Chapter 2 of 13 · Part I · The physics

第 2 章（共 13 章）· 第一部 · 物理

Inter-satellite links: geometry, propagation delay, the laser link budget and the +Grid星間鏈路：幾何、傳播延遲、雷射鏈路預算與 +Grid

Calculate inter-satellite hop lengths and one-way delays from plane and satellite counts. Use a far-field optical link budget to estimate the supported bit rate. Compare demonstrated laser rates by evidence type, then examine how acquisition time limits practical constellation topologies.本章從軌道面數與每面衛星數計算星間跳躍長度及單向延遲，再以遠場光學鏈路預算估計可支撐的位元率。雷射速率依證據類型比較，擷取時間則用來判斷星座拓樸的實作條件。

≈ 25 min · 2 panels · 8-question quiz≈ 25 分鐘 · 2 個面板 · 8 題測驗Jump to the quiz ↓跳到測驗 ↓

Before you start

開始之前

This chapter builds on Chapter 1. The orbital radius, the plane count of a shell and the seam of a polar constellation are used on almost every page below. Each chip links to its definition.

本章建立在第 1 章之上。軌道半徑、一個殼層的軌道面數，以及極軌星座的接縫，幾乎在下面每一頁都會用到。點選即可回到它的定義。

LEO低地球軌道（LEO）1 orbital plane軌道面1 shell殼層1 inclination傾角1 slant range斜距1 seam接縫1

New terms in this chapter (15)本章新名詞（15）

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。

Inter-satellite link (ISL)星間鏈路（ISL） A direct radio or laser link between two satellites, so traffic can cross the constellation entirely through space. 兩顆衛星之間直接的無線電或雷射鏈路，讓流量沿太空鏈路穿越星座。
Propagation delay傳播延遲 Distance divided by the speed of light in the medium. In vacuum 3.336 µs per kilometer. 距離除以介質中的光速。真空中每公里 3.336 µs。
Node delay節點延遲 Time a packet spends inside a satellite between arriving on one link and leaving on another. Unmeasured for Starlink. 封包從一條鏈路進入衛星到從另一條鏈路離開所花的時間。Starlink 的值仍待量測資料。
+Grid+Grid The topology that links each satellite to its two intra-plane neighbors and the same-index satellite in each adjacent plane. 把每顆衛星連到同面的兩個鄰居，以及相鄰兩面中同一編號衛星的拓樸。
Link budget鏈路預算 The accounting, in decibels, of transmit power, antenna gains and losses that yields received power. 以分貝記帳發射功率、天線增益與各項損耗，最後得到接收功率的計算。
Aperture口徑 The diameter of the telescope that launches or collects the beam. Gain scales with its square. 發射或收集光束的望遠鏡直徑。增益與其平方成正比。
Divergence發散角 The full angle over which a beam spreads, about 1.22λ/D for an aperture D. 光束擴散的全角，對口徑 D 約為 1.22λ/D。
Near field近場 Ranges shorter than the aperture's Fresnel distance, where the beam remains concentrated and requires a near-field model. 比口徑的 Fresnel 距離更短的範圍，光束仍集中，需要使用近場模型。
Pointing, acquisition and tracking (PAT)指向、擷取與追蹤（PAT） The control problem of aiming a microradian beam at a partner thousands of kilometers away and holding it there. 把微弧度級的光束對準數千公里外的對象並持續鎖住的控制問題。
Acquisition擷取 The search phase in which two terminals find each other's beam before data can flow. Seconds to tens of seconds today. 兩個終端在資料流動之前互相找到對方光束的搜尋階段。目前需要數秒到數十秒。
Point-ahead angle預指向角 The offset 2v_t/c between where a partner is seen and where the beam must be sent, because light takes time to arrive. 因光需要時間抵達，光束必須送往的方向與看到對象的方向之間相差的角度 2v_t/c。
Doppler shift多普勒頻移 The optical frequency offset v_r/λ caused by range rate. 0.645 GHz per km/s at 1,550 nm. 由距離變化率造成的光頻偏移 v_r/λ。在 1,550 nm 為每 km/s 0.645 GHz。
MotifMotif A local link pattern repeated identically by every satellite, searched over as an alternative to +Grid. 每顆衛星都以相同方式重複的局部連線樣式，作為 +Grid 之外的搜尋對象。
Temporary ISL暫時性星間鏈路 A link to a satellite that is only briefly within range, such as one in a crossing plane. 與只短暫進入範圍的衛星（例如交叉軌道面上的衛星）之間的鏈路。
DWDMDWDM Dense wavelength-division multiplexing: many independent channels on one beam, spaced 100 GHz or less apart. 高密度分波多工：在同一道光束上放多個獨立通道，間距 100 GHz 或更小。

2.1Latency is geometry: vacuum versus fiber, and the length of a hop延遲就是幾何：真空對光纖，以及一跳的長度

Recall

回顧

Section 1.1 gives the 550 km shell’s orbital radius, 6,921 km, period, 95.65 min, and speed, 7.585 km/s. Section 1.3 introduces planes, Walker patterns and seams. Section 1.4 explains the Phase I geometries 24 × 66 and 72 × 22.

第 1.1 節給出 550 km 高度的軌道半徑 6,921 km、週期 95.65 min 與速度 7.585 km/s，第 1.3 節介紹了軌道面、Walker 樣式與接縫，第 1.4 節則解釋了為什麼 24 × 66 與 72 × 22 這兩種 Phase I 幾何同時在文獻中流傳。

An inter-satellite link (ISL) directly connects two satellites by radio or laser. propagation delay equals distance divided by light speed in the medium. Satellite paths include ascent to the shell and descent to Earth. These extra slant ranges explain the roughly 3,000 km crossover. The per-kilometer advantage becomes useful once the great-circle distance offsets this extra travel.星間鏈路（ISL）是兩顆衛星之間直接的無線電或雷射連線，其基本時間成本是傳播延遲，也就是距離除以介質中的光速。3,000 km 這個門檻之所以存在，是因為衛星路徑得先爬到殼層再下來，比光纖路徑多出兩段斜距。因此大圓距離須足夠長，才能以每公里的速度優勢抵銷額外路程。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Evaluation conditions	In vacuum that speed is 299,792,458 m/s. Vacuum propagation takes 3.336 µs per kilometer. Fiber with refractive index 1.4675 takes 4.895 µs per kilometer, as used by Bhattacharjee et al. ^{[32, §II]} preprint.
Evaluation conditions	The speed ratio equals the refractive index, giving vacuum a 46.75% advantage per kilometer. Handley rounds this to "about 47%". He argues satellite paths "may beat any terrestrial fiber path for distances beyond about 3,000 km" ^{[3, §4]}.
評估條件	真空中的光速是 299,792,458 m/s，所以每公里花 3.336 µs，而在折射率 1.4675 的光纖裡^{[32, §II]}preprint，光走一公里要 4.895 µs。
星座配置	兩者的比值正是折射率本身，所以真空每公里快 46.75%，Handley 把它取整為「約 47%」，並由此推出這個領域的奠基主張：衛星路徑「在大約 3,000 km 以上的距離可能擊敗任何地面光纖路徑」^{[3, §4]}。

node delay is the time a packet spends inside a satellite between incoming and outgoing lasers. Public SpaceX measurements are needed to establish this quantity. Chaudhry and Yanikomeroglu assume 10 ms per satellite hop, including 1 ms processing ^{[33, §IV]} . Bhattacharjee et al. assume 1 ms ^[32] preprint .

Propagation-only studies, including Hypatia, StarCDN and SpaceMoE, assume zero. Across a 23-hop +Grid path, these assumptions differ by more than 200 ms, exceeding propagation delay. Each end-to-end ISL estimate therefore needs its node-delay assumption. This primer identifies that assumption throughout.

ISL 路徑的第二項是節點延遲，也就是封包從一道雷射進入衛星到從另一道雷射離開所花的時間，其公開量測證據仍待補充。Chaudhry 與 Yanikomeroglu 假設每個衛星跳躍 10 ms，其中 1 ms 是處理時間^{[33, §IV]}，Bhattacharjee 等人假設 1 ms^[32]preprint，而 Hypatia、StarCDN 與 SpaceMoE 這類只算傳播的研究則假設為零。在一條 23 跳的 +Grid 路徑上，這幾種慣例之間的差距超過 200 ms，比它們所疊加的傳播延遲還大，所以你讀到的任何端到端 ISL 延遲都必須附上它的節點延遲假設，而本教材每一次都會標示出來。

How long is one hop? The +Grid gives each satellite two links to fore-and-aft neighbors within its plane. Two further links reach same-index satellites in adjacent planes ^{[3, §3]} ^{[6, §3.1]}. Section 2.5 examines this baseline. A paper's hop length therefore tells you which filing it froze, and the two geometries put the long link on different terminals.一跳有多長？我們現在先定義、到第 2.5 節再細看的標準拓樸是 +Grid：每顆衛星保持兩條鏈路連到同面前後的鄰居，再以兩條鏈路連到左右相鄰兩面中編號相同的衛星[3, §3][6, §3.1]。因此一篇論文的跳躍長度會告訴你它凍結的是哪一份申報，而這兩種幾何把長鏈路放在相異的終端上。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Constellation configuration	Equal-altitude satellites have chord separation \(d = 2(R_E+h)\sin(\psi/2)\). Here \(\psi\) is their angular separation viewed from Earth’s center. Thus, the hop length is fixed by how many satellites share a plane and how many planes share the shell.
Plane configuration	The November 2018 filing uses 24 × 66. Its intra-plane chord is 2 × 6,921 km × sin(π/66) = 659 km. Chaudhry and Yanikomeroglu report 659.5 km ^{[33, §I, III]}. At the equator, same-index inter-plane links span 15° and 1,807 km.
Constellation configuration	The August 2019 filing uses 72 × 22. Intra-plane distance grows to 1,969 km, matching Ali and Zhang’s "about 1,950 km". Adjacent planes are 5° apart, giving 604 km equatorial separation, their "about 600 km" ^{[34, §1, 3]} preprint.
軌道高度	同一高度的兩顆衛星之間相隔軌道球面上的一條弦 \(d = 2(R_E+h)\sin(\psi/2)\)，其中 \(\psi\) 是從地心看兩者的夾角，所以跳躍長度由同一面有多少衛星、同一殼層有多少面所決定。
評估條件	對 2018 年 11 月申報的 24 × 66 幾何，同面弦長是 2 × 6,921 km × sin(π/66) = 659 km，Chaudhry 與 Yanikomeroglu 印出的是 659.5 km^{[33, §I, III]}，而同編號的面間弦在赤道跨越面與面之間的 15°，達到 1,807 km。
星座配置	對 2019 年 8 月申報的 72 × 22 幾何，角色對調：每面只有 22 顆衛星，同面弦長增到 1,969 km，對應 Ali 與 Zhang 的「約 1,950 km」，而 72 個相隔 5° 的面在赤道只相距 604 km，就是他們的「約 600 km」^{[34, §1, 3]}preprint。

