Chapter 8 of 13 · Part II · The research

第 8 章（共 13 章）· 第二部 · 研究

Computing in orbit: power, heat, radiation and the downlink bottleneck在軌運算：電力、散熱、輻射與下行瓶頸

This chapter derives solar-array, battery and radiator sizes, converts radiation exposure into device event rates, and examines orbital-server costs. You will also distinguish flight demonstrations from proposed orbital-computing systems.本章推導太陽能陣列、電池與散熱板的尺寸，把輻射暴露轉為元件事件率，並檢視軌道伺服器成本。你也會區分已飛行的示範與提案中的在軌運算系統。

≈ 33 min · 2 panels · 8-question quiz≈ 33 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 Chapters 1, 2 and 3. These earlier terms appear most often below, each chip links to its definition.

本章建立在第 1、2、3 章之上。下列較早定義的名詞在本章最常出現，點選即可回到它的定義。

Eclipse地影1 Sun-synchronous orbit太陽同步軌道1 Pass過頂1 ISL星間鏈路（ISL）2 Gateway閘道3

New terms in this chapter (10)本章新名詞（10）

Each link opens the term’s first definition.

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。

Orbital edge computing軌道邊緣運算（OEC）Satellite inference reduces the downlink to selected results.在衛星上推論，只下傳選定結果。
Downlink bottleneck下行瓶頸 The limit set by pass minutes times station rate on how much a satellite can send to the ground per orbit. 由過頂分鐘數乘以地面站速率決定的每圈可下傳資料量上限。
Specific power比功率 Watts of array output per kilogram of array mass. 每公斤陣列質量所產生的瓦數。
Depth of discharge放電深度（DoD） The fraction of a battery's capacity drawn each cycle, traded against cycle life. 每個循環取用的電池容量比例，與循環壽命互為取捨。
Radiator輻射散熱板 The surface that sheds a satellite's waste heat as infrared, at a rate set by its temperature to the fourth power. 把衛星廢熱以紅外線輻射出去的表面，速率由溫度的四次方決定。
Duty cycle工作週期 The fraction of time a payload runs when heat or energy forces it to pause. 當散熱或能量迫使酬載暫停時，酬載實際運行的時間比例。
Total ionising dose (TID)總游離劑量（TID） Cumulative radiation absorbed by silicon, in rad(Si), which degrades devices gradually. 矽累積吸收的輻射量，以 rad(Si) 計，使元件逐漸退化。
Single-event effect (SEE)單粒子效應（SEE） A fault caused by one particle, from a flipped bit to a destructive latch-up. 單一粒子造成的故障，從位元翻轉到破壞性閂鎖都算。
Single-event functional interrupt (SEFI)單粒子功能中斷（SEFI） A single-event fault that halts a device until it is reset or power-cycled. 使裝置停擺、直到重置或斷電重啟才恢復的單粒子故障。
Silent data corruption (SDC)靜默資料損毀（SDC）An incorrect computational result accompanied by a normal error status.產生錯誤計算結果，同時回報正常錯誤狀態。

Chapters 5–7 treat satellites as routers. This chapter examines them as computers through the progression from downlink limits to processor limits and measured thermal constraints. Orbital-edge work introduced filtering, Kodan addressed on-board processing, and flight measurements exposed heat limits in commodity hardware. Power, thermal, radiation and launch requirements then frame Suncatcher’s design and the record of flown systems.

第 5–7 章將衛星當作路由器，本章則從下行限制、處理器限制與實測熱控限制，檢視它作為電腦的條件。軌道邊緣研究引入資料過濾，Kodan 處理機上運算瓶頸，飛行量測則揭露商用硬體的散熱限制。電力、熱控、輻射與發射需求共同界定 Suncatcher 設計與已飛行系統的證據範圍。

8.1The downlink wall: orbital edge computing下行之牆：軌道邊緣運算

Recall

回顧

Section 3.6 gives Earth-observation examples: 200 Mbit/s stations, 15 GB per pass, and L2D2’s 90 → 21 minute latency reduction. Section 1.2 explains minute-scale passes.

第 3.6 節給了地球觀測下行的數字（200 Mbit/s 地面站、每次過頂 15 GB、L2D2 的 90 → 21 分鐘），第 1.2 節則說明了為何對單一地面站的過頂只有幾分鐘。

The downlink bottleneck follows contact time and station rate. Clustered passes make ground infrastructure a scaling constraint for raw-data delivery.

下行瓶頸由通聯時間與地面站速率決定，集中的過頂使地面設施成為原始資料交付的擴展限制。

Downlink contact and ground-station requirements
#	Reported values and conditions
1	Imaging nanosatellites generate data faster than ground contacts can remove it.
2	Denby and Lucia quantify this for Planet-class satellites.
3	A 200 Mbit/s station retrieves up to 15 GB in a 5–10 min session, with customer delivery about 5.5 hours after capture.
4	One mission reported 88% downlink packet loss.
5	An ideally placed station serves only nine satellites per orbit because their passes cluster in time ^{[60, §1, §3.3]}.
6	A 1,000-satellite bent-pipe constellation therefore requires 112 ideal stations.
7	In the paper’s scale study, increasing the constellation from 250 to 1,000 raises station count 3.5× (§7.1).
8	This downlink bottleneck is the product of contact time and station rate.
9	Section 9.3’s federated-learning studies encounter the same contact constraint.

下行通聯與地面站需求
#	數值、條件與證據
1	成像奈米衛星產生資料的速度，超過地面通聯可移除的速度。
2	Denby 與 Lucia 針對 Planet 類型衛星量化差距：200 Mbit/s 地面站在 5–10 分鐘通聯中最多取得 15 GB，客戶約在拍攝後 5.5 小時收到資料。
3	某任務報告 88% 下行遺失，而理想站點每圈僅服務九顆衛星，原因是過頂集中於相近時段 ^{[60, §1, §3.3]}。
4	1,000 顆彎管星座因此需要 112 座理想站點。
5	星座從 250 增至 1,000 顆時，論文的站點數增加 3.5 倍（§7.1）。
6	下行瓶頸就是通聯時間與站點速率的乘積，第 9.3 節聯邦學習也面對相同的通聯限制。

On-board filtering reduces the data that each ground contact must carry. Computational pipelines address processing time, with simulation and hardware assumptions defining the reported gains.

機上過濾減少每次通聯需承載的資料，運算管線則處理計算時長，模擬與硬體假設共同界定所報增益。

OEC: data reduction, processing and power assumptions
#	Reported values and conditions
1	Orbital edge computing, OEC, filters sensor data on the satellite and downlinks selected results.
2	In Denby and Lucia’s building example, the model retains 0.75 GB from each 15 GB set.
3	A 200 Mbit/s link clears it in about 30 s.
4	Station capacity rises from nine to 185 satellites per orbit, and a 1,000-satellite constellation needs six stations against 112.
5	The paper reports over 24× infrastructure reduction across its sweep (§3.3, §7.1).
6	Close satellite pipelines divide frames into parallel tiles and reduce processing delay over 617× relative to sequential execution, with absolute duration unspecified (§4.2, §7.2).
7	The model uses a Jetson TX2 industrial module in 7.5 W mode, against 7.1 W body-mounted or 14.2 W deployable solar.
8	Table 1 budgets 11.3 W detection, 0.5 W sleep, 3.5 W imaging and 1.13 W attitude control.
9	Full track coverage requires about 250 body-panel or 100 deployable-panel satellites (§3.1, §6, §7.3, Table 1).
10	All results use cote simulation, which separates their evidence from later proton and flight tests.

OEC 的資料縮減、處理與電力假設
#	數值、條件與證據
1	軌道邊緣運算 OEC 在衛星上過濾感測資料，只下傳選定結果。
2	Denby 與 Lucia 的建物案例從每組 15 GB 保留 0.75 GB，以 200 Mbit/s 約 30 秒送完。
3	每站每圈可服務衛星從九顆增至 185 顆，1,000 顆星座需要六站，原本則為 112 站，論文在整個掃描報告逾 24 倍設施減少（§3.3、§7.1）。
4	近距衛星管線把影像切塊平行處理，相較循序執行降低逾 617 倍延遲，絕對時長仍待提供（§4.2、§7.2）。
5	模型採 Jetson TX2 工業模組的 7.5 W 模式，配 7.1 W 機身或 14.2 W 展開式太陽能。
6	Table 1 預算為偵測 11.3 W、睡眠 0.5 W、成像 3.5 W、姿態控制 1.13 W，完整軌跡覆蓋各需約 250 或 100 顆（§3.1、§6、§7.3、Table 1）。
7	所有結果均來自 cote 模擬，證據範圍與後續質子、飛行測試分開。

Question問題	Calculation算式	Result結果
Is 15 GB per 10-minute session consistent with 200 Mbit/s?每次 10 分鐘通聯 15 GB 與 200 Mbit/s 一致嗎？	$15\times 8\,\text{Gbit} / 600\,\text{s}$	200 Mbit/scomputed, inputs ^{[60, §3.3]}計算值，輸入來自 ^{[60, §3.3]}
Fraction of raw data kept by the on-board model機上模型保留的原始資料比例	$0.75 / 15$	5%computed, the paper's Fig. 6 reports 5–25% across its scenarios計算值，論文 Fig. 6 在各情境報告 5–25%
Time to downlink 0.75 GB at 200 Mbit/s以 200 Mbit/s 下傳 0.75 GB 所需時間	$0.75\times 8\,\text{Gbit} / 0.2\,\text{Gbit/s}$	30 scomputed, matches the paper's "about 30 s"計算值，與論文的「約 30 秒」相符
Station ratio from the two counts the paper gives以論文給的兩個地面站數量算出的比值	$112 / 6$	18.7×computed, 185/9 = 20.6× for satellites per station, the paper's headline across its sweep is ">24×"計算值，每站衛星數 185/9 = 20.6×，論文在整個掃描範圍的標題數字是「>24×」

Figure 8.1. The downlink wall and the OEC pipeline. Onboard detection reduces the data per pass from 15 GB to 0.75 GB. One station can then serve 185 satellites per revolution, up from 9. For a 1,000-satellite constellation, the required station count falls from 112 to 6.圖 8.1。下行之牆與 OEC 管線。把偵測器搬到衛星上，使每次過頂必須承載的資料從 15 GB 縮為 0.75 GB，一座地面站每圈能服務的衛星數因此從 9 顆增為 185 顆，1,000 顆衛星的星座所需地面站從 112 座降為 6 座。Sources來源: ^{[60, §3.3, §7.1]}

Original figure note原始圖說出處

Drawn for this primer from Denby & Lucia, ASPLOS 2020, §3.3 and §7.1.

Kodan specializes models to ground context and chooses tile processing to meet image deadlines. It addresses the processor bottleneck that follows moving filters on board.

Kodan 依地表情境專門化模型，選擇圖塊處理方式來趕上影像期限，處理過濾器移上衛星後的運算瓶頸。

Kodan: processor constraints and evaluation
#	Reported values and conditions
1	Kodan, the group’s 2023 work with Microsoft, addresses the processor bottleneck after filtering moves on board.
2	Flight-heritage processors include the 250 MHz LEON SPARC, 466 MHz RAD5500 PowerPC and 12 MHz Mongoose-V on EO-1.
3	After decades of service, a processor “could be nearly half a century behind the state-of-the-art” ^{[83, §6]}.
4	Landsat 8 produces a frame every 22 s, while a real cloud filter needs 98 s.
5	Direct filtering therefore increases valuable downlink data only 9%, against an ideal threefold gain ^{[83, §2.1, Figs. 4–5]}.
6	Kodan specializes models to clustered geospatial contexts, selects tile sizes to meet deadlines, and skips processing for tiles confidently sent or discarded.
7	Prelaunch selection logic chooses each tile’s combination ^{[83, §3]}.
8	Evaluation runs seven segmentation networks on 15 W Jetson AGX Orin, 140 W Core i7-7800X and 180 W GTX 1070 Ti hardware. cote models the Landsat orbit, camera and ground segment.
9	Valuable-data density rises 89–97% over a saturated bent pipe, and full-coverage satellite count falls up to 12× against pipelined OEC ^{[83, §4, §5.1–5.2, Figs. 8, 11]}.

