass together. At 550 km, a 25° mask gives λ = 8.45° and slant range 1,123 km. One-way delay is 3.75 ms, and maximum zenith pass is 4.49 min. For 4,408 satellites, a uniform-sphere model gives about 24 visible satellites. Tanveer et al. measured 35–44 at mid-latitudes. This occurs because a 53° shell crowds its satellites toward those latitudes. |
| Plane configuration | Walker notation distinguishes co-rotating Delta patterns and Star patterns with a counter-rotating seam. At 550 km and 53°, J₂ precession is −4.49°/day, allowing inexpensive plane formation. A 650 km dawn–dusk SSO stays sunlit throughout the year. |
| Constellation configuration | The literature chiefly uses three frozen filings of the same 1,584-satellite shell. On 28 October 2026, the flown constellation had 11,190 satellites in orbit across roughly 340–570 km. Each number therefore needs its filing, its date and its evidence tag. |
| 軌道高度 | 圓形 LEO 軌道只由高度決定，在 550 km 得到 95.65 分鐘的週期與 7.585 km/s 的速度，也就是 CoNEXT 2019 標題中的 27,306 km/h，而地面軌跡以 6.983 km/s 移動，天頂衛星只有 1.83 ms 之遙。 |
| 軌道高度 | 高度真正發揮作用的地方在可見性，因為仰角遮罩同時決定了覆蓋半角 λ、斜距與最長過頂，所以 550 km 的 25° 遮罩給出 λ = 8.45°、相當於 3.75 ms 的 1,123 km 斜距，以及最多 4.49 分鐘的天頂過頂，並對 4,408 顆衛星給出約 24 顆可見的均勻球面估計，這比 Tanveer 等人在中緯度實測的 35–44 顆低得多，因為 53° 殼層會把衛星集中到那些緯度附近。 |
| 鏈路建立 | 殼層以 Walker 記法描述，Delta 型處處同向運行，而 Star 型帶著一道反向運行的接縫，同時 550 km、53° 下每天 −4.49° 的 J₂ 進動讓營運商能低成本地建立軌道面，也讓 650 km 的晨昏 SSO 永遠照得到陽光。 |
| 評估條件 | 最重要的是，文獻中的每一個 Starlink 幾何都是同一個 1,584 顆殼層的三份凍結申請文件之一，而 2026 年 10 月 28 日在軌的 11,190 顆實飛星座分布在約 340–570 km，因此每個數字都需要附上它的申請文件、日期與證據標記。 |
Where these ideas go next
這些概念接下來用在哪裡
| Measure or comparison參數或比較項目 | Values, conditions and evidence數值、條件與證據 |
|---|---|
| Plane configuration | Chapter 2 takes the planes and phase offsets of Section 1.3 and turns them into inter-satellite link lengths with the chord formula. Changing from 24 planes of 66 to 72 planes of 22 increases intra-plane hop distance from 659 km to 1,969 km. The seam also constrains topology. |
| Slant range | Chapter 3 uses Section 1.2’s pass and slant-range geometry to explain fifteen-second terminal reassignment and measured latency changes. Section 4.5 turns Sections 1.4–1.6’s filed-versus-flown comparison into the checklist used by later chapters. |
| 軌道面配置 | 第 2 章把第 1.3 節的軌道面與相位偏移用弦長公式轉成星間鏈路長度，24 面各 66 顆與 72 面各 22 顆之間的配置差異，對應為每一段同面跳躍 659 km 對 1,969 km 的距離差異，接縫則成為拓樸限制。 |
| 斜距 | 第 3 章用第 1.2 節的過頂與斜距解釋為什麼終端每 15 秒就被重新指派，以及實測延遲為何如此變動，而第 4.5 節則把第 1.4–1.6 節「申請與實飛」的教訓變成之後每一章都遵循的檢查清單。 |
Papers behind this chapter本章所依據的論文
ACM HotNets 2018Delay is Not an Option: Low Latency Routing in Space
ACM CoNEXT 2019Network Topology Design at 27,000 km/hour
ACM IMC 2020Exploring the "Internet from Space" with Hypatia
Sources include capacity comparisons by del Portillo, Cameron and Crawley [12] and Pachler et al. (IEEE ICC Workshops 2021). Ali et al. supply the ephemeris census [16].
del Portillo、Cameron 與 Crawley 的容量比較[12]、Pachler 等人的比較（IEEE ICC Workshops 2021），以及 Ali 等人的星曆普查[16]的數字與來源直接收錄於第 1.4 及 1.6 節，作為本教材對這些研究的介紹。