The inter-plane distance varies along the orbit. The ratio is computed from the spherical geometry in the table below.面間距離隨軌道位置改變。比值由下表的球面幾何算出。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Constellation configuration	Same-index satellites in planes separated by \(\Delta\Omega\) are farthest apart at the equator and closest at maximum latitude. Minimum separation is approximately \(\cos i\) times maximum separation. At 53°, this ratio is 0.60 (Ali & Zhang, arXiv 2602.07756, Sec. 3, Fig. 4b, qualitative statement).
Path length and hops	At 53° latitude, the 72-plane shell’s 604 km equatorial hop shrinks to 363 km. The 24-plane shell’s 1,807 km hop shrinks to 1,087 km. Both remain positive. This is the property that lets an inclined constellation keep its inter-plane links up all the way around the orbit.
Path length and hops	Line of sight sets the maximum hop. At 550 km, the link must clear Earth and an 80 km atmospheric exclusion layer. Using Earth radius 6,378 km gives 5,016 km maximum range ^{[17, Eq. 1, §IV.A]}. One-way propagation takes 16.7 ms.
星座配置	相隔 \(\Delta\Omega\) 的兩個面上同編號的兩顆衛星，在同時越過赤道時相距最遠，在同時到達最高緯度時相距最近，而對一個傾斜殼層來說兩者的比值約為 \(\cos i\)，在 53° 時等於 0.60（Ali 與 Zhang，arXiv 2602.07756，Sec. 3，Fig. 4b 給出定性敘述。
路徑長度與跳數	因此 72 面殼層 604 km 的赤道跳躍在 53° 緯度縮為 363 km，24 面殼層 1,807 km 的跳躍縮為 1,087 km，且兩者皆維持正值，這正是讓傾斜星座能在整圈軌道上維持面間鏈路的性質。
路徑長度與跳數	任何一跳的上限是視線：550 km 高的兩顆衛星只有在兩者之間的直線能避開大氣時才互相可見，取 80 km 的排除層與 6,378 km 的地球半徑，這個上限是 5,016 km^{[17, Eq. 1, §IV.A]}，這一跳單向要花 16.7 ms。

Question問題	Calculation算式	Result結果
Propagation delay per km, vacuum真空中每公里的傳播延遲	\(1/c = 1/(299{,}792{,}458\ \text{m/s})\)	3.336 µs/kmcomputed. C from the OJCOMS 2022 text計算值。c 取自 OJCOMS 2022 內文
Propagation delay per km, fiber光纖中每公里的傳播延遲	\(n/c,\ n = 1.4675\)	4.895 µs/km, +46.75%computed. N from ^[32]計算值。n 取自 ^[32]
Intra-plane chord, 66 per plane同面弦長，每面 66 顆	\(2 \times 6{,}921\ \text{km} \times \sin(\pi/66)\)	659 km → 2.20 mscomputed. R = 6,371 + 550 km計算值。R = 6,371 + 550 km
Intra-plane chord, 22 per plane同面弦長，每面 22 顆	\(2 \times 6{,}921\ \text{km} \times \sin(\pi/22)\)	1,969 km → 6.57 mscomputed. Ali & Zhang print "about 1,950 km"計算值。Ali 與 Zhang 印出「約 1,950 km」
Inter-plane chord at the equator, 24 planes赤道上的面間弦長，24 面	\(2 \times 6{,}921\ \text{km} \times \sin(15^\circ/2)\)	1,807 km → 6.03 mscomputed. ΔΩ = 360°/24計算值。ΔΩ = 360°/24
Inter-plane chord at the equator, 72 planes赤道上的面間弦長，72 面	\(2 \times 6{,}921\ \text{km} \times \sin(5^\circ/2)\)	604 km → 2.01 mscomputed. Ali & Zhang print "about 600 km"計算值。Ali 與 Zhang 印出「約 600 km」
Same chords at the highest latitude, i = 53°同一弦在最高緯度，i = 53°	\(\cos\psi = \cos\Delta\Omega\cos^2 i + \sin^2 i\)	1,087 km / 363 km, ratio 0.60 ≈ cos icomputed. Same-index pair at argument of latitude 90°計算值。同編號衛星在緯度幅角 90° 處
Line-of-sight limit at 550 km550 km 的視線極限	\(2\sqrt{(R_E+h)^2-(R_E+80\ \text{km})^2}\)	5,016 km → 16.7 mscomputed. R_E = 6,378 km and 80 km layer as in ^{[17, Eq. 1]}計算值。R_E = 6,378 km 與 80 km 排除層同 ^{[17, Eq. 1]}

Figure 2.1. The +Grid neighborhood of one satellite in the two Starlink Phase I geometries. Moving from 24 planes of 66 to 72 planes of 22 triples the intra-plane hop and divides the inter-plane hop by three. Thus, the terminal that carries the long, power-hungry link changes.圖 2.1。兩種 Starlink Phase I 幾何中一顆衛星的 +Grid 鄰域。從 24 面各 66 顆改為 72 面各 22 顆，同面跳躍變成三倍、面間跳躍縮為三分之一，所以承擔那條又長又耗功率鏈路的終端換了。Sources來源: ^[34] ^[33]

Original figure note原始圖說出處

Drawn for this primer from the chord lengths computed in the table above. Filings per Ali & Zhang, arXiv 2602.07756, Sec. 3 and Chaudhry & Yanikomeroglu, OJCOMS 2022, Sec. III.

End-to-end simulations of these grids generally model propagation and an assumed node delay. Section 3.3 takes up that story. Here the point is that geometry sets a floor, and the floor is rarely what a user measures.這類網格的端到端延遲模擬，通常以傳播延遲加上假設的節點延遲計算。第 3.3 節會接續這個故事。這裡的重點是幾何設定了下限，而使用者量到的很少是這個下限。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Path length and hops	Handley’s 1,150 km Phase 1 design gives New York–London RTT of 57–66 ms. Great-circle fiber gives 55 ms and measured Internet gives 76 ms ^{[3, Fig. 7]}. Ali and Zhang use 90 days of real Shell-1 ephemerides. Their four-terminal +Grid averages 89.0 ms and 23.4 hops, against 52.9 ms and 8.2 hops for stable links ^{[34, §5.5]} preprint.
Evaluation conditions	A Seychelles terminal routed through Nigeria’s PoP had minimum RTT of 181 ms. A direct laser path would give about 40 ms (Izhikevich et al., Proc. ACM MACS 8(1) / SIGMETRICS 2024, §7.2). The laser path exists, while routing policy sends traffic to a distant gateway.
評估條件	Handley 在 1,150 km Phase 1 設計上的紐約到倫敦路徑得到 57–66 ms 的往返時間，相對於大圓光纖的 55 ms 與實測網際網路的 76 ms^{[3, Fig. 7]}。
路徑長度與跳數	而在 90 天的真實 Shell-1 星曆上，Ali 與 Zhang 發現四終端 +Grid 在城市對之間平均 89.0 ms、23.4 跳，他們的穩定鏈路設計則只需 52.9 ms、8.2 跳^{[34, §5.5]}preprint。
PoP 覆蓋	真實網路是另一回事：一個流量落在奈及利亞 PoP 的塞席爾終端量到的最小往返時間是 181 ms，而直接雷射路徑大約只要 40 ms^{[35, §7.2]}，因為雷射路徑存在，但路由政策把流量送到了遙遠的閘道。

Panel 2.1面板 2.1

ISL hop lengths and one-way delayISL 跳躍長度與單向延遲

Planes P軌道面數 P

Satellites per plane S每面衛星數 S

Altitude高度

Latitude of the pair衛星對所在緯度

Intra-plane hop

同面跳躍

Inter-plane hop at this latitude

此緯度的面間跳躍

Inter-plane hop at the equator

赤道上的面間跳躍

Line-of-sight limit

視線極限

Hops across 180° of longitude

跨越 180° 經度的跳數

The intra-plane hop is the chord 2R sin(π/S). The inter-plane hop uses exact spherical geometry for equal argument of latitude and plane separation 360°/P. The d_{ashed approximation is d eq} cos(latitude). Delays are propagation only, with node delay set to zero. Phase offsets between planes, eccentricity and the real spread of altitudes are left out.同面跳躍是弦長 2R sin(π/S)。面間跳躍使用相隔 360°/P 的兩面上、位於相同緯度幅角的兩顆衛星的精確球面公式，虛線為 d_eq cos(緯度) 近似。延遲只含傳播，計算範圍排除節點延遲。面與面之間的相位偏移、偏心率與真實的高度分布皆列於模型範圍之外。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Model configuration	Model: circular orbits on a sphere of radius 6,371 km + altitude, inclination fixed at 53°, +Grid links between same-index satellites.
Evaluation conditions	The line-of-sight limit uses Chaudhry & Yanikomeroglu's 6,378 km radius and 80 km exclusion layer.
模型配置	模型：半徑 6,371 km + 高度的球面上的圓軌道，傾角固定 53°，+Grid 鏈路連接同編號衛星。
評估條件	視線極限採用 Chaudhry 與 Yanikomeroglu 的 6,378 km 半徑與 80 km 排除層。