Kodan 的處理器限制與評估
#	數值、條件與證據
1	推論一旦上了衛星，牆就移動了。
2	Kodan 是同一團隊與 Microsoft 在 2023 年的後續研究，它的出發點是衛星設計者可用的飛行履歷處理器慢到地面工程師很少見到的程度，LEON SPARC 只到 250 MHz，RAD5500 PowerPC 是 466 MHz，EO-1 上的 Mongoose-V 跑 12 MHz，因此運作二十年以上之後，機上處理器「可能落後最先進技術近半個世紀」^{[83, §6]}。
3	它量到的落差存在於兩個時鐘之間：Landsat 8 每 22 秒就看到一幀新影像，而一個實際的雲層過濾器每幀需要 98 秒，所以直接部署這個過濾器，下傳的高價值資料只增加 9%，而理想過濾器可帶來三倍^{[83, §2.1, Figs. 4–5]}。
4	Kodan 的回應是：把模型專門化到以聚類代表性資料集得到的地理情境，選擇每幀切成幾個圖塊，讓處理時間趕得上每幀期限，並對情境以高價值為主的圖塊直接下傳、以低價值為主的圖塊直接丟棄，略過處理，至於每個圖塊採用哪種組合，則由發射前計算好的選擇邏輯決定^{[83, §3]}。
5	在 15 W 的 Jetson AGX Orin、140 W 的 Core i7-7800X 與 180 W 的 GTX 1070 Ti 上執行七個雲層過濾分割網路，並以 cote 模擬器模擬 Landsat 8 的軌道、相機與地面段，這把飽和下行鏈路的資料價值密度相對於彎管提高 89% 到 97%，而且相對於管線式 OEC 做法，達到完整地面軌跡覆蓋所需的衛星數最多可減少 12 倍^{[83, §4, §5.1–5.2, Figs. 8, 11]}。

Tiansuan links orbital-edge concepts to flown satellites. Its asymmetric communication budget makes model deployment a separate challenge from downloading results.

天算把軌道邊緣概念連結到飛行衛星，上下行預算差距使模型部署與結果下載各有挑戰。

Tiansuan: missions and communication budgets
#	Reported values and conditions
1	Tiansuan provides flown systems.
2	Wang and Li describe Baoyun, launched 7 December 2021 as the “first cloud-native satellite”, and BUPT-1, launched 15 January 2023.
3	Phase-1 satellites 1–3 have 100–600 Mbps X-band downlinks and 0.1–1 Mbps uplinks, using ground-only communication.
4	Planned satellites 4–6 add ISLs, at least 1 Gbps down and 200 Mbps up ^{[84, §V, Tab. II]}.
7	The program describes cloudy-image rejection reducing processing “from about one day to about one hour”, with measured tables outside that paper’s scope.
8	Contact windows last 6–8 min about once daily (Wang et al., arXiv 2112.14957, §II.A, Fig. 1) preprint.
9	Section 8.3 examines peer-reviewed in-orbit measurements. The large downlink–uplink asymmetry makes new-model uploads slower than result downloads.

天算任務與通訊預算
#	數值、條件與證據
1	天算提供已飛行系統。
2	Wang 與 Li 描述 2021 年 12 月 7 日發射、稱為「第一顆雲原生衛星」的寶雲號，以及 2023 年 1 月 15 日發射的北郵一號。
3	第一階段第 1–3 顆採 100–600 Mbps X 頻段下行、0.1–1 Mbps 上行與純地面通訊，規劃的第 4–6 顆則加入 ISL、至少 1 Gbps 下行與 200 Mbps 上行 ^{[84, §V, Tab. II]}。
4	計畫描述機上去雲使處理時間「從約一天縮短到約一小時」，該文的證據為定性說明。
5	通聯視窗約每天一次、每次 6–8 分鐘（Wang 等，arXiv 2112.14957，§II.A、Fig. 1）預印本。
6	第 8.3 節會檢視同儕審查的在軌量測。
7	上下行速率差距使新模型上傳比結果下載慢得多。

8.2Power: solar, batteries and eclipse電力：太陽能、電池與地影

Recall

回顧

Section 1.3 defined the eclipse fraction, nodal precession and the dawn–dusk sun-synchronous orbit, and Section 1.1 gave the 95.65 min period at 550 km.

第 1.3 節定義了地影比例、節點進動與晨昏太陽同步軌道，第 1.1 節給出 550 km 的 95.65 分鐘週期。

Orbital solar output combines irradiance with illumination duration. Comparing yearly energy requires an explicit ground-site sun-hours assumption beside the claimed multiplier.

在軌太陽能輸出結合輻照度與日照時間，比較全年能量時，須在宣稱倍數旁列出地面日照時數假設。

Solar irradiance, cell efficiency and illumination
#	Reported values and conditions
1	Orbital power depends on irradiance and illumination duration.
2	Suncatcher assumes 1.361 kW/m² for a Sun-facing panel above the atmosphere ^{[36, p. 10]}.
4	Current III-V multijunction cells have nominal efficiency near 30%, reaching 34%, with flight-array maximum-power densities around 380–430 W/m² ^{[66, Tab. 3-1]} agency report.
5	Google claims “up to 8× more solar energy per year” than a mid-latitude ground panel ^{[36, p. 2]}.
7	This combines 1,361 versus 1,000 W/m² irradiance with continuous dawn–dusk illumination versus roughly five equivalent full-sun ground hours.
8	Under that ground assumption, the product is about 6.5.
9	Pénot and Balakrishnan use “approximately five times” preprint, and secondary reports of Starcloud’s white paper say “over 5×” company.
10	The ground-panel sun-hours assumption explains most of the 5–8 range, so the assumption belongs beside the multiplier.

太陽輻照度、電池效率與日照
#	數值、條件與證據
1	在軌電力取決於輻照度與日照時間。
2	Suncatcher 採大氣層外正對太陽的 1.361 kW/m² ^{[36, p. 10]}。
3	現行 III-V 多接面電池名目效率約 30%、最高 34%，飛行陣列最大功率密度約 380–430 W/m² ^{[66, Tab. 3-1]} 機構報告。
4	Google 宣稱年太陽能可達中緯度地面面板的八倍 ^{[36, p. 2]}，結合 1,361 對 1,000 W/m² 輻照度，以及晨昏連續日照對地面每日約五個等效全日照小時。
5	在此地面假設下乘積約 6.5。
6	Pénot 與 Balakrishnan 採「約五倍」預印本，Starcloud 白皮書的二手報告為「超過 5 倍」公司。
7	5–8 的範圍主要由地面日照時數假設決定，引用倍數時須連同這個條件。

Array specific power determines structural mass for a given output. Battery capacity also depends on allowed discharge depth, linking eclipse storage mass to cycle life.

陣列比功率決定指定輸出所需質量，電池容量則取決於允許放電深度，使地影儲能質量與循環壽命相連。

Array and battery mass parameters
#	Reported values and conditions
1	Power density determines array area, while specific power and battery energy density determine mass.
2	NASA’s flight hardware survey clusters near 30 W/kg, with ROSA at 100 W/kg and the best entries at 200 W/kg ^[66] agency report.
3	Commercial lithium-ion cells provide 150–270 Wh/kg.
4	Space-grade cells trade density for cycle life and 5–15 years of service.
5	Depth of discharge, the capacity fraction drawn each cycle, controls that life.
6	BUPT-1 targets 30%, averaged 16% over two weeks, and briefly exceeded 50% during a compute-and-transmit burst.
7	Its authors cite about one-quarter life reduction when average discharge rises from 25% to 30% ^{[85, §4, Tabs. 4–5]}.
8	Delivering 400 Wh per eclipse at 30% discharge requires a 1,333 Wh battery, increasing eclipse-related mass.

陣列與電池質量參數
#	數值、條件與證據
1	功率密度決定面積，另外兩個數字決定質量。
2	陣列的比功率，即每公斤陣列質量的輸出瓦數，在 NASA 調查的飛行硬體中集中於約 30 W/kg，捲出式 ROSA 陣列為 100 W/kg，最佳者達 200 W/kg^[66]機構報告。
3	商用鋰離子電池儲能密度 150 到 270 Wh/kg，而太空級電池「往往犧牲能量密度以換取更好的循環壽命」，以達到 5 到 15 年的服役期（同一來源）。
4	這些電池的壽命取決於放電深度，即每次循環取用的容量比例，而研究文獻中唯一一個飛行資料點顯示它被管得多嚴：北郵一號設計放電深度 30%，兩週內平均 16%，在一次運算加傳輸的突發負載中短暫超過 50%，作者並引述平均放電深度從 25% 升到 30% 時電池壽命約損失四分之一^{[85, §4, Tabs. 4–5]}。
5	因此一顆每次地影需供應 400 Wh、放電深度 30% 的電池，必須是一顆 1,333 Wh 的電池，這個三倍因子正是地影在質量上昂貵的原因。

Eclipse adds both battery storage and solar-array recharge capacity. Dawn–dusk orbits reduce that burden while changing ground-access latency.

地影同時增加電池儲能與陣列充電容量，晨昏軌道可降低負擔，也會改變地面存取延遲。

Eclipse geometry and orbit-selection trade
#	Reported values and conditions
1	Eclipse duration follows orbital geometry.
2	At 550 km, orbital radius is 6,921 km.
3	With the Sun in the orbital plane, the shadow half-angle is $\arcsin(6371/6921) \approx 67.0^\circ$.
4	Darkness spans 2 × 67.0° of 360°, or fraction 0.372, giving 35.6 min in a 95.65 min orbit.
5	Battery power carries the payload during darkness.
6	Array sizing grows by $1/(1-0.372) = 1.59$ to recharge during roughly 60 sunlit minutes.
7	A dawn–dusk sun-synchronous plane follows the terminator through matched nodal precession and has nearly continuous sunlight during most of the year.
8	Suncatcher selects this orbit at 650 km ^{[36, p. 2]}.
10	SpaceX’s 2026 filing promises solar operation “more than 99 percent” of the time company via press. Starcloud’s second satellite reportedly targets SSO press. Suncatcher also acknowledges increased latency to some ground locations (p. 2), a trade examined in Section 13.5.