Stop and think停下來想一想

Which terminal carries the longest link in each case, and by how much does the sum of the two hop delays change?兩種情況下最長的鏈路各自落在哪個終端？兩段跳躍延遲的總和改變了多少？

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Evaluation conditions	Set P = 24, S = 66 and then P = 72, S = 22, keeping the total at 1,584.
Path length and hops	Then raise the latitude to 53° in both and explain why the inter-plane hop stays at or above 0.60 of its equatorial value.
評估條件	先設 P = 24、S = 66，再設 P = 72、S = 22，總數都維持 1,584。
路徑長度與跳數	接著把兩者的緯度都調到 53°，解釋為什麼面間跳躍始終維持在赤道值的 0.60 倍以上。

2.2The optical link budget decides the rate光學鏈路預算決定速率

Geometry fixes how long a bit takes to arrive. The link budget, the decibel accounting of transmit power, antenna gains and losses, fixes how many bits can arrive per second. The price is that a spot that small must be aimed to a few microradians. This is the subject of Section 2.4.幾何決定一個位元要多久才到達。鏈路預算，也就是以分貝記帳發射功率、天線增益與各項損耗，則決定每秒能到達多少位元。發散角只有數十微弧度，所以飛行 2,000 km 後到達的光斑直徑是數十公尺，對照無線電的數十公里。代價是這麼小的光斑必須瞄準到幾微弧度，這是第 2.4 節的主題。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Evaluation conditions	A free-space optical link follows Friis form: \(P_R = P_T\,G_T\,G_R\,(\lambda/4\pi d)^2\,L_{\text{other}}\). For diffraction-limited aperture \(D\), gain is \(G \approx (\pi D/\lambda)^2\). Full divergence angle is \(\theta \approx 1.22\lambda/D\) ^{[36, p. 8, Eq. 1]}.
Aperture gain	Gain grows with the square of \(D/\lambda\). A 10 cm aperture at 1,550 nm gives 106 dB gain. A 0.3 m dish at 23 GHz gives 37 dB [computed below]. The divergence is tens of microradians, so the spot that arrives after 2,000 km is tens of meters across rather than tens of kilometers.
評估條件	對自由空間光鏈路而言，預算的形式與任何無線電鏈路相同的 Friis 式 \(P_R = P_T\,G_T\,G_R\,(\lambda/4\pi d)^2\,L_{\text{other}}\)，其中口徑為 \(D\) 的繞射極限望遠鏡增益是 \(G \approx (\pi D/\lambda)^2\)，而光束離開它時的全發散角是 \(\theta \approx 1.22\lambda/D\)^{[36, p. 8, Eq. 1]}。
評估條件	讓雷射勝出的兩個因素就寫在這些公式裡：增益隨 \(D/\lambda\) 的平方成長，所以 1,550 nm 的 10 cm 口徑有 106 dB 增益，而 23 GHz 的 0.3 m 碟形天線只有 37 dB［下方計算］。

The far-field formula applies beyond the aperture’s Fresnel distance. Within that distance, the beam remains concentrated in the near field.遠場公式只在口徑的 Fresnel 距離之外成立，在此距離之內光束仍集中，鏈路處於近場。面板 2.2 標出這個邊界並在其下方夾住公式。第 2.6 節再回頭談這個區域能做到什麼。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Evaluation conditions	For a symmetric confocal link, the waist lies midway between transceivers. Suncatcher gives Fresnel distance as \(L = \pi a^2/\lambda\). A 5 cm beam radius, or 10 cm aperture, at 1.55 µm gives about 5 km. This ideal calculation excludes beam quality, aperture truncation and pointing jitter ^{[36, p. 8]}. The arXiv and Joule versions agree.
Near-field link model	Formation links of 100–200 m lie deep within the near field. The receiving aperture collects almost all launched power within its extent. Applying \(1/d^2\) there would predict received power above transmitted power, so a near-field model is required.
Evaluation conditions	Panel 2.2 marks the boundary and clamps the formula below it. Section 2.6 returns to what this regime makes possible.
評估條件	對於光束腰位於兩個收發機正中間的對稱共焦鏈路，Suncatcher 的作者把這個距離寫成 \(L = \pi a^2/\lambda\)，在 1.55 µm 下對 5 cm 的光束半徑（即 10 cm 口徑）約為 5 km，這是忽略光束品質、口徑截斷與指向抖動的最佳情況^{[36, p. 8]}，論文的 arXiv 版與 Joule 版在這個值上一致。
近場鏈路模型	因此編隊飛行衛星之間 100–200 m 的鏈路深處於近場，發出的功率幾乎全部被接收口徑收集（除了被口徑截掉的部分），所以 \(1/d^2\) 公式會預測出比發射還多的接收功率，該區域須改用近場模型。

A worked budget shows where the commercial rates come from.一份完整算出的預算能說明商用速率從哪裡來。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Power budget	Assume a Starlink-class terminal with 1 W transmit power, two 10 cm apertures and 2,000 km range. Add Suncatcher’s 3 dB optical/coupling loss and a further 3 dB pointing allowance.
Evaluation conditions	Each aperture contributes 106.1 dB, the free-space term costs 264.2 dB. The result is −28.0 dBm. Received power is 1.58 µW, or 1.23 × 10¹³ photons per second. Each 1,550 nm photon carries 1.281 × 10 −19 J.
Power budget	Receiver photon requirements determine the data rate. Suncatcher estimates 196 photons per bit for commercial 400G PM-16QAM transceivers. On-off keying needs about 71, and the Shannon–Hartley limit is about 1.39. The infinite-bandwidth, shot-noise limit equals 2 ln 2 ^{[36, p. 8, Fig. 1]} peer-reviewed. These requirements convert 1.58 µW into 63 Gbps, 174 Gbps and 8.9 Tbps.
Evaluation conditions	TBIRD’s measured 100 Gbps transceiver reached its FEC threshold near −41 dBm ^{[37, §II]}. The worked budget has 13 dB margin at 2,000 km. At 5,000 km, free-space loss rises 8 dB and margin falls to 5 dB.
Link or data rate	Dividing TBIRD’s threshold by 100 Gbps gives about 6 photons per bit. Its pre-amplified DP-QPSK receiver is much more sensitive than the 196-photon telecom receiver. Panel 2.2’s margin and rate tiles therefore describe separate receiver classes.
功率預算	取一個 Starlink 等級的終端：1 W 發射功率、兩端各 10 cm 口徑、2,000 km 距離、如 Suncatcher 論文假設的 3 dB 光學與耦合損耗，再加 3 dB 的指向誤差餘裕。
能量	每個口徑貢獻 106.1 dB，自由空間項耗掉 264.2 dB，結果是 −28.0 dBm，即 1.58 µW，以 1,550 nm 光子 1.281 × 10⁻¹⁹ J 的能量換算是每秒 1.23 × 10¹³ 個光子。
功率預算	這些接收功率能支撐的位元率取決於接收機每個位元需要多少光子：Suncatcher 論文估計 PM-16QAM（商用 400G 相干收發機所用的調變）約需 196 光子/位元，開關鍵控約 71，而 Shannon–Hartley 極限約 1.39，也就是無限頻寬、散粒雜訊極限下的 2 ln 2^{[36, p. 8, Fig. 1]}peer-reviewed，三者各自把 1.58 µW 換成 63 Gbps、174 Gbps 與 8.9 Tbps。
評估條件	唯一的實測錨點來自 TBIRD，它的 100 Gbps 收發機在約 −41 dBm 到達 FEC 門檻^{[37, §II]}，讓這份預算在 2,000 km 有 13 dB 的餘裕，到 5,000 km 時自由空間項多出 8 dB，餘裕縮為 5 dB。
鏈路或資料速率	把這個門檻除以 100 Gbps 只得到約 6 光子/位元，所以 TBIRD 的接收機（一個帶前置放大的 DP-QPSK 設計）與 196 光子的電信零件是各異且靈敏得多的等級，面板 2.2 的餘裕格與速率格各自描述一種接收機，兩者的接收能力各異。

Question問題	Calculation算式	Result結果
Aperture gain, D = 10 cm, λ = 1,550 nm口徑增益，D = 10 cm，λ = 1,550 nm	\(G = (\pi D/\lambda)^2\)	4.11 × 10¹⁰ = 106.1 dBcomputed. The Suncatcher paper's 105.1 dB implies ~80% aperture efficiency計算值。Suncatcher 論文的 105.1 dB 對應約 80% 口徑效率
Free-space term at 2,000 km2,000 km 的自由空間項	\((\lambda/4\pi d)^2\)	3.80 × 10⁻²⁷ = −264.2 dBcomputed. −272.2 dB at 5,000 km計算值。5,000 km 時為 −272.2 dB
Received power, 1 W, two 10 cm apertures, 6 dB losses接收功率，1 W、兩個 10 cm 口徑、6 dB 損耗	\(0 + 106.1 + 106.1 - 264.2 - 6\ \text{dBW}\)	−58.0 dBW = −28.0 dBm = 1.58 µWcomputed. 3 dB other loss per Suncatcher (Joule p. 8), 3 dB pointing allowance計算值。3 dB 其他損耗依 Suncatcher（Joule p. 8），3 dB 指向餘裕
Photon rate at 1,550 nm1,550 nm 的光子速率	\(P_R / (hc/\lambda)\)	1.23 × 10¹³ photons/scomputed. Photon energy 1.281 × 10⁻¹⁹ J計算值。光子能量 1.281 × 10⁻¹⁹ J
Supportable rate at 196 / 71 / 1.39 photons per bit在 196 / 71 / 1.39 光子/位元下可支撐的速率	\(\dot n / \text{PPB}\)	63 Gbps / 174 Gbps / 8.9 Tbpscomputed. PPB values for PM-16QAM, OOK and the Shannon–Hartley limit from Suncatcher (Joule p. 8, Fig. 1)計算值。PM-16QAM、OOK 與 Shannon–Hartley 極限的 PPB 取自 Suncatcher（Joule p. 8，Fig. 1）
Margin above TBIRD's −41 dBm threshold高於 TBIRD −41 dBm 門檻的餘裕	\(-28.0 - (-41.0)\)	13 dB at 2,000 km. 5 dB at 5,000 kmcomputed. Threshold from Schieler et al. ICSOS 2023 Sec. II計算值。門檻取自 Schieler 等人 ICSOS 2023 Sec. II
Photons per bit implied by that threshold該門檻隱含的每位元光子數	\(10^{-4.1}\ \text{mW} / (1.281\times10^{-19}\ \text{J} \times 10^{11}\ \text{bit/s})\)	≈ 6.2 photons/bitcomputed. A pre-amplified coherent receiver, a distinct design from the 196-PPB COTS part計算值。這是帶前置放大的相干接收機，與 196 PPB 的 COTS 零件屬於相異設計
Spot diameter at 2,000 / 5,000 km2,000 / 5,000 km 處的光斑直徑	\(\theta d,\ \theta = 1.22\lambda/D = 18.9\ \mu\text{rad}\)	38 m / 95 mcomputed. Suncatcher (Joule p. 8) gives the same 95 m at 5,000 km but calls it the minimum spot radius計算值。Suncatcher（Joule p. 8）在 5,000 km 給出同樣的 95 m，但稱之為光斑半徑的下限
Gain of a 0.3 m Ka-band dish at 23 GHz23 GHz、0.3 m Ka 頻段碟形天線的增益	\((\pi \times 0.3 / 0.013)^2\)	5.2 × 10³ = 37 dBcomputed. About 70 dB per end below the 10 cm optical aperture計算值。比 10 cm 光學口徑每端低約 70 dB

Figure 2.2. The waterfall starts with 1 W. Two 10 cm apertures add 212 dB, while 2,000 km of free space removes 264 dB. Losses remove another 6 dB, leaving 1.58 µW. This is 13 dB above TBIRD’s 100 Gbps decoding threshold.圖 2.2。以瀑布圖呈現的鏈路預算：1 W 進入，兩個 10 cm 口徑加上 212 dB，2,000 km 的自由空間扣掉 264 dB，再扣 6 dB 損耗，到達 1.58 µW，比 TBIRD 100 Gbps 接收機停止解碼的功率高 13 dB。Sources來源: ^[36] ^{[37, §II]}

Original figure note原始圖說出處

Drawn for this primer from the calc table above. Formula per Agüera y Arcas et al., Joule 2026, Eq. 1. Threshold per Schieler et al., ICSOS 2023, Sec. II.

Iridium’s four 23 GHz Ka-band crosslinks are the operational radio ISLs (eoPortal, Iridium NEXT). Their narrowband service prioritizes agility and weather independence over bit rate.Iridium 的四條 23 GHz Ka 頻段交叉鏈路仍是唯一運作中的無線電 ISL（eoPortal，Iridium NEXT），它們服務的是窄頻業務，對它而言靈活度與對天氣的耐受性比每秒位元數更重要。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Link or data rate	Suncatcher describes commercial terminals covering thousands of kilometers, with maximum rates from 1 Gbps to 100 Gbps ^{[36, pp. 3, 8]} peer-reviewed . This supports the plausibility of SpaceX’s claimed sustained 100 Gbps beyond 5,000 km with multi-watt amplifiers. Independent verification remains necessary. The authors place these rates below cluster requirements, which reach roughly 10 Tbps per link.
Capacity comparison	A radio link carrying 2.5 Gbps over 5,000 km needs at least 19 times the antenna diameter of a laser terminal. It also needs over twice the power and mass ^{[17, §II]}. This follows from the roughly 70 dB gain per end attributed to wavelength above.
鏈路或資料速率	這套算術就是為什麼長距離商用雷射終端落在 Suncatcher 作者描述的區間，這些終端通常為數千公里的鏈路距離設計，最高資料速率在 1 Gbps 到 100 Gbps 之間^{[36, pp. 3, 8]}peer-reviewed，為什麼 SpaceX 宣稱每道雷射在 5,000 km 以上持續 100 Gbps 在多瓦放大器下說得通且仍待獨立驗證，也是為什麼同一群作者斷定這類鏈路與緊密耦合 ML 叢集每秒數 Tb 的需求仍有差距，而他們的叢集每條鏈路需要約 10 Tbps 的量級。
容量比較	它也解釋了為什麼另一條路在容量上已被放棄：要在 5,000 km 上傳 2.5 Gbps，無線電鏈路需要至少 19 倍的天線直徑，以及超過兩倍於雷射終端的功率與質量^{[17, §II]}，這是上表歸因於波長本身的每端 70 dB 差距的結果。

Panel 2.2面板 2.2

Link budget calculator鏈路預算計算器

Transmit power發射功率

Aperture (both ends)口徑（兩端相同）

Range (log scale)距離（對數刻度）

Other losses incl. pointing其他損耗（含指向）

Photons per bit (Suncatcher, Joule p. 8)每位元光子數（Suncatcher，Joule p. 8）

Aperture gain, each end

每端口徑增益

Free-space term

自由空間項

Received power

接收功率

Spot diameter

光斑直徑

Supportable rate

可支撐速率

Margin vs TBIRD −41 dBm

相對 TBIRD −41 dBm 的餘裕

Near-field boundary

近場邊界

Below the near-field boundary π(D/2)²/λ, the symmetric confocal distance that the Suncatcher paper uses, the formula is clamped to its value at the boundary. This occurs because the beam remains concentrated inside it and the far-field expression would exceed the transmitted power.在近場邊界 π(D/2)²/λ（Suncatcher 論文採用的對稱共焦距離）以下，公式被夾在邊界處的值，因為在邊界內光束仍集中，遠場式會算出超過發射功率的結果。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Model configuration	Model: far-field Friis budget P_R = P_T G² (λ/4πd)² / L, with G = (πD/λ)². Fixed wavelength is 1,550 nm, divergence is 1.22λ/D, and photon energy is 1.281 × 10⁻¹⁹ J. Rate equals photon rate divided by photons per bit.
Power budget	The chart holds the current power, apertures and losses and sweeps the range from 0.1 to 5,000 km.
Evaluation conditions	The model excludes aperture efficiency, beam quality, truncation, background light and real receiver FEC behavior. The calculation table rounds terms to 0.1 dB. The panel’s default consequently differs by under 0.1 dB.
模型配置	模型：遠場 Friis 預算 P_R = P_T G² (λ/4πd)² / L，G = (πD/λ)²，λ 固定 1,550 nm，發散角 1.22λ/D，光子能量 1.281 × 10⁻¹⁹ J，速率 = 光子速率 ÷ 每位元光子數。
功率預算	圖表固定目前的功率、口徑與損耗，將距離從 0.1 掃到 5,000 km。
模型配置	口徑效率、光束品質、截斷、背景光與真實接收機的 FEC 行為皆列於模型範圍之外，而算表中的範例把每一項四捨五入到 0.1 dB，所以面板的預設值與它差距小於 0.1 dB。

Stop and think停下來想一想

Set range to 200 m. Use the clamp note to explain the received-power limit as range decreases. Identify the resulting rate limit.然後把距離設為 200 m，根據夾住的說明解釋為什麼鏈路縮短後接收功率會達到上限，以及在那裡改由什麼限制速率。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Evaluation conditions	Keep 1 W and 6 dB losses. Find the aperture giving 10 dB margin above −41 dBm at 5,000 km.
評估條件	維持 1 W 與 6 dB 損耗，找出讓 5,000 km 鏈路仍高於 −41 dBm 門檻 10 dB 的口徑。

2.3What has flown and what is specified已經飛過的與已經規範的

The rates in circulation come from three kinds of document, and the table tags each one. The per-laser rate in this primer rests on indirect SpaceX reports, with a primary document still required.流傳中的速率來自三類文件，表格為每一項加上標籤。同儕審查的飛行結果只存在於少數任務。標準與主管機關申報列出終端的性能要求，實際表現則須由量測確認。本教材的每道雷射速率依據為間接報導，SpaceX 原始文件仍待補充。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Evaluation conditions	Peer-reviewed flight results exist for a handful of missions, standards and regulatory filings specify what a terminal must do rather than what it did. The main Starlink figures come from secondary reports of Travis Brashears’s SpaceX talk at SPIE Photonics West on 30 January 2024. Other secondary sources relay the Starlink technology page.
Evaluation conditions	The one unambiguous record is TBIRD, a 3U payload on a 6U CubeSat that sent 200 Gbps
TBIRD: channel configuration	as two 100 Gbps DP-QPSK channels on COTS coherent transceivers
TBIRD: range and aperture	from about 450–530 km to a 1 m telescope with adaptive optics over 600–1,400 km
TBIRD: transferred data	moving a record 4.8 TB in a roughly five-minute pass and more than 33 TB with complete data recovery across 22 passes
TBIRD: power	while drawing 100 W ^{[37, §I–IV, Figs. 4–10]}.
Evaluation conditions	That pass averages 128 Gbps over 300 s [computed], and the mission's selective-repeat ARQ with 1,752 virtual channels kept the retransmission overhead below 1%. This is the number to remember when later chapters ask whether a transport protocol can afford a space link.
評估條件	而主導討論的 Starlink 數字則來自 SpaceX 的 Travis Brashears 在 2024 年 1 月 30 日 SPIE Photonics West 演講經記者報導的內容，或是由二手網站轉述的 Starlink 技術頁面。
TBIRD 酬載與速率	具明確量測紀錄的任務是 TBIRD：一個搭在 6U 立方衛星上的 3U 酬載，以 COTS 相干收發機上的兩個 100 Gbps DP-QPSK 通道送出 200 Gbps
TBIRD：距離與孔徑	從約 450–530 km 高度、經 600–1,400 km 的鏈路傳到一座配備自適應光學的 1 m 望遠鏡
TBIRD：過頂資料量	在約五分鐘的一次過頂中傳了創紀錄的 4.8 TB
TBIRD：活動總資料量	在 22 次過頂中完整復原超過 33 TB 的傳輸資料
TBIRD：功率	耗電 100 W^{[37, §I–IV, Figs. 4–10]}。
評估條件	那次過頂在 300 s 內平均 128 Gbps［計算值］，而該任務具 1,752 個虛擬通道的選擇性重傳 ARQ 把重傳負擔壓在 1% 以下，這是當後面章節評估傳輸協定在太空鏈路上的額外負擔時要記住的數字。