地影幾何與軌道選擇取捨
#	數值、條件與證據
1	地影時長由軌道幾何決定。
2	550 km 的圓軌道半徑為 6,921 km，太陽位於軌道面時，陰影半角為 $\arcsin(6371/6921) \approx 67.0^\circ$。
3	衛星在 360° 中有 2 × 67.0° 處於地影，比例 0.372，在 95.65 分鐘軌道中為 35.6 分鐘。
4	地影時由電池供應酬載，陣列需放大 $1/(1-0.372) = 1.59$ 倍，在約 60 分鐘日照內充回電池。
5	晨昏太陽同步軌道藉節點進動追隨晨昏線，一年多數時候接近連續日照。
6	Suncatcher 選擇 650 km 晨昏軌道 ^{[36, p. 2]}。
7	SpaceX 2026 申請宣稱太陽能運作時間「超過 99%」公司（經媒體），Starcloud 第二星也據報導以 SSO 為目標媒體。
8	Suncatcher 同時承認部分地面位置的延遲會增加（p. 2），第 13.5 節將檢視這項取捨。

Question問題	Calculation算式	Result結果
Eclipse half-angle at 550 km, Sun in the orbital plane550 km、太陽在軌道面內的地影半角	$\arcsin\!\left(\frac{6371}{6921}\right)$	67.0°computed, R_E = 6,371 km, h = 550 km計算值，R_E = 6,371 km，h = 550 km
Eclipse fraction and duration地影比例與時長	$\frac{2\times 67.0^\circ}{360^\circ}\times 95.65\,\text{min}$	0.372 · 35.6 mincomputed, period from Section 1.1計算值，週期取自第 1.1 節
Array oversize factor to recharge during sunlight為在日照期充電所需的陣列放大倍數	$1/(1-0.372)$	1.59×computed, charge losses neglected計算值，忽略充電損耗
Array area for a 700 W accelerator, continuous sun vs 550 km700 W 加速器的陣列面積，連續日照 vs 550 km	$\frac{700}{400}\;;\;\frac{700}{400\times 0.628}$	1.75 m² · 2.79 m²computed, 400 W/m² from NASA SST-SOA 2026 Table 3-1計算值，400 W/m² 取自 NASA SST-SOA 2026 Table 3-1
Energy the battery must deliver per eclipse at 700 W700 W 下每次地影電池須供應的能量	$700\,\text{W}\times 35.6/60\,\text{h}$	415 Whcomputed計算值
Battery capacity and mass at 30% DoD放電深度 30% 下的電池容量與質量	$\frac{415}{0.30}\;;\;\frac{1383}{270}\ldots\frac{1383}{150}$	1,383 Wh · 5.1–9.2 kgcomputed, 150–270 Wh/kg from NASA SST-SOA 2026, DoD target from ^[85]計算值，150–270 Wh/kg 取自 NASA SST-SOA 2026，DoD 目標取自 ^[85]
The "8×" solar multiplier decomposed「8 倍」太陽能倍數的拆解	$\frac{1361}{1000}\times\frac{24}{5}$	≈ 6.5computed, 1,361 W/m² from ^{[36, p. 10]}, ~5 equivalent full-sun hours per day is this primer's mid-latitude assumption計算值，1,361 W/m² 取自 ^{[36, p. 10]}，每天約 5 個等效全日照小時是本教材對中緯度的假設
Suncatcher's bus estimate checked檢驗 Suncatcher 的平台估算	$105\,\text{m}^2\times 1.361\times 0.22\times 0.9$	28.3 kWcomputed, inputs ^{[36, p. 10]} (105 m², 22%, 90% packing), paper states ≈28 kW計算值，輸入取自 ^{[36, p. 10]}（105 m²、22%、90% 填充率），論文寫約 28 kW

Flight hardware, historical estimates and proposed compute platforms occupy separate power scales. Whole-satellite power-to-mass ratios help compare them while retaining their evidence tags.

飛行硬體、歷史估計與運算提案各有電力尺度，整星功率質量比可協助比較，並保留各自證據標籤。

Published satellite power budgets
#	Reported values and conditions
1	Published power budgets span four orders of magnitude.
2	Denby and Lucia pair 7.5 W Jetson operation with 7.1 W body solar, requiring intermittent work and 0.5 W sleep ^{[60, Tab. 1]}.
3	BUPT-1 is a 17.44 kg, 12U satellite with about 40 W peak solar, 16 Wh per orbit and a 2 × 115 Wh battery.
4	Its four-core Raspberry Pi uses 4.82 W, and Atlas 200 DK uses 10.19 W at full power ^{[85, Tabs. 1, 3–4]}.
5	Bhattacherjee et al.’s rough 2020 Starlink estimate gives about 1.5 kW average solar, with a 225–350 W server consuming 15–23% ^{[2, §4]}.
6	Suncatcher’s analogue uses a 575 kg V2 Mini, 105 m² of 22%-efficient panels and about 28 kW ^{[36, p. 10]}.
8	SpaceX’s filing assumes 100 kW computing per satellite tonne company via press.
9	Computed whole-satellite ratios are 2.3 W/kg for BUPT-1, 49 W/kg for Suncatcher’s analogue and 100 W/kg for SpaceX’s assumption.
10	Flight evidence currently establishes the first scale, while the higher computing ratios require demonstration.

已發表衛星電力預算
#	數值、條件與證據
1	文獻電力預算橫跨四個數量級。
2	Denby 與 Lucia 以 7.1 W 機身太陽能供應 7.5 W Jetson，因此需間歇運算並以 0.5 W 睡眠 ^{[60, Tab. 1]}。
3	北郵一號為 17.44 kg、12U 衛星，太陽能峰值約 40 W，每圈取得 16 Wh，電池為 2 × 115 Wh。
4	Pi 四核心耗 4.82 W，Atlas 200 DK 全功率耗 10.19 W ^{[85, Tabs. 1, 3–4]}。
5	Bhattacherjee 等人粗估 2020 年 Starlink 平均太陽能約 1.5 kW，225–350 W 伺服器占 15–23% ^{[2, §4]}。
6	Suncatcher 類比採 575 kg V2 Mini、105 m² 面板與 22% 效率，產生約 28 kW ^{[36, p. 10]}。
7	SpaceX 申請假設每噸衛星 100 kW 運算公司（經媒體）。
8	整星功率質量比依序為北郵一號 2.3 W/kg、類比平台 49 W/kg、SpaceX 假設 100 W/kg。
9	飛行證據目前建立第一種尺度，較高運算比值仍待展示。

Panel 8.1面板 8.1

Power budget of a compute satellite運算衛星的電力預算

Payload power酬載功率

Array power density陣列功率密度

Array specific power陣列比功率

Eclipse fraction地影比例

Depth of discharge放電深度

Battery energy density電池能量密度

Array area

陣列面積

Array mass

陣列質量

Battery energy per eclipse

每次地影電池能量

Battery mass

電池質量

Orbit-average yield per m²

每 m² 的軌道平均產出

Power-system mass

電力系統質量

The model sizes an array to power the payload and recharge its battery during a 95.65 min orbit. Array power equals payload power divided by one minus the eclipse fraction. Battery capacity covers the eclipse at the chosen discharge depth. NASA SST-SOA 2026 provides density ranges (agency report), while eclipse fractions 0.37 and 0 represent maximum 550 km eclipse and dawn–dusk conditions. Charging losses, conversion losses, degradation, pointing, structure, harnesses and bus power lie outside the calculation, making these masses lower bounds.

此模型依日照期間的供電與充電需求計算陣列，再依地影能量及放電深度計算電池。來源範圍與省略項目列於表中。

條件、數值與證據
#	條件與結果
1	此模型把陣列尺寸定為能在一圈 95.65 分鐘內供應酬載並把電池充回（陣列功率 = 酬載 ÷（1 − 地影比例）），並把電池尺寸定為能以所選放電深度撐過地影。
2	功率密度、比功率與 Wh/kg 範圍取自 NASA SST-SOA 2026（機構報告），地影比例 0.37 是上面算出的 550 km 最大值，0 則是晨昏軌道。
3	它忽略充電與轉換損耗、陣列退化、指向損失、結構與線束質量，以及衛星平台自身的用電，所以這裡的每個質量都是下限。

Stop and think停下來想一想

Set the payload to 700 W, the eclipse fraction to 0.37 and the depth of discharge to 30%, then slide the eclipse fraction to 0. How much power-system mass disappears, and which component accounts for most of it? Now return to 0.37 and raise the depth of discharge to 80%. The battery mass falls, so what did you trade away, and which flown number in this section tells you how much it costs?

把酬載設為 700 W、地影比例 0.37、放電深度 30%，然後把地影比例滑到 0。電力系統質量少了多少，主要是哪個元件貢獻的？再回到 0.37，把放電深度拉到 80%。電池質量下降了，那你付出了什麼代價，本節哪個飛行數字告訴你代價有多大？

8.3Heat: the binding constraint散熱：真正的束縛

A radiator’s temperature and emissivity set its radiative heat rejection. Earth-facing absorption reduces net cooling, and the assumed backload needs its estimate status beside the result.

散熱板溫度與發射率決定輻射排熱，朝地吸收則降低淨散熱，因此背景負載假設須連同估計狀態解讀。

Radiative heat flux and Earth-facing backload
#	Reported values and conditions
1	Vacuum cooling relies on infrared emission from spacecraft surfaces.
2	Stefan–Boltzmann heat flux is $q = \varepsilon\sigma T^4$, with emissivity ε and σ = 5.670 × 10⁻⁸ W m⁻² K⁻⁴.
3	A radiator is the dedicated heat-emitting surface.
4	At emissivity 0.9, one face emits about 284 W/m² at 273 K, 413 at 300 K, 535 at 320 K, and 766 at 350 K.
5	Deep space provides a cold sink, while electronics temperature limits the radiator’s upper operating temperature.
6	Heat must flow from the hotter chip to the cooler radiator.
7	Earth-facing surfaces also absorb planetary infrared and reflected sunlight.
8	This primer assumes 100–240 W/m² of Earth-facing backload as an order-of-magnitude estimate, with handbook verification still required.

輻射熱通量與朝地背景負載
#	數值、條件與證據
1	真空中的太空船靠表面紅外線輻射散熱，史特凡–波茲曼定律給出熱通量 $q = \varepsilon\sigma T^4$，ε 為發射率，σ = 5.670 × 10⁻⁸ W m⁻² K⁻⁴。
2	輻射散熱板是專用排熱表面，發射率 0.9 時單面在 273 K 輻射約 284 W/m²，300 K 為 413，320 K 為 535，350 K 為 766。
3	深空提供低溫熱沉，電子元件則限制散熱板的最高工作溫度，熱從較熱晶片流向較冷散熱板。
4	朝地面另吸收地球紅外線與反射陽光。
5	本教材以 100–240 W/m² 作背景熱負載的數量級假設，手冊驗證仍待補充。

Chip heat must cross every interface before reaching a radiating surface. Each temperature drop reduces emission, so chamber tests, flight evidence and press descriptions have separate scopes.

晶片熱量需穿越各介面才能抵達散熱表面，每次溫降都降低輻射，因此艙測、飛行證據與媒體描述各有範圍。

Radiator sizing and prototype thermal evidence
#	Reported values and conditions
1	A 700 W H100-class accelerator preprint requires about 1.3 m² of one-sided radiator at 320 K, or 1.7 m² at 300 K, before backload.
2	These areas follow 700/535 and 700/413 and resemble the 1.75 m² solar array required in continuous sunlight.
3	Heat must first cross the die, interface material, spreader, heat pipe and structural joints.
4	Each temperature drop lowers radiator emission because the formula uses radiator temperature.
5	NASA describes the difficulty of closely stacked electronics and notes deployable-radiator volume constraints, while numerical W/m² values remain outside that summary ^{[66, Tab. 7-1]} agency report.
6	Google reports thermal-vacuum validation of heat pipes and radiators in September 2026, with orbital validation still pending company.
7	Press accounts describe layered TIM/aluminum/copper spreaders and chip shutdowns every 15–20 min for cooling press.
8	This would impose a duty cycle, the fraction of operating time. Google’s posts leave that press-reported behavior open (fact base Part C, item 34).