System系統	Rate and conditions速率與條件	Status狀態	Source來源
TBIRD	200 Gbps, LEO → ground, 600–1,400 km	flown 2022–23. 4.8 TB per pass, <10 µrad RMS pointing2022–23 年飛行。每次過頂 4.8 TB，指向 <10 µrad RMS	Schieler et al., ICSOS 2023 peer-reviewed
LCRD	1.244 Gbit/s DPSK, GEO, 10 cm telescope	operating since Dec 20212021 年 12 月起運作	eoPortal mission summary agency
EDRS / Tesat LCT	1.8 Gbit/s over 45,000 km, GEO ↔ LEO	operating. 5.6 Gbps homodyne BPSK shown LEO–LEO (TerraSAR-X–NFIRE)運作中。LEO–LEO 曾示範 5.6 Gbps 零差 BPSK（TerraSAR-X–NFIRE）	ESA statement agency. Kaushal & Kaddoum, IEEE COMST 2017, Sec. II.B peer-reviewed
SDA OCT v3.0.1	2.5 Gbps OOK-NRZ or 1.25 Gbps Manchester. ≥3 dB margin. ≤100 s cold start	standard, 19 Sep 2023, Tranche 1. Irradiance specified at 5,500 km標準，2023 年 9 月 19 日，Tranche 1。輻照度規範於 5,500 km	SDA OCT Standard v3.0.1, Tables 2-5, 3-2, reqs OCT-016/030–037 standard
Mynaric CONDOR Mk3	0.313–2.5 Gbps, >6,500 km, 80 mm aperture, 4 W optical	product page. Higher rates listed as upcoming產品頁面。更高速率列為即將推出	Mynaric product page company
Amazon Kuiper OISL	100 Gbps over ~1,000 km, KuiperSat-1 ↔ -2	demonstration, Dec 2023. Terminal count unpublished2023 年 12 月示範。終端數仍待公布	Amazon, 14 Dec 2023 company
SpaceX Starlink lasers	100 Gbps sustained, 200 Gbps peak per link. >5,400 km. ~9,000 lasers. 42 PB/day. ~266,141 acquisitions/day. 99% uptime	SPIE talk of 30 Jan 2024 as reported. Primary document required2024 年 1 月 30 日 SPIE 演講的報導。原始文件待補	TechSpot. Hackaday company via secondary
Starlink V2 Mini page	"three optical inter-satellite links", "up to 200 Gbps". >13,000 bidirectional links (2025 report)	company page relayed by a secondary site由二手網站轉述的公司頁面	NewSpace Economy, 29 May 2026 company via secondary

Two distinctions explain the rates. Both are the 2026 state of the art in their markets.比較速率時須掌握兩項差異。SpaceX 則在自家衛星之間跑專有的相干鏈路，速率達電信等級。兩者都是各自市場的 2026 年最先進水準。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Link or data rate	The standardized military rate and claimed commercial rate differ fortyfold because their requirements differ. SDA mandates direct-detection on-off keying, 3 dB margin and a 100 s cold-start budget for cross-vendor interoperability. SpaceX uses proprietary coherent links at telecom rates between its satellites.
Evaluation conditions	SpaceX’s figures are internally consistent and await independent verification. Daily traffic of 42 PB implies mean mesh traffic of 3.9 Tbps [computed]. The talk’s 5.6 Tbps therefore uses a peak or another definition (fact base Part C item 17). One preprint gives a range above the 5,016 km visibility limit. That figure requires a SpaceX source and falls outside this model (Part C item 15).
Model configuration	Ali and Zhang and StarCDN model 100 Gbps per laser direction, while TinyLEO uses 200 Gbps. These values retain their company-claim evidence tags.
鏈路或資料速率	第一，軍用標準速率與商用宣稱速率相差四十倍，是因為它們回答的是各異問題：SDA 標準規定一種簡單的直接偵測開關鍵控波形、3 dB 餘裕與 100 s 冷啟動預算，好讓各異廠商的終端能互通。
評估條件	第二，SpaceX 的數字內部一致但仍待外部驗證：每天 42 PB 換算為網狀網路平均 3.9 Tbps 的流量［計算值］，演講中的 5.6 Tbps 因此是峰值或各異定義（事實庫 Part C 第 17 項），而某篇預印本中出現、超過 5,016 km 視線極限的距離數字仍待 SpaceX 來源，本教材使用的數值範圍將其排除（Part C 第 15 項）。
評估條件	當後面的章節像 Ali 與 Zhang 和 StarCDN 一樣把 Starlink 雷射建模為每方向 100 Gbps，或像 TinyLEO 一樣採用 200 Gbps 時，它採用的是一項公司宣稱，證據標籤也跟著它走。

2.4Pointing, acquisition and the terminal count指向、擷取與終端數量

Pointing aims the telescope using partner ephemerides. Acquisition searches until each terminal detects its partner’s beam. Tracking then holds beam alignment against platform vibration through a closed loop requiring at least 1 kHz bandwidth ^{[38, §III]}. The transmitter must aim ahead of the partner's observed position.指向是根據星曆對對象位置的知識瞄準發射望遠鏡。擷取是兩個終端來回掃描直到各自偵測到對方光束的搜尋階段。追蹤則是之後對抗平台振動、把光束保持在中心的閉迴路，需要至少 1 kHz 的迴路頻寬^{[38, §III]}。發射端須瞄準對象觀測位置的前方。教科書公式依 Kaushal 與 Kaddoum Sec. II.B］。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Acquisition	A 38 m beam at 2,000 km must hit a 10 cm aperture moving at 7.6 km/s. Pointing, acquisition and tracking (PAT) maintains this alignment.
Accuracy	Required accuracy ranges from sub-microradian to a few microradians. Kaushal and Kaddoum specify "sub micro-radian pointing accuracy" (Sec. II.A). TBIRD maintained under 10 µrad RMS through 10 Hz bus feedback ^[37]. A 10 cm aperture has 18.9 µrad divergence, so a 10 µrad error already costs several decibels.
Constellation configuration	Light travels for \(d/c\) each way while the partner moves transversely by \(v_t \cdot 2d/c\). The required point-ahead angle is \(2v_t/c\). One transverse orbital velocity gives about 51 µrad, and counter-moving satellites give about 100 µrad, several beam widths. Co-moving neighbors within one plane have nearly zero transverse velocity and point-ahead [computed below. Textbook formula per Kaushal & Kaddoum Sec. II.B].
擷取	一道在 2,000 km 處寬 38 m 的光束必須落在一個以 7.6 km/s 飛行的 10 cm 口徑上，讓這件事成立的學問叫指向、擷取與追蹤（PAT）。
評估條件	要求的精度是次微弧度到幾微弧度：Kaushal 與 Kaddoum 要求「次微弧度的指向精度」（Sec. II.A），TBIRD 以 10 Hz 的回饋迴路對本體維持在 10 µrad RMS 以下^[37]，而 10 cm 口徑 18.9 µrad 的發散角意味著 10 µrad 的誤差已經要付出數個分貝的預算。
星座配置	光要 \(d/c\) 才到達，回程的信標又要同樣的時間，期間對象橫向移動了 \(v_t \cdot 2d/c\)，所以光束必須以預指向角 \(2v_t/c\) 超前：一個軌道速度的橫向運動約 51 µrad，兩顆反向運行的衛星約 100 µrad，是光束寬度的數倍，而同面同向的鄰居其橫向速度與預指向角都接近零［下方計算。

Stable +Grid links also ease coherent reception. The receiver’s pull-in range defines the operating limit. The slowly varying links sit comfortably inside it.這是 +Grid 的穩定鏈路之所以真的被建起來的另一個原因：操作限制由相干接收機的牽入範圍決定，而緩慢變化的鏈路落在此範圍之內。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Doppler shift	Range rate adds carrier Doppler shift \(v_r/\lambda\). At 1,550 nm, each km/s of closing speed shifts the carrier by 0.645 GHz [computed].
Frequency	Kaushal and Kaddoum report up to ±7.5 GHz between LEO and GEO. Oppositely moving LEO satellites can exceed this (Sec. II.B). TBIRD’s COTS receiver tolerated roughly −17 to +21 ppm, or ±3–4 GHz at 193 THz. Before each pass, it shifted its local oscillator about +1.5 GHz using ephemerides. This recovered 30% of its data ^{[37, §IV, Figs. 9–10]}.
Constellation configuration	A crossing link between counter-moving satellites at 10–15 km/s would see 6.5–9.7 GHz. This gives 33–50 ppm, beyond that receiver window. A same-index adjacent-plane link in the 53° shell varies from 604 to 363 km twice per orbit. Its range rate is about 0.27 km/s and Doppler shift about 0.17 GHz [computed].
頻率	距離變化率為相干接收機添了第二個問題，即載波的多普勒頻移 \(v_r/\lambda\)，在 1,550 nm 每 km/s 的接近速度就是 0.645 GHz［計算值］。
都卜勒補償	Kaushal 與 Kaddoum 引述 LEO 與 GEO 之間可達 ±7.5 GHz，並指出兩顆反向運行的 LEO 衛星會看到更多（Sec. II.B），而 TBIRD 在軌上展示了這對電信接收機的意義：它的 COTS 收發機只能容忍約 −17 到 +21 ppm 的窗口，在 193 THz 大約是 ±3–4 GHz，所以該任務在每次過頂前依星曆把本地振盪器預先偏移約 +1.5 GHz，並因此多救回 30% 的資料^{[37, §IV, Figs. 9–10]}。
星座配置	以 10–15 km/s 反向運行的衛星之間的交叉鏈路會看到 6.5–9.7 GHz，即 33–50 ppm，落在這個窗口之外。
頻率	而 53° 殼層中同編號相鄰面鏈路的長度每圈只在 604 與 363 km 之間振盪兩次，距離變化率約 0.27 km/s、頻移 0.17 GHz［計算值］。

Figure 2.3. Left, the point-ahead geometry: the beacon arriving from the partner shows where it was d/c ago. The transmit beam must lead that direction by 2v_t/c. Right, the three phases of link setup and the times published for each.圖 2.3。左：預指向幾何，從對象到達的信標顯示它在 d/c 之前的位置，發射光束必須比那個方向超前 2v_t/c。右：鏈路建立的三個階段與各階段已公布的時間。Sources來源: ^{[38, §II.B, III]} ^[32] ^[41]

Original figure note原始圖說出處

Drawn for this primer from Kaushal & Kaddoum, IEEE COMST 2017, Secs. II.B and III. Setup times from Bhattacharjee et al., arXiv 2301.05285, Sec. II and SDA OCT v3.0.1, OCT-016.

How long does setup take?建立需要多久？Handley 則記錄 EDRS「在一分鐘內」完成擷取^{[3, §3]}。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Evaluation conditions	Bhattacharjee et al. collect vendor acquisition figures ^{[32, §II]} preprint. Mynaric CONDOR requires about 30 s initially and about 2 s after orbital-parameter exchange. Tesat and General Atomics require "tens of seconds". Chaudhry and Yanikomeroglu give 2–30 s for next-generation terminals and "a few milliseconds" for a hypothetical later generation ^{[33, Tab. 1]}. SDA allows 100 s cold start (OCT-016) standard. Handley reports EDRS acquisition "in under a minute" ^{[3, §3]}.
Acquisition	SpaceX reports about 266,141 daily acquisitions across about 9,000 lasers through secondary SPIE coverage company via secondary . This implies roughly 30 acquisitions per laser daily, or one every 49 minutes [computed]. This is roughly half an orbit, suggesting most lasers maintain long-lived links. The talk reports some lasting weeks. A minority repoint about once per orbit.
鏈路建立	Bhattacharjee 等人彙整了廠商數字：Mynaric 的 CONDOR 第一次建立鏈路約需 30 s，交換過軌道參數後的後續鏈路約 2 s，而 Tesat 與 General Atomics 的終端需要「數十秒」^{[32, §II]}preprint。
評估條件	Chaudhry 與 Yanikomeroglu 把下一代終端列為 2–30 s，而「幾毫秒」只屬於再下一代的假設性終端^{[33, Tab. 1]}。
評估條件	SDA 標準允許冷啟動最多 100 s（OCT-016）standard。
擷取	SpaceX 自己的數字，據 SPIE 演講的報導約 9,000 道雷射每天約 266,141 次擷取company via secondary，換算為每道雷射每天約 30 次、即每 49 分鐘一次［計算值］，正好是半圈軌道，告訴你大多數 Starlink 雷射維持長壽命的鏈路（同一演講說有些持續數週），而少數每圈重新指向一次左右。

Question問題	Calculation算式	Result結果
Point-ahead for one orbital velocity of transverse motion一個軌道速度橫向運動的預指向角	\(2 v_t / c,\ v_t = 7.585\ \text{km/s}\)	50.6 µradcomputed. ≈ 101 µrad for counter-moving satellites at 15 km/s計算值。反向運行、15 km/s 時約 101 µrad
Doppler shift per km/s at 1,550 nm1,550 nm 每 km/s 的多普勒頻移	\(\Delta f = v_r/\lambda\)	0.645 GHz = 3.3 ppmcomputed. Carrier 193.4 THz計算值。載波 193.4 THz
Crossing link at 10 / 15 km/s closing speed接近速度 10 / 15 km/s 的交叉鏈路	\(10 \times 0.645,\ 15 \times 0.645\)	6.5 GHz (33 ppm) / 9.7 GHz (50 ppm)computed. TBIRD's receiver window was −17 to +21 ppm計算值。TBIRD 接收機的窗口為 −17 到 +21 ppm
Range rate of a same-index adjacent-plane link, 72 planes同編號相鄰面鏈路的距離變化率，72 面	\((604-363)\ \text{km} \times \pi / (95.65\ \text{min}/2)\)	≈ 0.27 km/s → 0.17 GHzcomputed. Sinusoidal approximation, two cycles per orbit計算值。正弦近似，每圈兩個週期
Acquisitions per laser per day每道雷射每天的擷取次數	\(266{,}141 / 9{,}000\)	≈ 30 per day, one per ≈ 49 mincomputed. Both inputs from the SPIE talk as reported by TechSpot計算值。兩個輸入皆來自 TechSpot 報導的 SPIE 演講
Average mesh traffic from 42 PB/day由每天 42 PB 推得的網狀平均流量	\(42\times10^{15} \times 8 / 86{,}400\ \text{s}\)	3.9 Tbpscomputed. The talk's 5.6 Tbps is a peak or a different definition計算值。演講中的 5.6 Tbps 是峰值或各異定義

Topology design also depends on the simultaneous link count per satellite. Starlink’s planned count has fallen as its design matured. The 2016 FCC filing listed five lasers, which Handley used in 2018. The 2018 filing reduced this to four.

Chaudhry and Yanikomeroglu, Bhattacherjee and Singla, and subsequent +Grid simulators used four. Starlink’s current technology page gives three optical ISLs per V2 Mini. Ali and Zhang and TinyLEO repeat this company figure. Each terminal serves one partner at a time.

A full +Grid therefore requires over three terminals per satellite. Section 2.5 examines Ali and Zhang’s results. The fact base models current Starlink with three terminals. Four-terminal results retain a legacy label, and five-terminal configurations belong to historical discussion.

拓樸設計者需要的最後一個量是一顆衛星同時能持有幾條鏈路，而對 Starlink 而言，隨著設計成熟這個數字一直在下降。2016 年的 FCC 申報列了五個雷射元件，Handley 在 2018 年以五條建構他的拓樸。2018 年的申報把數量修為四，Chaudhry 與 Yanikomeroglu、Bhattacherjee 與 Singla 都採用了這個數字，所有 +Grid 模擬器也都繼承了它。而目前的 Starlink 技術頁面寫每顆 V2 Mini 載有三條光學星間鏈路，Ali 與 Zhang 和 TinyLEO 的作者都從公司頁面轉述了這個數字。因為一個終端一次只服務一個對象，完整的 +Grid 需要超過三個終端，第 2.5 節會說明 Ali 與 Zhang 嘗試時發現了什麼。事實庫的規則是：為目前的 Starlink 建模時用三個終端，把四終端的結果標為舊版，五終端配置則限於歷史設計的討論。

Laser terminals per Starlink satellite每顆 Starlink 衛星的雷射終端數	Where the number comes from數字來源	Who models it哪些研究採用
5	2016 FCC filing, "five laser components"2016 年 FCC 申報，「五個雷射元件」 FCC filing	^{[3, §3]} (fifth link for crossing satellites)^{[3, §3]} （第五條鏈路給交叉衛星）
4	2018 FCC filing, cited in ^{[17, §II]}2018 年 FCC 申報，引述於 ^{[17, §II]} FCC filing	^{[1, §3.1, fn. 3]} . Hypatia . ^[40] . All +Grid tools^{[1, §3.1, fn. 3]} 。 Hypatia 。 ^[40] 。所有 +Grid 工具
3	Starlink technology page for V2 Mini, relayed by NewSpace Economy (29 May 2026)V2 Mini 的 Starlink 技術頁面，由 NewSpace Economy 轉述（2026 年 5 月 29 日） company via secondary	^{[34, §2]} . ^{[39, §2.1]}^{[34, §2]} 。 ^{[39, §2.1]}

2.5Topologies: +Grid, seams, motifs and temporary links拓樸：+Grid、接縫、motif 與暫時性鏈路

Recall

回顧

Section 1.3 distinguished the Walker Delta pattern. Its planes spread over 360° of right ascension, from the Walker Star pattern. Its planes spread over 180° and therefore meet at a seam where neighboring planes move in opposite directions.

第 1.3 節區分了軌道面分布在 360° 升交點赤經上的 Walker Delta 樣式，與分布在 180° 上、因此在相鄰面反向運行的接縫處相遇的 Walker Star 樣式。

The +Grid is attractive because all four of its links are quasi-static. Two intra-plane links connect satellites with fixed relative positions. Two inter-plane links connect same-index neighbors whose separation varies between equatorial and high-latitude values. Once acquired, these links can last an orbit or longer.

This is exactly the regime the acquisition times of Section 2.4 allow. Whether the breathing is survivable depends on the inclination. In polar Walker Star patterns such as Iridium, same-index separation scales with cosine of latitude and reaches zero at the pole. Across the seam, neighbors move in opposite directions.

Iridium links co-moving satellites, keeping four 23 GHz crosslinks on each side of the seam (eoPortal, Iridium NEXT).