散熱板尺寸與原型熱控證據
#	數值、條件與證據
1	700 W 的 H100 級加速器預印本，在 320 K 需約 1.3 m² 單面散熱板，300 K 需約 1.7 m²，兩者由 700/535 與 700/413 計得，背景熱負載另計。
2	面積與連續日照所需 1.75 m² 陣列相近。
3	熱先經晶粒、熱介面材料、均熱片、熱管及結構接合，每次溫降都會降低散熱板輻射。
4	NASA 指出緊密堆疊電子元件的散熱困難及展開板體積限制，該摘要的 W/m² 數值仍待補充 ^{[66, Tab. 7-1]} 機構報告。
5	Google 於 2026 年 9 月報告熱真空艙驗證，軌道驗證仍待完成公司。
6	媒體另描述 TIM／鋁／銅分層均熱片，以及每 15–20 分鐘停機降溫媒體，這會形成酬載工作週期，Google 文章則將該媒體說法留待確認（事實庫 Part C，第 34 項）。

BUPT-1 shows how shared conduction paths and body temperatures limit concurrent payloads. Its measurements support short intermittent compute tasks and explicit thermal scheduling.

北郵一號顯示共享傳導路徑與星體溫度如何限制並行酬載，量測支持短間歇任務及明確的熱控排程。

BUPT-1: in-orbit thermal and power measurements
#	Reported values and conditions
1	Xing et al.’s flight study identifies conduction as an early thermal limit.
2	BUPT-1 carried two Raspberry Pi 4Bs and two Huawei Atlas 200 DKs over 6,000 orbits at 487.6–494.7 km.
3	The 12U satellite weighed 17.44 kg and had an internal design range of −10 to 30 °C ^{[85, §2, Tab. 1]}.
4	Above 75% load, Pi temperature crossed 80 °C in about 50 min and saturated near 82 °C, while board surface temperature rarely exceeded 15 °C.
5	This 67 K interface gap produced about 5% throttling and roughly 10% higher YOLOv3 and YOLOv5-Lite latency (§3.1–3.2, Fig. 3).
6	One Atlas reached the 30 °C satellite-surface limit after 540 min, while two reached it in about 40 min.
7	The OS terminated one at about 50 min (§3.2, Fig. 6).
8	Orbit heating was 2–4× slower than a ground replica: Pi saturation took 86 versus 39 min, and Atlas 147 versus 88 min (Table 3).
9	The cold body delayed heating while the final ceiling stayed similar.
10	Eclipse changed surface temperature about ±5 °C, and a daylight-started Atlas ended about 8 °C hotter at the chip (§3.4).
11	Orbital power was lower: Pi 4.82 versus 5.92 W, and Atlas 10.19 versus 11.48 W.
12	Energy per task fell 2–10%, attributed to the cold environment (§4, Tables 4–5).
13	Recommendations are short intermittent tasks, better conduction paths, surplus-sunlight scheduling, and discharge depth at or below 30% (§7).

北郵一號的在軌熱與電力量測
#	數值、條件與證據
1	Xing 等人的飛行研究指出熱傳導是早期限制。
2	北郵一號在 487.6–494.7 km 飛行逾 6,000 圈，搭載兩片 Pi 4B 與兩片 Atlas 200 DK。
3	12U 星體重 17.44 kg，內部設計範圍為 −10 至 30 °C ^{[85, §2, Tab. 1]}。
4	負載超過 75% 時，Pi 約 50 分鐘越過 80 °C、在約 82 °C 飽和，同板表面卻很少超過 15 °C。
5	67 K 介面落差使頻率約降 5%，YOLOv3、YOLOv5-Lite 延遲約增 10%（§3.1–3.2，Fig. 3）。
6	一片 Atlas 需 540 分鐘讓衛星表面達 30 °C，兩片同跑約 40 分鐘即達，其中一片約 50 分鐘被 OS 終止（§3.2，Fig. 6）。
7	在軌升溫比地面慢 2–4 倍：Pi 飽和為 86 對 39 分鐘，Atlas 為 147 對 88 分鐘（Table 3）。
8	低溫星體延緩升溫，最終上限仍相近。
9	地影使表面變動約 ±5 °C，日照啟動的 Atlas 結束時晶片約多 8 °C（§3.4）。
10	Pi 在軌對地面功耗為 4.82 對 5.92 W，Atlas 為 10.19 對 11.48 W，單任務能量少 2–10%，作者歸因於低溫（§4，Tables 4–5）。
11	建議是短間歇任務、改善導熱、在多餘日照時運算，並維持最多 30% 放電深度（§7）。

Figure 8.2. Heat travels from die through interfaces and structure to the radiator, with a temperature drop at each step. Emission then follows εσT⁴ at the radiator temperature. The 3 K sky sets a distant lower bound, electronics limit the upper temperature, and Earth-facing surfaces absorb infrared and reflected sunlight.圖 8.2。熱從晶粒經介面與結構抵達散熱板，每一步都出現溫降，再以散熱板溫度的 εσT⁴ 輻射出去。3 K 冷空提供遙遠的低溫下界，電子元件限制最高溫度，朝地面另吸收紅外線與反射日光。Sources來源: ^{[85, §3.1, Fig. 3]}

Original figure note原始圖說出處

Drawn for this primer from the Stefan–Boltzmann law and Xing et al., MobiCom 2024, §3.1 and Fig. 3.

Question問題	Calculation算式	Result結果
One-sided radiator flux at 300 K, ε = 0.9300 K、ε = 0.9 的單面散熱板輻射通量	$0.9\times 5.670\times 10^{-8}\times 300^4$	413 W/m²computed, Stefan–Boltzmann, 0 K sink, zero backload計算值，史特凡–波茲曼，0 K 冷空，背景負載設零
The same at 273 K, 320 K and 350 K273 K、320 K 與 350 K 時的同一數值	$0.9\,\sigma T^4$	284 · 535 · 766 W/m²computed計算值
One-sided radiator area for a 700 W accelerator700 W 加速器所需的單面散熱板面積	$700/535\;;\;700/413$	1.3 m² (320 K) · 1.7 m² (300 K)computed, before backload, two-sided halves the area計算值，背景負載另計，雙面可將面積減半
Radiator area per kilowatt at 300 K300 K 時每千瓦所需散熱板面積	$1000/413$	2.4 m²/kW one-sidedcomputed, 1.2 m²/kW two-sided計算值，雙面為 1.2 m²/kW
Net flux with a 240 W/m² backload on an Earth-facing face at 300 K朝地面在 300 K 承受 240 W/m² 背景負載時的淨通量	$413-240$	173 W/m²computed, backload is this primer's order-of-magnitude estimate計算值，背景負載為本教材的數量級估計
Energy of a 3-hour Pi run against one orbit's harvest on BUPT-1北郵一號上 Pi 跑 3 小時的能量對一圈採集的能量	$4.82\,\text{W}\times 3\,\text{h}\;;\;16\,\text{Wh}$	14.5 Wh vs 16 Whcomputed, inputs ^{[85, Tabs. 3–4, Fig. 13]}, the paper's experiments ran 3 h of compute over about two orbits計算值，輸入取自 ^{[85, Tabs. 3–4]}、Fig. 13，論文的實驗在約兩圈內運算 3 小時
Energy saving per task in orbit, Atlas and YOLO-Fastest在軌每任務的能量節省，Atlas 與 YOLO-Fastest	$1-\frac{94.9}{106.2}\;;\;1-\frac{21}{21.38}$	10.6% · 1.8%computed, J per 100 images from ^{[85, §4.3]}, the paper summarises this as 2–10%計算值，每 100 張影像的焦耳數取自 ^{[85, §4.3]}，論文總結為 2–10%
Usable battery energy on BUPT-1 at the 30% DoD target北郵一號在 30% 放電深度目標下可用的電池能量	$2\times 115\times 0.30$	69 Whcomputed, about 7 h of a 10.19 W Atlas, or 14 h of a 4.82 W Pi計算值，約可供 10.19 W 的 Atlas 跑 7 小時，或 4.82 W 的 Pi 跑 14 小時

Panel 8.2面板 8.2

Radiator sizing散熱板尺寸估算

Radiator temperature散熱板溫度

Emissivity發射率

Backload on the Earth-facing face朝地面的背景熱負載

Radiating sides輻射面數

Heat to reject須排出的熱

εσT⁴ per side

每面 εσT⁴

Net rejection per m² of plate

每 m² 板面的淨排熱

Radiator area

散熱板面積

Area per kW

每 kW 面積

The radiator model separates plate heat rejection from the chip-to-plate conduction path. Reference settings and flight evidence are listed below.

Conditions and reported evidence
#	Evidence record
1	Net plate heat rejection equals sides × εσT⁴ minus one Earth-facing backload.
2	The chart varies temperature for the selected heat load and retains the 700 W, one-sided reference of 1.3–1.7 m² at 320–300 K.
3	BUPT-1’s 5–10 W boards drove chip temperatures above 80 °C in about 50 min ^[85].
4	This illustrates the separate conduction chain before the radiator.
5	Solar loading, view factors, die-to-radiator drops and radiator mass lie outside the panel.

此散熱模型區分板面排熱與晶片到板面的傳導。表中列出參考設定、飛行證據及模型範圍。

條件、數值與證據
#	條件與結果
1	每平方公尺板面的淨排熱等於面數 × εσT⁴，再減去一次朝地背景負載。
2	圖中依選定熱量變動溫度，保留 700 W 單面在 320–300 K 所需 1.3–1.7 m² 的參考。
3	北郵一號的 5–10 W 板子約 50 分鐘使晶片超過 80 °C ^[85]，說明散熱板之前還有獨立的傳導鏈。
4	日照負載、視角因子、晶粒至散熱板的溫降及板子質量，均在面板模型範圍之外。

Stop and think停下來想一想

Hold the heat at 700 W and move the radiator from 300 K to 350 K. The area falls by roughly (350/300)⁴, but the die must now sit above 350 K plus every interface drop. Which flight measurement shows the size of this drop on a small satellite? Explain its implications for the Suncatcher prototype’s reported duty cycle.

把熱固定在 700 W，把散熱板從 300 K 調到 350 K。面積大約按 (350/300)⁴ 下降，但晶粒現在必須坐在 350 K 再加上每個介面的落差之上。本節哪個飛行數字告訴你這個落差在小衛星上可以多大，這又對媒體報導的 Suncatcher 原型 15–20 分鐘工作週期意味著什麼？

8.4Radiation: TID, SEE, SEFI and SDC輻射：TID、SEE、SEFI 與 SDC

Recall

回顧

Section 8.2 places Suncatcher in a sunlit 650 km dawn–dusk orbit. Section 8.1 establishes that OEC’s Jetson TX2 results came from simulation. Both facts matter here, because altitude sets the dose and the Jetson is one of the few accelerators with a published proton test.

第 8.2 節為了日照把 Suncatcher 的叢集放在 650 km 的晨昏軌道，第 8.1 節則指出 OEC 對 Jetson TX2 的所有結果都來自模擬。這兩點在此都很重要，因為高度決定劑量，而 Jetson 是少數有公開質子測試結果的加速器之一。

Radiation produces cumulative degradation and individual particle faults. Total ionising dose, TID, measures deposited energy in rad(Si), progressively shifting transistor thresholds and increasing leakage. A single-event effect, SEE, comes from one particle striking a sensitive node, ranging from repairable memory flips to destructive latch-up. A single-event functional interrupt, SEFI, halts the device until reset or a power cycle.