+Grid 吸引人之處在於它的四條鏈路都是準靜態的。兩條同面鏈路連接相對位置固定的衛星，兩條面間鏈路連接同編號衛星，兩者的間距只在赤道值與高緯度值之間起伏，所以一旦擷取就能維持整圈軌道甚至更久，這正是第 2.4 節的擷取時間所允許的運作方式。承受這種間距變化的能力取決於傾角。在 Iridium 這類極軌 Walker Star 中，同編號間距隨緯度的餘弦縮小，在極點上方收縮為零，而在接縫處相鄰面朝反方向運行，所以 Iridium 只連接同向運行的衛星，它的四條 23 GHz 交叉鏈路始終維持在接縫同側（eoPortal，Iridium NEXT）。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Power budget	At 53° inclination, minimum separation is 0.60 of its equatorial value, allowing links to stay active at high latitude. A 72-plane shell needs an inter-plane budget for 604 km equatorial crossings. Its 1,969 km intra-plane links dominate the power budget.
Evaluation conditions	Handley identified the inclined seam analogue in 2018. A fifth laser bridging "the NE-bound and SE-bound meshes" in a 53° shell would be "often down while realigning" ^{[3, §3]}.
功率預算	在 Starlink 的 53° 殼層中，間距只縮到赤道值的 0.60，因此鏈路在最高緯度附近也能維持運作，面間鏈路預算只要按赤道穿越的 604 km（72 面殼層）設計即可，而 1,969 km 的同面鏈路主導了功率預算。
評估條件	Handley 在 2018 年就看到了接縫的傾斜版本：他觀察到第五道雷射必須橋接 53° 殼層的「東北向與東南向網格」，而且「在重新對準時經常中斷」^{[3, §3]}。

The +Grid is nonetheless only one point in a design space. Bhattacherjee and Singla search repeated local link patterns called motifs. These can reach several planes or indices away. They retain co-moving partners to preserve long link lifetimes.然而 +Grid 只是設計空間中的一個點。Bhattacherjee 與 Singla 搜尋了 motif，也就是每顆衛星都以相同方式重複、但可能連到相隔數個面或數個編號，相對於最近鄰居的連法形成另一種選擇的局部連線樣式，並保留只連同向對象的限制以維持鏈路壽命。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Path length and hops	The objective Φ1 sums traffic-weighted stretch and ISL hop count across city pairs. On 24 × 66 geometry, motifs vary across three latitude zones. Starlink improves over +Grid by 54% at 5,014 km and 40% at 2,006 km. The latter is the minimum +Grid connectivity range and the power-limited worst case. Kuiper improves 45% at 5,440 km and 4% at 1,761 km. A 40 × 40 reference +Grid averages stretch 1.25 and 10.57 hops ^{[1, §3.1, §4.3, §6, Tab. 1]}.
Power budget	Longer links require more power and reduce hops. Each hop adds an uncertain node delay and consumes two terminals. The motif results connect Section 2.2’s link budget with topology. Closing a 5,000 km link permits a sparser, faster graph.
路徑長度與跳數	以 Φ1（各城市對伸展比加 ISL 跳數的流量加權總和）在 24 × 66 幾何上衡量，當允許最長 5,014 km 的鏈路時，在三個緯度區各自變化的 motif 在 Starlink 上勝過 +Grid 54%，在 2,006 km 下勝出 40%，這是 +Grid 本身仍能連通的最短距離，也是論文對功率受限雷射設定的最壞情況，對 Kuiper（5,440 km 下 45%、1,761 km 下 4%）與一個 40 × 40 的參考星座增益較小，而 +Grid 在該參考星座上的平均伸展比為 1.25、跳數 10.57^{[1, §3.1, §4.3, §6, Tab. 1]}。
功率預算	教訓是：較長的鏈路耗更多功率但省掉跳數，而由於每一跳都加上一個數值待定的節點延遲並消耗兩個終端，motif 的結果其實是對第 2.2 節預算的直接論證：誰能閉合 5,000 km 的鏈路，誰就得到更稀疏、更快的圖。

temporary ISLs connect satellites that enter range briefly. Examples include crossing-plane partners and nearby-plane satellites at high latitude. A crossing-plane temporary link lasted about 283 s per STK encounter ^{[17, §IV.B]}. Acquisition must consume a small fraction of that interval to preserve the gain.另一種放寬是允許暫時性星間鏈路，也就是連到只短暫進入範圍的衛星，例如交叉面上的衛星或高緯度時鄰近面上的衛星。他們 STK 模擬中一條交叉面暫時鏈路每次相遇約持續 283 s^{[17, §IV.B]}，所以只有在鏈路能在這段時間的一小部分內建立時增益才是真的。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Neighbor counts	At 1,700 km range, a satellite has 10 permanent partners. Including temporary partners raises this to 22 at the equator and 40 at 47° latitude.
Whole-network link count	the whole 24 × 66 network holds 17,436 permanent links against 48,180 when temporary ones are included
Routing latency	and routing over all of them cuts average latency on intercontinental pairs by 14.6–23.5 ms
Sydney–São Paulo latency	Sydney to São Paulo falling from 180.78 to 157.35 ms with 10 ms of node delay per hop ^{[33, Tabs. 2–4, Fig. 16]}.
Link setup	Bhattacharjee et al. charge 1 s setup at each path change. New York–Istanbul mean latency then rises from 25.9 ms to 123.9 ms.
100 ms setup delay	with 100 ms it averages 35.7 ms
Fiber-equality setup threshold	Tolerable setup delay makes mean satellite latency equal to fiber. It ranges from 2.3 ms for New York–London at 1,500 km to 80.63 ms for New York–Hanoi at 5,016 km ^{[32, Figs. 2–4]} preprint.
Link setup	Against the 2–30 s of today's terminals those tolerances are three orders of magnitude away. This is why every paper that treats ISLs as instantly reconfigurable. Other topology and routing studies assume setup performance beyond current terminals (Part C item 56). These two groups explicitly model setup.
星座配置	Chaudhry 與 Yanikomeroglu 數了它們：在 1,700 km 的範圍內，一顆衛星有 10 個永久對象，但在赤道有 22 個永久加暫時對象、在 47° 緯度有 40 個。
評估條件	整個 24 × 66 網路有 17,436 條永久鏈路，含暫時鏈路則為 48,180 條。
延遲比較	在所有鏈路上路由可把洲際城市對的平均延遲降低 14.6–23.5 ms，雪梨到聖保羅在每跳 10 ms 節點延遲下從 180.78 降到 157.35 ms^{[33, Tabs. 2–4, Fig. 16]}。
鏈路建立	Bhattacharjee 等人把條件量化：若每次路徑改變都計入 1 s 的建立延遲，紐約到伊斯坦堡的平均延遲從 25.9 ms 變成 123.9 ms，100 ms 時平均 35.7 ms，而可容忍的建立延遲（定義為衛星路徑平均延遲等於光纖時的值）從 1,500 km 範圍下紐約–倫敦的 2.3 ms 到 5,016 km 下紐約–河內的 80.63 ms^{[32, Figs. 2–4]}preprint。
鏈路建立	相對於今日終端的 2–30 s，這些容忍值差了三個數量級，這就是為什麼每一篇把 ISL 當成可即時重組的論文（事實庫列出除這兩組之外的所有拓樸與路由研究，Part C 第 56 項）描述的都是一種建立性能超越現有硬體的終端。

Figure 2.4. Three ways to wire one satellite. The +Grid holds four nearest, long-lived links. A motif repeats a longer co-moving pattern on every satellite and trades link power for fewer hops. A temporary link to a satellite in a crossing plane exists for minutes and pays off only if acquisition drops to milliseconds.圖 2.4。三種為一顆衛星布線的方式。+Grid 持有四條最近、長壽命的鏈路。motif 在每顆衛星上重複一個更長的同向樣式，以鏈路功率換取更少的跳數。連到交叉面衛星的暫時性鏈路只存在數分鐘，唯有擷取縮短到毫秒才划算。Sources來源: ^{[1, §4.1, Fig. 6]} ^[33] ^[17] ^[32]

Original figure note原始圖說出處

Drawn for this primer from Bhattacherjee & Singla, CoNEXT 2019, §4.1 and Fig. 6. Chaudhry & Yanikomeroglu, VTM 2021, Sec. IV.B and OJCOMS 2022, Table 4. Bhattacharjee et al., arXiv 2301.05285.

The most recent evidence pushes the design space back toward stability. The +Grid is a baseline tied to a filing whose full deployment remained unrealized. SpaceX’s orbital topology remains proprietary ^{[39, §2.1]}. Section 5.2 treats topology papers as a design space.最新的證據把設計空間推回穩定的一側。結論就是本教材從此採用的框架：+Grid 是對一份完整部署仍待實現的申報校準的建模基準，SpaceX 的在軌拓樸仍屬專有資訊^{[39, §2.1]}，而第 5.2 節把拓樸論文當成設計空間，並另行核對實際部署。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Path length and hops	Ali and Zhang use 90 days of real Shell-1 ephemerides from October–December 2024. Their links remain feasible for an entire orbit. Stable links give 52.9 ms and 8.2 hops, while simulated annealing gives 49.3 ms and 12.0 hops. The +Grid gives 89.0 ms and 23.4 hops. At 100 Gbps per direction, max-min-fair capacity rises from 7.5 Tbps to 17.5 Tbps.
Evaluation conditions	With three terminals, the alternating three-link grid becomes disconnected on real data. Stable links retain 77–80 ms latency ^{[34, §5.5–5.6, Tabs. 2–3]} preprint.
評估條件	Ali 與 Zhang 只用在整圈軌道上都可行的鏈路建構拓樸，資料是 2024 年 10 到 12 月共 90 天的真實 Shell-1 星曆。
路徑長度與跳數	在這些資料上，他們的穩定鏈路設計與模擬退火設計各自達到 52.9 ms、8.2 跳與 49.3 ms、12.0 跳，相對於 +Grid 的 89.0 ms、23.4 跳，而在每 ISL 方向 100 Gbps 下最大最小公平容量為 17.5 Tbps 對 7.5 Tbps。
星座配置	在每顆衛星三個終端時，交替的三鏈路網格在真實資料上分成多個連通分量，穩定鏈路設計仍能以 77–80 ms 運作^{[34, §5.5–5.6, Tabs. 2–3]}preprint。

2.6Short links: the Suncatcher regime短距鏈路：Suncatcher 的區域

Fig. 1）。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Evaluation conditions	The earlier budgets cover hundreds to thousands of kilometers. Free-space losses of 264–272 dB limit long-range terminals to roughly 100–200 Gbps (Section 2.2).
Constellation configuration	Project Suncatcher reduces link distance by four orders of magnitude. Its 81-satellite planar lattice has roughly 1 km radius in a 650 km dawn–dusk orbit. Nearest-neighbor spacing varies from roughly 100 to 200 m twice per orbit ^{[36, pp. 2–4]}.
Power budget	A 10 cm aperture at 100–200 m lies within its roughly 5 km confocal near field (Section 2.2). Received power is sufficient for the link. To a telecom transceiver, the connection resembles a long fiber patch cord.
Bench-test rate	The authors' bench test with off-the-shelf components reached 800 Gbps per direction, 1.6 Tbps bidirectional, over a short free-space path (p. 3).
DWDM design target	The target is roughly 10 Tbps per link from 24 × 400G channels. DWDM means dense wavelength-division multiplexing, here on a 100 GHz grid
100 GHz and 75 GHz grids	which gives 9.6 Tbps bidirectional, or 12.8 Tbps on a 75 GHz grid
Received-power requirement	with a required received power of about −20 dBm per channel, roughly 0.24 mW for all 24 channels
Pointing requirement	and a pointing accuracy of about 1.0 µrad. Beam wander stays within 10% of the 5 cm beam radius at 5 km. Commercial long-range terminals already demonstrate this accuracy (p. 8).
Power budget	With sufficient power, capacity depends on independent beams per aperture. A 10 cm aperture supports a 2 × 2 array of 5 cm systems at 1.25 km. It supports a 4 × 4 array of 2.5 cm systems at 0.32 km. Sub-aperture imaging resolution sets these ranges. Coherent detection rejects adjacent-beam crosstalk, and total bandwidth scales inversely with distance (pp. 3, 8. Fig. 1).
評估條件	以上一切都假設鏈路長達數百到數千公里，而第 2.2 節的預算顯示這類鏈路每個終端的上限約在 100–200 Gbps，因為自由空間項耗掉 264–272 dB。
星座配置	Google 的 Project Suncatcher 走相反的路，把距離縮小四個數量級：81 顆衛星在 650 km 的晨昏軌道上以約 1 km 半徑的平面晶格飛行，最近鄰間距每圈在約 100 到 200 m 之間振盪兩次^{[36, pp. 2–4]}。
功率預算	在 100–200 m 處，10 cm 的口徑完全處於自身近場之內（依第 2.2 節的共焦公式，近場延伸約 5 km），所以接收功率已足以支撐鏈路，鏈路對電信收發機來說就像一條很長的光纖跳線。
功率預算	作者用現成元件做的桌上測試在短距自由空間路徑上達到每方向 800 Gbps、雙向 1.6 Tbps（p. 3），設計目標是每條鏈路約 10 Tbps 的量級，來自 24 × 400G 的 DWDM 通道，即在 100 GHz 格點上的高密度分波多工，得到雙向 9.6 Tbps，75 GHz 格點則為 12.8 Tbps，每通道所需接收功率約 −20 dBm，24 個通道合計約 0.24 mW，指向精度則需約 1.0 µrad，才能在 5 km 處把光束漂移限制在 5 cm 光束半徑的 10% 以內，而這在商用長距離終端已展示的能力範圍之內（p. 8）。
功率預算	因為功率充裕，限制變成一個口徑能容納多少道獨立光束：單一 10 cm 口徑可在 1.25 km 容納 2 × 2 的 5 cm 系統陣列，或在 0.32 km 容納 4 × 4 的 2.5 cm 系統陣列，這些距離由每個子口徑的成像解析度決定，而相干偵測會抑制相鄰光束的串音，所以總頻寬與距離成反比（pp. 3, 8。

The evidence supports the link demonstration and leaves the cluster design open. The paper specifies per-link rate. Fabric design still requires terminal counts, switching during lattice motion and a collective-operation latency budget (fact base Part D item 21).此處須區分鏈路示範與叢集設計的證據範圍。而且該論文規範每條鏈路的速率，整體網路結構則仍待說明：每顆衛星帶幾個終端、晶格起伏時鏈路如何切換、跨越整個叢集的集體運算延遲預算長什麼樣，皆仍待說明（事實庫 Part D 第 21 項）。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Bench and flight evidence	The 1.6 Tbps figure is a bench test in a company-authored paper. A peer-reviewed demonstration between satellites at 100 m to a few kilometers remains to be established.
Evaluation conditions	The Suncatcher prototype launched on 1 October 2026 omits an inter-satellite link, and the first two-satellite test is planned with Planet for 2027.
Model configuration	Those gaps are where Chapter 11 begins, with Panel 11.2 reusing the budget model of Panel 2.2 at 0.05–5 km.
桌面與在軌證據	1.6 Tbps 是一篇公司作者論文中的桌上測試，衛星之間 100 m 到數公里的自由空間示範仍待同儕審查的紀錄。
星座配置	2026 年 10 月 1 日發射的 Suncatcher 原型機的酬載配置排除星間鏈路，第一次雙衛星測試計畫與 Planet 合作於 2027 年進行。
模型配置	這些空缺正是第 11 章的起點，其中面板 11.2 會在 0.05–5 km 重用面板 2.2 的預算模型。

Chapter summary

本章摘要

The flown record is TBIRD's 200 Gbps. The standardized rate is SDA's 2.5 Gbps.飛行紀錄是 TBIRD 的 200 Gbps。標準化速率是 SDA 的 2.5 Gbps。

Measure or comparison參數或比較項目	Values, conditions and evidence數值、條件與證據
Node delay	Vacuum propagation costs 3.336 µs per kilometer, against 4.895 µs in fiber. The 47% advantage offsets extra path length beyond about 3,000 km. Papers assume 0, 1 or 10 ms node delay, pending public measurements.
Path length and hops	Chord lengths depend on the filing. For 24 × 66, intra-plane and inter-plane hops are 659 km and 1,807 km. For 72 × 22, they are 1,969 km and 604 km. At 53°, inter-plane distance falls to 0.60 of its equatorial value. Maximum line-of-sight range is 5,016 km.
Evaluation conditions	At 2,000 km, the far-field budget gives 106 dB per 10 cm aperture and 264 dB free-space loss. Transmitting 1 W delivers 1.58 µW. This supports 63 Gbps at 196 photons per bit and exceeds TBIRD’s measured threshold by 13 dB. Long-range lasers consequently operate around 1–200 Gbps. A 100–200 m near-field link can reach roughly 10 Tbps.
Evaluation conditions	The SpaceX figures of 100 Gbps sustained and 200 Gbps peak are company claims via journalists.
Acquisition	Current acquisition takes 2–30 s. Temporary-link gains require millisecond setup, favoring quasi-static practical links. +Grid remains a modeling baseline. Current Starlink satellites carry three terminals, and real ephemerides split a three-link grid into disconnected components.
節點延遲	ISL 在真空中每公里花 3.336 µs，光纖則是 4.895 µs，這 47% 的優勢在約 3,000 km 以上才會回本，再加上一個仍待公開量測、論文設為 0、1 或 10 ms 的節點延遲。
路徑長度與跳數	跳躍長度由弦長公式決定，因而由論文凍結的申報決定：24 × 66 是同面 659 km、面間 1,807 km，72 × 22 是 1,969 km 與 604 km，面間跳躍在 53° 縮到赤道值的 0.60，視線在 5,016 km 結束。
評估條件	遠場鏈路預算中每個 10 cm 口徑 106 dB、2,000 km 的自由空間損耗 264 dB，從 1 W 送出 1.58 µW，對 196 光子/位元的電信接收機是 63 Gbps，比 TBIRD 的實測門檻高 13 dB。
評估條件	這套算術就是長距離雷射停留在 1–200 Gbps、而 100–200 m 近場鏈路能載約 10 Tbps 的原因。
評估條件	SpaceX 的持續 100 Gbps 與峰值 200 Gbps 是經記者轉述的公司宣稱。
擷取	擷取今日需 2–30 s，暫時性鏈路卻要毫秒級才划算，所以實際的拓樸由準靜態鏈路組成，本文將 +Grid 定位為建模基準，Starlink 的實際拓樸則仍待公開，Starlink 衛星帶三個終端，早期模型則採四或五個，而在真實星曆上三鏈路網格會分成多個連通分量。

Where these ideas go next

這些概念接下來用在哪裡

Chapter 3 adds the ground segment. It explains how PoPs shape measured Starlink latency alongside the hop lengths calculated here. Chapter 4 puts the ISL rate, the terminal count, the setup delay and the node delay into the parameter sheet with their tags. Chapter 5 revisits +Grid, motifs and stable links as a design space. Chapter 11 applies Section 2.6’s near-field budget to the Suncatcher cluster.

第 3 章加入地面段，說明為什麼實測的 Starlink 延遲主要受 PoP 配置影響，與這裡計算的跳躍長度各有適用條件。第 4 章把 ISL 速率、終端數、建立延遲與節點延遲連同標籤放進參數表。第 5 章把 +Grid、motif 與穩定鏈路當成設計空間重新討論，而第 11 章把第 2.6 節的近場預算帶進 Suncatcher 叢集。

Papers behind this chapter本章所依據的論文

IEEE VTM 2021Laser Intersatellite Links in a Starlink Constellation: A Classification and Analysis IEEE OJCOMS 2022Temporary Laser Inter-Satellite Links in Free-Space Optical Satellite Networks arXiv 2301.05285Laser Inter-Satellite Link Setup Delay: Quantification, Impact, and Tolerable Value ICSOS 2023Recent On-Orbit Results and ARQ Performance Analysis for the TBIRD 200-Gbps Mission arXiv 2602.07756LEO Topology Design Under Real-World Deployment Constraints CoNEXT 2019Network Topology Design at 27,000 km/hour

2.1Latency is geometry: vacuum versus fiber, and the length of a hop延遲就是幾何：真空對光纖，以及一跳的長度

ISL hop lengths and one-way delayISL 跳躍長度與單向延遲

2.2The optical link budget decides the rate光學鏈路預算決定速率

Link budget calculator鏈路預算計算器

2.3What has flown and what is specified已經飛過的與已經規範的

2.4Pointing, acquisition and the terminal count指向、擷取與終端數量

2.5Topologies: +Grid, seams, motifs and temporary links拓樸：+Grid、接縫、motif 與暫時性鏈路

2.6Short links: the Suncatcher regime短距鏈路：Suncatcher 的區域

Papers behind this chapter本章所依據的論文

Check your understanding檢驗你的理解