Silent data corruption, SDC, returns an incorrect result with a normal error status. In training, that result can enter all-reduce and spread through every model replica. Device tests express event occurrence against dose, and an assumed orbital dose rate converts those results into event-rate estimates.

輻射造成累積退化與單一粒子故障。總游離劑量 TID 以 rad(Si) 衡量沉積能量，逐漸改變電晶體臨界電壓與漏電。單粒子效應 SEE 則來自一顆粒子擊中敏感節點，範圍從可修復記憶體翻轉到破壞性閂鎖。單粒子功能中斷 SEFI 使裝置停擺，直到重置或斷電重啟。靜默資料損毀 SDC 則回傳錯誤結果，錯誤狀態仍顯示正常，訓練時可能經 all-reduce 傳播至各模型副本。元件測試把事件發生與劑量相連，再依假設的軌道劑量率換算事件率。

Radiation margins depend on altitude, shielding and the tested device. The published Trillium versions report separate maximum test doses, so the selected source version matters.

輻射餘裕取決於高度、屏蔽與受測元件，Trillium 各版本報告的最高測試劑量各異，因此須標明採用版本。

Altitude, shielding and cumulative-dose tests
#	Reported values and conditions
1	Altitude influences the dose environment.
2	Bhattacherjee et al. proposed commodity hardware with software hardening below an inner Van Allen boundary near 643 km. They cited the ISS at 408 km ^{[2, §4]}.
3	Suncatcher’s 650 km design lies near that boundary.
4	Google estimates 150 rad(Si) annually behind 10 mm aluminum-equivalent shielding, or 750 rad(Si) over five years ^{[36, p. 5]} ^{[36, p. 9]}.
7	A Trillium TPU v6e underwent 67 MeV proton testing at UC Davis Crocker Nuclear Laboratory.
8	Its most sensitive HBM showed irregularities after 2 krad(Si), “almost 3×” the mission dose.
9	The chip survived the highest tested cumulative dose, with zero TID-attributed hard failures.
10	Joule reports 10 krad(Si) ^{[36, p. 5]}, while the June 2026 arXiv v2 reports 15 krad(Si) ^{[108, §2.3]}.
13	This primer uses the peer-reviewed value.
14	Both tests support a substantial cumulative-dose margin under the stated shielding, shifting attention toward computational correctness.

高度、屏蔽與累積劑量測試
#	數值、條件與證據
1	高度影響劑量環境。
2	Bhattacherjee 等人主張，在約 643 km 的內范艾倫帶界線以下，商用硬體搭配軟體強化或可使用，並引述 408 km 國際太空站 ^{[2, §4]}。
3	Suncatcher 的 650 km 設計接近此界線。
4	Google 估計 10 mm 鋁當量屏蔽後，每年約 150 rad(Si)、五年 750 rad(Si) ^{[36, p. 5]} ^{[36, p. 9]}，並在 UC Davis Crocker 核子實驗室以 67 MeV 質子測試 Trillium TPU v6e。
5	最敏感的 HBM 在 2 krad(Si) 後出現異常，接近任務劑量三倍，整顆晶片則存活至最高測試累積劑量。
6	Joule 為 10 krad(Si) ^{[36, p. 5]}，2026 年 6 月 arXiv v2 為 15 krad(Si) ^{[108, §2.3]}，本教材採同儕審查值。
7	兩者都支持此屏蔽條件下的累積劑量餘裕，使設計焦點轉向計算正確性。

Silent corruption can occur much more often than a TPU-wide halt. End-to-end checks therefore matter for training correctness, even when cumulative-dose survival has margin.

靜默損毀可能比整顆 TPU 停擺頻繁得多，因此即使累積劑量存活有餘裕，端到端檢查仍關係到訓練正確性。

Trillium: dose-based event rates
#	Reported values and conditions
1	Joule reports SDC around one event per 17 rad, equivalent to roughly one failed inference per three million at one inference per second.
2	HBM uncorrectable errors occur about once per 44 rad, averaged across 203 events.
3	TPU SEFIs occur about once per 5 krad per chip, while host CPU and RAM SEFIs occur per 450 and 400 rad.
4	Workload-specific SDC rates are 14.4–20 rad per event, mainly in core logic and on-chip SRAM ^{[36, p. 9]} ^{[36, pp. 5–6]}.
7	At 150 rad annually, this gives about nine SDC events, 3.4 uncorrectable memory errors and 0.03 TPU SEFIs per chip-year.
8	TPU crashes therefore average roughly 33 chip-years apart, host CPU/RAM hangs about 17 months apart, and SDC about six weeks apart.
9	This ordering makes end-to-end correctness checks important, including redundant computation and checksummed collectives. Section 10.3 connects these requirements to the companion primer’s failure-handling chapter.

Trillium 的劑量事件率
#	數值、條件與證據
1	Joule 報告 SDC 約每 17 rad 一次，每秒一次推論時約每三百萬次失敗一次。
2	HBM 不可更正錯誤約每 44 rad 一次，平均自 203 事件。
3	TPU SEFI 約每晶片 5 krad 一次，主機 CPU 與 RAM 則各每 450、400 rad 一次。
4	SDC 依工作負載為每次 14.4–20 rad，主要來自核心邏輯與片上 SRAM ^{[36, p. 9]} ^{[36, pp. 5–6]}。
5	每年 150 rad 下，約每晶片年九次 SDC、3.4 次記憶體錯誤與 0.03 次 TPU SEFI。
6	TPU 當機平均約相隔 33 晶片年，主機 CPU／RAM 停擺約相隔 17 個月，SDC 則約六週一次。
7	這個頻率排序使端到端正確性檢查成為需求，例如冗餘運算與帶檢查碼的集合通訊，第 10.3 節會連結至姊妹教材的故障處理章。

Question問題	Calculation算式	Result結果
Silent corruptions per chip-year at 650 km650 km 每晶片年的靜默損毀次數	$150\,\text{rad/yr} \,/\, 17\,\text{rad}$	≈ 8.8 (≈ 9)computed, inputs ^{[36, p. 9]}, both from Joule計算值，輸入取自 ^{[36, p. 9]}，皆出自 Joule
Inferences per corruption at one inference per second每秒一次推論時每次損毀之間的推論數	$3.156\times 10^{7}\,\text{s} \,/\, 8.8$	≈ 3.6 millioncomputed, consistent with the paper's "≈1 per 3 million"計算值，與論文的「約每 300 萬次一次」一致
Uncorrectable HBM errors per chip-year每晶片年不可更正 HBM 錯誤次數	$150/44$	3.4computed, 44 rad per event from Joule p. 9 (203 events)計算值，每次事件 44 rad 取自 Joule p. 9（203 次事件）
TPU SEFIs per chip-year, and host SEFIs每晶片年 TPU SEFI 次數，以及主機 SEFI	$150/5000\;;\;150/450 + 150/400$	0.03 (1 per 33 chip-years) · 0.71 per host-yearcomputed, rates from Joule pp. 6, 9計算值，事件率取自 Joule pp. 6、9
Margin and time to the HBM onset dose到 HBM 異常起始劑量的餘裕與時間	$2000/750\;;\;2000/150$	2.7× · 13 yearscomputed, the paper says "almost 3×"計算值，論文寫「幾乎 3 倍」
An illustrative 1,000-chip orbital cluster一個示意性的 1,000 晶片軌道叢集	$1000\times 8.8 / 365\;;\;1000\times 0.03$	≈ 24 SDC per day · 30 TPU SEFIs per yearcomputed, the 1,000-chip size is this primer's choice, an illustrative design choice計算值，1,000 晶片為本教材選定的示意規模。

Beam tests and flight observations describe particular devices and radiation environments. Converting results across hardware and altitude requires the relevant cross-sections and exposure model.

射束與飛行觀察描述特定元件及輻射環境，跨硬體、高度換算時，需要相應截面與暴露模型。

Device-specific beam and flight evidence
#	Reported values and conditions
1	Device-specific beam evidence varies substantially.
2	NASA Goddard tested the Jetson TX2 with 200 MeV protons at MGH Burr Center and observed power-cycle-requiring SEFIs in every run.
3	Mean upset cross-section was 1.02 × 10⁻⁹ cm², ranging from 2.50 × 10⁻¹⁰ to 4.17 × 10⁻⁹.
4	Tests also recorded a Linux-load failure and one catastrophic device failure, with the two boards accumulating about 680 and 60 rad(Si) ^[110] agency report.
5	A 2025 heavy-ion study found CPU, GPU and peripheral SEEs, including latch-up, in Jetson Orin NX and Xavier NX.
6	Its abstract calls them “promising candidates”, with cross-sections requiring the full study ^[86].
7	In orbit, Xing et al.’s four standard Pi and Atlas boards at about 490 km recorded zero SEE computational errors over six months ^{[85, §6]}.
8	That evidence concerns those boards and altitude.
9	Converting it into rates for an HBM accelerator at 650 km requires device cross-sections and the relevant dose environment.

各元件的射束與飛行證據
#	數值、條件與證據
1	各元件的射束證據差異很大。
2	NASA Goddard 在 MGH Burr 中心以 200 MeV 質子測試 Jetson TX2 ^[60]，每輪都有需斷電重啟的 SEFI。
3	平均翻轉截面為 1.02 × 10⁻⁹ cm²，範圍 2.50 × 10⁻¹⁰ 至 4.17 × 10⁻⁹，另有 Linux 載入失敗及一次災難性元件故障，兩板累積約 680 與 60 rad(Si) ^[110] 機構報告。
4	2025 年重離子研究在 Orin NX、Xavier NX 的 CPU、GPU、周邊觀察到 SEE 與閂鎖，摘要稱它們為「有前景的候選」，截面需查完整研究 ^[86]。
5	Xing 等人的四片原版 Pi、Atlas 在約 490 km 運行六個月，記錄 SEE 計算錯誤為零 ^{[85, §6]}。
6	這項證據適用於那些板子與高度，換算 650 km HBM 級加速器的事件率，仍需元件截面與相應劑量環境。

Effect效應	What happens發生什麼	Measured value量測值	Source and tag來源與標籤
TID, HBMTID，HBM	Gradual degradation, irregularities appear逐漸退化，開始出現異常	after 2 krad(Si), vs ≈750 rad(Si) in 5 years2 krad(Si) 之後，對比 5 年約 750 rad(Si)	Trillium, 67 MeV protons ^{[36, p. 5]}Trillium，67 MeV 質子^{[36, p. 5]}
TID, whole chipTID，整顆晶片	Chip survived the highest tested dose整顆晶片存活至最高測試劑量	10 krad(Si) (Joule) · 15 krad(Si) (arXiv v2 §2.3)10 krad(Si)（Joule）· 15 krad(Si)（arXiv v2 §2.3）	^[36] , arXiv v2 preprint^[36] ， arXiv v2 預印本
SDCSDC	Incorrect result with normal error status錯誤結果，錯誤狀態顯示正常	≈1 per 17 rad → ≈9 per chip-year (computed)約每 17 rad 一次 → 每晶片年約 9 次（計算值）	^{[36, p. 9]}^{[36, p. 9]}
HBM UECCHBM 不可更正錯誤	Memory error detected by ECC and requiring recovery beyond ECCECC 已偵測、需採 ECC 以外恢復方式的記憶體錯誤	≈1 per 44 rad, averaged over 203 events約每 44 rad 一次（203 次事件平均）	^[36] ^[36]
SEFI, TPUSEFI，TPU	Chip halts until reset晶片停擺直到重置	≈1 per 5 krad per chip每顆晶片約每 5 krad 一次	^{[36, p. 9]}^{[36, p. 9]}
SEFI, Jetson TX2SEFI，Jetson TX2	System hang, power cycle required系統當掉，必須斷電重啟	every run at 200 MeV, σ_SEU mean 1.02 × 10⁻⁹ cm²200 MeV 每一輪都發生，σ_SEU 平均 1.02 × 10⁻⁹ cm²	Wyrwas, NASA GSFC 2019 agency reportWyrwas，NASA GSFC 2019 機構報告
SEE, COTS in orbitSEE，在軌商用元件	Computational errors from single events單粒子造成的計算錯誤	zero observed over 6 months at ≈490 km約 490 km、六個月內觀察值為零	^{[85, §6]} peer-reviewed^{[85, §6]} 同儕審查

Figure 8.3. The Trillium radiation-effects ladder shows dose per event or cumulative onset dose on a logarithmic axis. Reference lines mark one year, about 150 rad, and five years, about 750 rad, at 650 km. Events to the left occur several times per chip-year, making silent corruption and memory errors frequent design concerns.圖 8.3。Trillium 輻射效應階梯，以對數軸列出每事件劑量或累積異常起始劑量，並標記 650 km 一年約 150 rad、五年約 750 rad。位於一年線左側的事件每晶片年會發生多次，因此靜默損毀與記憶體錯誤是頻繁的設計考量。Sources來源: ^{[36, pp. 5–6, 9]}

Original figure note原始圖說出處

Drawn for this primer from Agüera y Arcas et al., Joule 2026, pp. 5–6, 9, dose rate from the same paper.

8.5Mass, launch cost and the server-in-orbit arithmetic質量、發射成本與「伺服器上軌道」的算術

Orbital-server cost combines hardware mass, supporting power and launch price. The historical comparison separates the latency case from the substantial launch burden.

軌道伺服器成本結合硬體質量、支援電力與發射價格，歷史比較將延遲優勢與發射負擔分開評估。

Historical orbital-server cost assumptions
#	Reported values and conditions
1	Orbital economics depend on launch price per kilogram and mass per useful kilowatt, including power and cooling hardware.
2	Bhattacherjee et al.’s HotNets 2020 study places a 64-core HPE ProLiant DL325 Gen10 on each Starlink satellite.
3	It weighs 15.6 kg, about 6% of the satellite’s mass and 1% of volume.
4	Power is 225 W idle and 350 W loaded, or roughly 20% of the estimated 1.5 kW solar output ^{[2, §4]}.
5	Falcon 9 launch costs about $42,000, implying about $2,700/kg.
6	Terrestrial ownership costs about $5,000 annually, making the orbital server roughly three times as expensive over three years.
7	Satellite life is five years against a three-year terrestrial refresh (§4–5).
8	Launch alone equals 2.8 times the three-year terrestrial cost, explaining the paper’s “cautiously encouraging” latency result alongside unfavorable economics.

歷史軌道伺服器成本假設
#	數值、條件與證據
1	軌道上的每一瓦都必須連同支撐它的陣列、電池與散熱板的公斤數一起被送上去，所以在軌運算的經濟學可以化約為「每公斤發射價格」乘以「每有用千瓦的公斤數」。
2	第一篇為網路社群做這道算術的論文是 Bhattacherjee 等人 2020 年在 HotNets 的思想實驗，他們在每顆 Starlink 衛星上放一台 64 核心的 HPE ProLiant DL325 Gen10 伺服器。
3	這台伺服器重 15.6 kg，作者估計約為當時 Starlink 衛星質量的 6%、體積的 1%，閒置耗電 225 W、負載下 350 W，對比他們估計的約 1.5 kW 平均太陽能，所以一台「強悍」伺服器的電力負擔約為 20%^{[2, §4]}。
4	以 Falcon 9 的每公斤價格發射它約需 42,000 美元，隱含約每公斤 2,700 美元，而由於資料中心伺服器的總持有成本約每年 5,000 美元，即使衛星的五年壽命長於地面伺服器三年的汰換週期，軌道伺服器三年下來仍約貴三倍（§4–5）。
5	計算表顯示光是發射就相當於地面三年成本的 2.8 倍，這正是該論文在延遲上的結論為「審慎樂觀」，在價格上卻令人卻步的原因。

Suncatcher compares amortized launched-power cost with terrestrial energy spending under a projected launch-price decline. Additional accelerator, cooling, communication and replacement costs define a broader economic study.

Suncatcher 在發射降價推估下，比較已發射電力攤提與地面能源支出，加速器、散熱、通訊與更換成本則屬更完整的經濟評估。

Suncatcher: projected launch and power costs
#	Reported values and conditions
1	Suncatcher’s economic case depends on lower launch prices.
2	It starts at $3,600/kg for reusable Falcon 9 and fits 18–24% cost reduction per cumulative-mass doubling, approximately 20%.
3	The projected mid-2030s $200/kg requires about 370,000 additional tonnes, or roughly 1,800 Starship launches.
4	Modeled Starship floors are below $60/kg at ten uses and at most $15/kg at one hundred ^{[36, pp. 6, 9–10, Table 1]}.
6	For a 575 kg, 28 kW bus over five years, launched power costs about $14,700 per kW-year today and $810 at $200/kg.
7	The US machine-learning data-center comparison is $570–3,000 per kW-year, using $0.06–0.25/kWh and PUE 1.09–1.4.
8	At $200/kg the authors call amortized launch cost roughly comparable to energy cost on a per-kW basis.
9	This is a launched-power comparison.
10	Accelerators, radiators, ISL terminals and five-year cluster replacement require additional cost accounting.

Suncatcher 的發射與電力成本推估
#	數值、條件與證據
1	Suncatcher 的經濟論證依賴更低的發射價格。
2	論文從可重複使用 Falcon 9 的每公斤 3,600 美元出發，擬合累積質量加倍時成本下降 18–24%、約 20%。
3	2030 年代中期每公斤 200 美元的推估，需再發射約 370,000 公噸、約 1,800 次 Starship。
4	模型下限在十次重用時低於 60 美元，一百次時最多 15 美元 ^{[36, pp. 6, 9–10, Table 1]}。
5	575 kg、28 kW 平台攤五年，已發射電力現價約每 kW·年 14,700 美元，200 美元/kg 時約 810 美元。
6	地面機器學習資料中心比較值為 570–3,000 美元，採 0.06–0.25 美元/kWh 與 PUE 1.09–1.4。
7	作者因此認為 200 美元/kg 時，按 kW 攤提的發射成本可接近能源成本。
8	此比較限於已發射電力，加速器、散熱板、ISL 終端與五年叢集更換仍需另計。

Question問題	Calculation算式	Result結果
Launch price implied by HotNets 2020HotNets 2020 隱含的發射價格	$\$42{,}000 / 15.6\,\text{kg}$	≈ $2,700/kgcomputed, inputs ^{[2, §4]}計算值，輸入取自 ^{[2, §4]}
Launch alone against three years of terrestrial TCO光是發射對比地面三年總持有成本	$\$42{,}000 / (3\times\$5{,}000)$	2.8×computed, TCO from the same paper計算值，總持有成本取自同一論文
The same server at $3,600/kg and at $200/kg同一台伺服器在每公斤 3,600 與 200 美元時	$15.6\times 3600\;;\;15.6\times 200$	$56,160 · $3,120computed, prices from ^{[36, p. 10]}計算值，價格取自 ^{[36, p. 10]}
Launched-power price, 575 kg / 28 kW / 5 years已發射電力價格，575 kg／28 kW／5 年	$\frac{575\times 3600}{28\times 5}\;;\;\frac{575\times 200}{28\times 5}$	≈ $14,800 · ≈ $820 per kW·yrcomputed, the paper gives $14,700 and $810計算值，論文給 14,700 與 810 美元
Terrestrial power spend per kW·yr, both ends地面每 kW·年電力支出的兩端	$8766\,\text{h}\times 0.06\times 1.09\;;\;8766\times 0.25\times 1.4$	≈ $573 · ≈ $3,068computed, matches the paper's $570–3,000計算值，與論文的 570–3,000 美元相符
Launch cost per watt at 49 W/kg of whole satellite整星 49 W/kg 時每瓦的發射成本	$3600/49\;;\;200/49$	≈ $73/W · ≈ $4.1/Wcomputed, 49 W/kg from Section 8.2計算值，49 W/kg 取自第 8.2 節
McCalip's orbital vs terrestrial cost per GWMcCalip 每 GW 的軌道對地面成本	$51.1/15.9$	3.2×computed, inputs via Fierce Network (press)計算值，輸入經 Fierce Network（媒體）

Independent orbital-cost estimates remain above terrestrial alternatives. Uncertainty in bus mass propagates directly into launched-power cost, before adding the rest of the compute system.

獨立估計的軌道成本仍高於地面方案，平台質量的資料缺口會直接傳入已發射電力成本，其他運算系統成本也需加入。

Independent cost and mass estimates
#	Reported values and conditions
1	Independent estimates give higher orbital costs.
2	Varda’s Andrew McCalip estimates $51.1 billion for 1 GW orbital solar compute against $15.9 billion on Earth, excluding compute hardware in both.
3	Fierce Network reports these figures press, a ratio near 3.2 alongside Bhattacherjee’s earlier factor of three.
4	V2 Mini mass also remains a source uncertainty.
5	Suncatcher assumes 575 kg, while secondary sources range from below 600 to about 800 kg (fact base Part C, item 20).
6	A primary SpaceX mass figure would resolve that range, and launched-power cost scales directly with mass.
7	Panel 8.1 gives 44 kg of array and battery for 700 W at 550 km.
8	Launching that mass costs about $158,000 at $3,600/kg or $8,800 at $200/kg, before radiators, structure and accelerators.

獨立成本與質量估計
#	數值、條件與證據
1	獨立估計得到較高的軌道成本。
2	Fierce Network 報告 Varda 的 Andrew McCalip 估計，1 GW 軌道太陽能運算為 511 億美元、地面為 159 億，兩者都另計運算硬體媒體，比值約 3.2，接近 Bhattacherjee 先前的三倍。
3	V2 Mini 質量也是資料缺口，Suncatcher 採 575 kg，二手來源從 600 kg 以下到約 800 kg（事實庫 Part C，第 20 項），需要 SpaceX 一手值來界定範圍。
4	已發射電力成本隨質量等比例變動。
5	面板 8.1 在 550 km、700 W 下給出陣列加電池 44 kg，按 3,600 或 200 美元/kg 發射，約需 158,000 或 8,800 美元，散熱板、結構與加速器另計。

8.6What has flown哪些真的飛了

Flight records establish on-board computation at several hardware scales. Mission telemetry, peer-reviewed measurements and operator announcements each support a specific level of evidence.

飛行紀錄建立各種硬體尺度的機上運算，任務遙測、同儕審查量測與業者宣布則各支持特定證據程度。

Flown systems and evidence status
#	Reported values and conditions
1	Flight records need their evidence tags.
2	ESA’s Φ-Sat-1 carried CloudScout, a 2.1 MB convolutional model on Myriad 2, with 325 ms inference, 1.8 W and 92% accuracy.
3	Its 2020 paper preceded in-orbit validation ^[87].
4	Baoyun, launched December 2021, and BUPT-1, January 2023, provide peer-reviewed thermal, power and radiation measurements ^[85].
5	Three-Body launched twelve satellites on 14 May 2025, with operator claims of 744 TOPS and an eight-billion-parameter model per satellite.
6	Those press-reported claims differ from government figures (fact base Part D, item 28) company via press.
7	Starcloud-1 carried an H100 on a 60 kg satellite into a 325 km orbit in November 2025 for about eleven months.
8	Company demonstrations ran Gemma and nanoGPT, with power, temperature and throughput telemetry still awaiting publication company.
9	Its duration and altitude define a separate radiation regime from a five-year mission.
10	Google and Planet’s Suncatcher MVP launched on Transporter-18 on 1 October 2026, established contact, and was “operating as expected” company.
11	Press accounts describe four Trillium TPUs, about 1 kW solar, a 15–20 min duty cycle and ground-only communication press.

已飛行系統與證據狀態
#	數值、條件與證據
1	飛行紀錄須連同證據標籤解讀。
2	ESA 的 Φ-Sat-1 搭載 Myriad 2 上的 2.1 MB CloudScout，推論為 325 ms、1.8 W，準確率 92%，其 2020 年論文早於在軌驗證 ^[87]。
3	2021 年 12 月寶雲號與 2023 年 1 月北郵一號提供同儕審查的熱、電力與輻射量測 ^[85]。
4	三體於 2025 年 5 月 14 日發射十二顆，業者宣稱各 744 TOPS、八十億參數模型，媒體轉述數字與政府資料有差異（事實庫 Part D，第 28 項）公司（經媒體）。
5	Starcloud-1 於 2025 年 11 月把一顆 H100 隨 60 kg 衛星送入 325 km 軌道，任務約十一個月。
6	公司示範 Gemma 與 nanoGPT，功率、溫度、吞吐量遙測仍待公開公司，其高度與時長界定另一種輻射環境。
7	Google、Planet 的 Suncatcher MVP 於 2026 年 10 月 1 日搭乘 Transporter-18 發射、建立聯繫，回報「運作如預期」公司。
8	媒體描述四顆 Trillium TPU、約 1 kW 太陽能、15–20 分鐘工作週期與純地面通訊媒體。

System系統	Date日期	Compute and what it showed運算硬體與所展示的內容	Status and tag狀態與標籤
Φ-Sat-1 / CloudScout ^[88]Φ-Sat-1／CloudScout^[88]	2020	Myriad 2 VPU, 325 ms and 1.8 W per inference, 92% accuracyMyriad 2 VPU，每次推論 325 ms、1.8 W，準確率 92%	Flown, paper pre-dates in-orbit validation peer-reviewed已飛行，論文早於在軌驗證同儕審查
Baoyun and BUPT-1 (Tiansuan)寶雲號與北郵一號（天算）	Dec 2021 · Jan 20232021 年 12 月 · 2023 年 1 月	2 × Raspberry Pi 4B, 2 × Atlas 200 DK on BUPT-1, thermal, power and SEE measured北郵一號上 2 × Raspberry Pi 4B、2 × Atlas 200 DK，量測了熱、電力與 SEE	Flown, measured peer-reviewed已飛行、有量測同儕審查
Three-Body Computing Constellation三體計算星座	14 May 20252025 年 5 月 14 日	12 satellites, 744 TOPS each and an 8B model per satellite, claimed12 顆衛星，宣稱每顆 744 TOPS、每顆 80 億參數模型	Flown, figures inconsistent company via press已飛行，各方數字有差異公司（經媒體）
Starcloud-1Starcloud-1	Nov 20252025 年 11 月	One H100 on a 60 kg satellite at 325 km. Gemma inference and nanoGPT demonstration, telemetry pending.325 km、60 kg 衛星搭載一顆 H100，示範 Gemma 推論與 nanoGPT，遙測待公開。	Flown, measurements pending company已飛行，量測待公開公司
Suncatcher MVP (Google with Planet)Suncatcher MVP（Google 與 Planet）	1 Oct 20262026 年 10 月 1 日	Four Trillium TPUs, ≈1 kW, 15–20 min duty cycle, ground-only communication (press-reported)四顆 Trillium TPU、約 1 kW、15–20 分鐘工作週期、純地面通訊（媒體報導）	Flown, in contact company, specs press已飛行、已聯繫公司，規格媒體
Two Planet satellites for Suncatcher為 Suncatcher 打造的兩顆 Planet 衛星	20272027 年	TPUs plus two spacecraft flying in tandem with a high-bandwidth crosslinkTPU，加上兩艘以高頻寬交叉鏈路串聯飛行的太空船	Proposed company提案公司
Suncatcher 81-satellite clusterSuncatcher 81 顆衛星叢集	undated日期待定	Dawn–dusk SSO at 650 km, ≈28 kW per satellite, ≈10 Tbps links targeted650 km 晨昏 SSO，每顆約 28 kW，鏈路目標約 10 Tbps	Design study peer-reviewed設計研究同儕審查
SpaceX orbital-compute filingSpaceX 軌道運算申請	filed 20262026 年申請	Up to one million satellites, 100 kW per tonne, >99% solar operation最多一百萬顆衛星，每公噸 100 kW，>99% 時間太陽能運作	Proposed company via press提案公司（經媒體）

Flown systems compute independently and downlink their results. A shared-job link between compute satellites remains an open flight capability. Planet’s planned 2027 pair will test tandem flight and “high-bandwidth cross-link communications” company. Its scope is two nodes, while a larger fabric requires further demonstration. James Manyika also places useful operational systems beyond the next few years press. Figure 8.4 shows flight hardware growing from about 2 W to about 1 kW in six years, alongside proposed clusters and gigawatt-scale systems.

已飛行系統各自運算，再把結果下傳。承載共同工作的運算衛星交叉鏈路，仍是待展示的飛行能力。Planet 規劃的 2027 年雙星將測試串聯飛行與「高頻寬交叉鏈路通訊」公司，範圍為兩個節點，更大的網路架構需後續示範。James Manyika 也把實用系統的時程放在往後數年之後媒體。圖 8.4 顯示飛行硬體在六年內從約 2 W 增至約 1 kW，旁列的提案則涵蓋叢集與吉瓦規模。

Figure 8.4. Orbital computing from 2020 to 2027. Flown hardware grows from 1.8 W inference to a press-reported ≈1 kW TPU prototype, with independent computation and downlinked results. A two-satellite compute crosslink test is planned for 2027, while cluster-scale designs await dates.圖 8.4。2020–2027 年在軌運算。已飛行硬體從 1.8 W 推論增至媒體報導約 1 kW TPU 原型，皆各自運算並下傳結果。雙運算衛星交叉鏈路規劃於 2027 年測試，叢集設計日期仍待定。Sources來源: ^[84] ^[36]

Original figure note原始圖說出處

Drawn for this primer from Giuffrida et al. 2020, Wang & Li 2023, Xing et al. 2024, Live Science (Three-Body), NVIDIA and DCD (Starcloud-1), Google and Planet announcements, Joule 2026. Tags as in the table above.

Chapter summary

本章摘要

Orbital edge computing reduces the data sent through limited ground contacts, while Kodan addresses the resulting processor bottleneck through model specialization. Solar arrays and eclipse batteries determine power-system mass, with dawn–dusk orbits reducing storage demand. Radiator emission follows εσT⁴, and flight measurements show that the conduction path can constrain cooling first. Trillium’s shielded cumulative-dose margin shifts attention toward frequent silent corruption and memory errors. Suncatcher’s launched-power comparison depends on a projected launch-price decline, while independent studies estimate higher total orbital costs. Flown systems currently establish independent on-board computing, with shared-job crosslinks still awaiting demonstration.

軌道邊緣運算縮小有限地面通聯需承載的資料，Kodan 則以模型專門化處理後續的處理器瓶頸。太陽能陣列與地影電池決定電力系統質量，晨昏軌道降低儲能需求。散熱板遵循 εσT⁴，飛行量測也顯示傳導路徑可能先成為限制。Trillium 的屏蔽累積劑量餘裕，使設計焦點轉向頻繁的靜默損毀與記憶體錯誤。Suncatcher 的已發射電力比較依賴發射降價推估，獨立研究則估出更高總成本。飛行系統目前建立各自的機上運算，承載共同工作的交叉鏈路仍待示範。

Where these ideas go next

這些概念接下來用在哪裡

Chapter 9 studies caching, visibility-constrained federated learning and on-board inference under these compute limits, returning to inference in Section 9.4. Section 10.3 uses the radiation ladder for distributed-training failure models. Chapter 11 applies the power, thermal and launch constraints to Suncatcher.

第 9 章要問：以本章已算出價格的運算能力，一個星座能提供哪些服務，從逆著軌道移動的快取，到受可見性限制的聯邦學習，並在第 9.4 節回到機上推論。輻射階梯會在第 10.3 節以分散式訓練的故障模型再次出現，而電力、散熱與發射的數字則成為第 11 章 Suncatcher 叢集的限制條件。

Papers behind this chapter本章所依據的論文

ASPLOS 2020Orbital Edge Computing: Nanosatellite Constellations as a New Class of Computer System ASPLOS 2023Kodan: Addressing the Computational Bottleneck in Space ACM HotNets 2020In-orbit Computing: An Outlandish Thought Experiment? ACM MobiCom 2024Deciphering the Enigma of Satellite Computing with COTS Devices: Measurement and Analysis Joule 2026 / arXiv 2511.19468Toward a Future Space-Based, Highly Scalable AI Infrastructure System Design

Question問題	Calculation算式	Result結果
Is 15 GB per 10-minute session consistent with 200 Mbit/s?每次 10 分鐘通聯 15 GB 與 200 Mbit/s 一致嗎？	\(15\times 8\,\text{Gbit} / 600\,\text{s}\)	200 Mbit/scomputed, inputs ^{[60, §3.3]}計算值，輸入來自 ^{[60, §3.3]}
Fraction of raw data kept by the on-board model機上模型保留的原始資料比例	\(0.75 / 15\)	5%computed, the paper's Fig. 6 reports 5–25% across its scenarios計算值，論文 Fig. 6 在各情境報告 5–25%
Time to downlink 0.75 GB at 200 Mbit/s以 200 Mbit/s 下傳 0.75 GB 所需時間	\(0.75\times 8\,\text{Gbit} / 0.2\,\text{Gbit/s}\)	30 scomputed, matches the paper's "about 30 s"計算值，與論文的「約 30 秒」相符
Station ratio from the two counts the paper gives以論文給的兩個地面站數量算出的比值	\(112 / 6\)	18.7×computed, 185/9 = 20.6× for satellites per station, the paper's headline across its sweep is ">24×"計算值，每站衛星數 185/9 = 20.6×，論文在整個掃描範圍的標題數字是「>24×」

#	數值、條件與證據
1	地影時長由軌道幾何決定。
2	550 km 的圓軌道半徑為 6,921 km，太陽位於軌道面時，陰影半角為 \(\arcsin(6371/6921) \approx 67.0^\circ\)。
3	衛星在 360° 中有 2 × 67.0° 處於地影，比例 0.372，在 95.65 分鐘軌道中為 35.6 分鐘。
4	地影時由電池供應酬載，陣列需放大 \(1/(1-0.372) = 1.59\) 倍，在約 60 分鐘日照內充回電池。
5	晨昏太陽同步軌道藉節點進動追隨晨昏線，一年多數時候接近連續日照。
6	Suncatcher 選擇 650 km 晨昏軌道 ^{[36, p. 2]}。
7	SpaceX 2026 申請宣稱太陽能運作時間「超過 99%」公司（經媒體），Starcloud 第二星也據報導以 SSO 為目標媒體。
8	Suncatcher 同時承認部分地面位置的延遲會增加（p. 2），第 13.5 節將檢視這項取捨。

Question問題	Calculation算式	Result結果
Eclipse half-angle at 550 km, Sun in the orbital plane550 km、太陽在軌道面內的地影半角	\(\arcsin\!\left(\frac{6371}{6921}\right)\)	67.0°computed, R_E = 6,371 km, h = 550 km計算值，R_E = 6,371 km，h = 550 km
Eclipse fraction and duration地影比例與時長	\(\frac{2\times 67.0^\circ}{360^\circ}\times 95.65\,\text{min}\)	0.372 · 35.6 mincomputed, period from Section 1.1計算值，週期取自第 1.1 節
Array oversize factor to recharge during sunlight為在日照期充電所需的陣列放大倍數	\(1/(1-0.372)\)	1.59×computed, charge losses neglected計算值，忽略充電損耗
Array area for a 700 W accelerator, continuous sun vs 550 km700 W 加速器的陣列面積，連續日照 vs 550 km	\(\frac{700}{400}\;;\;\frac{700}{400\times 0.628}\)	1.75 m² · 2.79 m²computed, 400 W/m² from NASA SST-SOA 2026 Table 3-1計算值，400 W/m² 取自 NASA SST-SOA 2026 Table 3-1
Energy the battery must deliver per eclipse at 700 W700 W 下每次地影電池須供應的能量	\(700\,\text{W}\times 35.6/60\,\text{h}\)	415 Whcomputed計算值
Battery capacity and mass at 30% DoD放電深度 30% 下的電池容量與質量	\(\frac{415}{0.30}\;;\;\frac{1383}{270}\ldots\frac{1383}{150}\)	1,383 Wh · 5.1–9.2 kgcomputed, 150–270 Wh/kg from NASA SST-SOA 2026, DoD target from ^[85]計算值，150–270 Wh/kg 取自 NASA SST-SOA 2026，DoD 目標取自 ^[85]
The "8×" solar multiplier decomposed「8 倍」太陽能倍數的拆解	\(\frac{1361}{1000}\times\frac{24}{5}\)	≈ 6.5computed, 1,361 W/m² from ^{[36, p. 10]}, ~5 equivalent full-sun hours per day is this primer's mid-latitude assumption計算值，1,361 W/m² 取自 ^{[36, p. 10]}，每天約 5 個等效全日照小時是本教材對中緯度的假設
Suncatcher's bus estimate checked檢驗 Suncatcher 的平台估算	\(105\,\text{m}^2\times 1.361\times 0.22\times 0.9\)	28.3 kWcomputed, inputs ^{[36, p. 10]} (105 m², 22%, 90% packing), paper states ≈28 kW計算值，輸入取自 ^{[36, p. 10]}（105 m²、22%、90% 填充率），論文寫約 28 kW

#	Reported values and conditions
1	Vacuum cooling relies on infrared emission from spacecraft surfaces.
2	Stefan–Boltzmann heat flux is \(q = \varepsilon\sigma T^4\), with emissivity ε and σ = 5.670 × 10⁻⁸ W m⁻² K⁻⁴.
3	A radiator is the dedicated heat-emitting surface.
4	At emissivity 0.9, one face emits about 284 W/m² at 273 K, 413 at 300 K, 535 at 320 K, and 766 at 350 K.
5	Deep space provides a cold sink, while electronics temperature limits the radiator’s upper operating temperature.
6	Heat must flow from the hotter chip to the cooler radiator.
7	Earth-facing surfaces also absorb planetary infrared and reflected sunlight.
8	This primer assumes 100–240 W/m² of Earth-facing backload as an order-of-magnitude estimate, with handbook verification still required.

#	數值、條件與證據
1	真空中的太空船靠表面紅外線輻射散熱，史特凡–波茲曼定律給出熱通量 \(q = \varepsilon\sigma T^4\)，ε 為發射率，σ = 5.670 × 10⁻⁸ W m⁻² K⁻⁴。
2	輻射散熱板是專用排熱表面，發射率 0.9 時單面在 273 K 輻射約 284 W/m²，300 K 為 413，320 K 為 535，350 K 為 766。
3	深空提供低溫熱沉，電子元件則限制散熱板的最高工作溫度，熱從較熱晶片流向較冷散熱板。
4	朝地面另吸收地球紅外線與反射陽光。
5	本教材以 100–240 W/m² 作背景熱負載的數量級假設，手冊驗證仍待補充。

Question問題	Calculation算式	Result結果
One-sided radiator flux at 300 K, ε = 0.9300 K、ε = 0.9 的單面散熱板輻射通量	\(0.9\times 5.670\times 10^{-8}\times 300^4\)	413 W/m²computed, Stefan–Boltzmann, 0 K sink, zero backload計算值，史特凡–波茲曼，0 K 冷空，背景負載設零
The same at 273 K, 320 K and 350 K273 K、320 K 與 350 K 時的同一數值	\(0.9\,\sigma T^4\)	284 · 535 · 766 W/m²computed計算值
One-sided radiator area for a 700 W accelerator700 W 加速器所需的單面散熱板面積	\(700/535\;;\;700/413\)	1.3 m² (320 K) · 1.7 m² (300 K)computed, before backload, two-sided halves the area計算值，背景負載另計，雙面可將面積減半
Radiator area per kilowatt at 300 K300 K 時每千瓦所需散熱板面積	\(1000/413\)	2.4 m²/kW one-sidedcomputed, 1.2 m²/kW two-sided計算值，雙面為 1.2 m²/kW
Net flux with a 240 W/m² backload on an Earth-facing face at 300 K朝地面在 300 K 承受 240 W/m² 背景負載時的淨通量	\(413-240\)	173 W/m²computed, backload is this primer's order-of-magnitude estimate計算值，背景負載為本教材的數量級估計
Energy of a 3-hour Pi run against one orbit's harvest on BUPT-1北郵一號上 Pi 跑 3 小時的能量對一圈採集的能量	\(4.82\,\text{W}\times 3\,\text{h}\;;\;16\,\text{Wh}\)	14.5 Wh vs 16 Whcomputed, inputs ^{[85, Tabs. 3–4, Fig. 13]}, the paper's experiments ran 3 h of compute over about two orbits計算值，輸入取自 ^{[85, Tabs. 3–4]}、Fig. 13，論文的實驗在約兩圈內運算 3 小時
Energy saving per task in orbit, Atlas and YOLO-Fastest在軌每任務的能量節省，Atlas 與 YOLO-Fastest	\(1-\frac{94.9}{106.2}\;;\;1-\frac{21}{21.38}\)	10.6% · 1.8%computed, J per 100 images from ^{[85, §4.3]}, the paper summarises this as 2–10%計算值，每 100 張影像的焦耳數取自 ^{[85, §4.3]}，論文總結為 2–10%
Usable battery energy on BUPT-1 at the 30% DoD target北郵一號在 30% 放電深度目標下可用的電池能量	\(2\times 115\times 0.30\)	69 Whcomputed, about 7 h of a 10.19 W Atlas, or 14 h of a 4.82 W Pi計算值，約可供 10.19 W 的 Atlas 跑 7 小時，或 4.82 W 的 Pi 跑 14 小時

Question問題	Calculation算式	Result結果
Silent corruptions per chip-year at 650 km650 km 每晶片年的靜默損毀次數	\(150\,\text{rad/yr} \,/\, 17\,\text{rad}\)	≈ 8.8 (≈ 9)computed, inputs ^{[36, p. 9]}, both from Joule計算值，輸入取自 ^{[36, p. 9]}，皆出自 Joule
Inferences per corruption at one inference per second每秒一次推論時每次損毀之間的推論數	\(3.156\times 10^{7}\,\text{s} \,/\, 8.8\)	≈ 3.6 millioncomputed, consistent with the paper's "≈1 per 3 million"計算值，與論文的「約每 300 萬次一次」一致
Uncorrectable HBM errors per chip-year每晶片年不可更正 HBM 錯誤次數	\(150/44\)	3.4computed, 44 rad per event from Joule p. 9 (203 events)計算值，每次事件 44 rad 取自 Joule p. 9（203 次事件）
TPU SEFIs per chip-year, and host SEFIs每晶片年 TPU SEFI 次數，以及主機 SEFI	\(150/5000\;;\;150/450 + 150/400\)	0.03 (1 per 33 chip-years) · 0.71 per host-yearcomputed, rates from Joule pp. 6, 9計算值，事件率取自 Joule pp. 6、9
Margin and time to the HBM onset dose到 HBM 異常起始劑量的餘裕與時間	\(2000/750\;;\;2000/150\)	2.7× · 13 yearscomputed, the paper says "almost 3×"計算值，論文寫「幾乎 3 倍」
An illustrative 1,000-chip orbital cluster一個示意性的 1,000 晶片軌道叢集	\(1000\times 8.8 / 365\;;\;1000\times 0.03\)	≈ 24 SDC per day · 30 TPU SEFIs per yearcomputed, the 1,000-chip size is this primer's choice, an illustrative design choice計算值，1,000 晶片為本教材選定的示意規模。

Question問題	Calculation算式	Result結果
Launch price implied by HotNets 2020HotNets 2020 隱含的發射價格	\(\$42{,}000 / 15.6\,\text{kg}\)	≈ $2,700/kgcomputed, inputs ^{[2, §4]}計算值，輸入取自 ^{[2, §4]}
Launch alone against three years of terrestrial TCO光是發射對比地面三年總持有成本	\(\$42{,}000 / (3\times\$5{,}000)\)	2.8×computed, TCO from the same paper計算值，總持有成本取自同一論文
The same server at $3,600/kg and at $200/kg同一台伺服器在每公斤 3,600 與 200 美元時	\(15.6\times 3600\;;\;15.6\times 200\)	$56,160 · $3,120computed, prices from ^{[36, p. 10]}計算值，價格取自 ^{[36, p. 10]}
Launched-power price, 575 kg / 28 kW / 5 years已發射電力價格，575 kg／28 kW／5 年	\(\frac{575\times 3600}{28\times 5}\;;\;\frac{575\times 200}{28\times 5}\)	≈ $14,800 · ≈ $820 per kW·yrcomputed, the paper gives $14,700 and $810計算值，論文給 14,700 與 810 美元
Terrestrial power spend per kW·yr, both ends地面每 kW·年電力支出的兩端	\(8766\,\text{h}\times 0.06\times 1.09\;;\;8766\times 0.25\times 1.4\)	≈ $573 · ≈ $3,068computed, matches the paper's $570–3,000計算值，與論文的 570–3,000 美元相符
Launch cost per watt at 49 W/kg of whole satellite整星 49 W/kg 時每瓦的發射成本	\(3600/49\;;\;200/49\)	≈ $73/W · ≈ $4.1/Wcomputed, 49 W/kg from Section 8.2計算值，49 W/kg 取自第 8.2 節
McCalip's orbital vs terrestrial cost per GWMcCalip 每 GW 的軌道對地面成本	\(51.1/15.9\)	3.2×computed, inputs via Fierce Network (press)計算值，輸入經 Fierce Network（媒體）

8.1The downlink wall: orbital edge computing下行之牆：軌道邊緣運算

8.2Power: solar, batteries and eclipse電力：太陽能、電池與地影

Power budget of a compute satellite運算衛星的電力預算

8.3Heat: the binding constraint散熱：真正的束縛

Radiator sizing散熱板尺寸估算

8.4Radiation: TID, SEE, SEFI and SDC輻射：TID、SEE、SEFI 與 SDC

8.5Mass, launch cost and the server-in-orbit arithmetic質量、發射成本與「伺服器上軌道」的算術

8.6What has flown哪些真的飛了

Papers behind this chapter本章所依據的論文

Check your understanding檢驗你的理解