Spacecraft Design

Subsystems, power, thermal and mission requirements: systems engineering and budgets, orbits and the space environment, solar arrays and batteries, thermal balance, structures, delta-v, attitude control, communications links and reliability, with six labs. Free, self-paced, and tied to NASA’s Landsat 9, Europa Clipper and small-spacecraft technology.

NASA/Kim Shiflett (KSC-20210927-PH-KLS04_0013, Sept. 27, 2021)NASA/Ben Smegelsky (KSC-20240124-PH-JBS01_0071)NASA/Liz Wilk (KSC-20221109-PH-LNW01_0001)NASA (ISS066-E-080762, Nov. 8, 2021)

Courses › AERO 430

Download the PDF study guide

About this course

This is a free self-study course outline written by Saving Planets. It is not a university course, it carries no academic credit, and no school is involved.

Its scope follows a one-semester senior spacecraft design course for aerospace engineers. It is modeled on the topics and depth of MIT 16.851 Satellite Engineering (free on MIT OpenCourseWare), using NASA’s free Systems Engineering Handbook and Small Spacecraft Technology State of the Art report, which we link where they help. None of those authors, schools or agencies endorses this page.

What we add: every unit ties to real work with a cited public source (NASA’s Landsat 9, Europa Clipper and PACE missions and NASA’s small-spacecraft technology survey), every number on the page is re-computed by a checking script before it goes live, and every lab has a free simulation or a spreadsheet.

Work through it in order. Each unit has goals, key ideas, equations, step-by-step examples, practice with full answers, common mistakes, flashcards and a quiz. Your progress is saved only in this browser.

How this course helps save the planet

Earth-observing satellites are spacecraft design made useful: power, thermal, pointing and communications all have to work for years so scientists can track forests, water, crops and climate.

Good design also means long life and less waste in orbit. Each unit ends with a short, sourced section. Values that are not from a source are labeled as sample or textbook values.

Back to top

Before you start

Prerequisites

  • Orbital Mechanics: orbits, periods and Δv.
  • Thermodynamics: heat transfer and radiation basics.
  • Circuits: power, voltage and current.
  • Flight Dynamics & Controls and Aerospace Structures: attitude control, stiffness and loads.

How to study

  • Start every design from requirements, and keep a budget (mass, power, Δv, link) for every subsystem.
  • Carry margins and say where they live.
  • Track units: watts versus watt-hours, kelvin for radiation, decibels for links.
  • Check every answer against a real mission’s order of magnitude.
  • Sketch the spacecraft and its orbit before computing anything.
  • Do every practice problem on paper before opening the answer, and retake the quizzes a few days later.

Lab equipment (for the wet labs)

  • A computer or tablet for the free PhET Blackbody Spectrum and Circuit Construction Kit simulations.
  • Spreadsheet software (any free one works), or Python.
  • NASA mission pages and the Small Spacecraft Technology report in a web browser.
  • A calculator.

Back to top

Suggested 15-week schedule

About 6 to 9 hours a week: reading, practice problems and, in lab weeks, the lab.

WeekUnitTopicsReading
1Mission Requirements and Systems EngineeringRequirements and budgets; Lab ANASA SE Handbook
2Orbits and the Space EnvironmentOrbits and environment; Lab BMIT 16.851
3Power Generation: Solar ArraysSolar arrays; Lab CNASA SST SOA
4Energy Storage and the Power BudgetBatteries and power budget; Lab DNASA SST SOA
5Thermal ControlThermal control; Lab EMIT 16.851
6Structures, Mechanisms and Launch LoadsStructures and launch loadsMIT 16.851
7Propulsion and the Delta-v BudgetΔv budgets; midterm practiceMIT 16.851
8Attitude Determination and Control SubsystemADCS requirementsMIT 16.851
9Attitude Determination and Control SubsystemSensors, actuators and momentumNASA SST SOA
10Communications and Data HandlingLink budgetsMIT 16.851
11Communications and Data HandlingData handling; Lab FNASA Landsat 9
12Reliability, Testing and End of LifeReliability and redundancyNASA SE Handbook
13Reliability, Testing and End of LifeTesting and calibrationNASA Landsat 9
14Reliability, Testing and End of LifeOperations and disposalNASA SE Handbook
15Reliability, Testing and End of LifeReview; final practiceMIT 16.851

Back to top

Your progress

Tick units and labs as you finish them, and take the quizzes. Progress and quiz scores are saved only in this browser, never sent to us.

Turn on JavaScript to track progress.

Back to top

Unit 1 · Week 1

Mission Requirements and Systems Engineering

Mission objectives, requirements, the project life cycle, trade studies, subsystem budgets, and design margins.

Learning objectives

By the end of this unit you can:

  • Turn mission goals into measurable requirements.
  • Build a mass budget with margin.
  • Run a simple weighted trade study.
  • Explain why margins shrink through a project.

Key concepts

  • A mission starts with objectives; requirements make them measurable and verifiable (a number, a unit and a test).
  • Projects move through phases from concept to operations, with reviews that check requirements are met.
  • Every resource gets a budget: mass, power, Δv, data, pointing and cost, each with a margin.
  • Early designs carry large margins (often 20–30%, textbook values) because estimates are uncertain; margins shrink as hardware matures.
  • Trade studies score options against weighted criteria; the weights matter as much as the scores.

Key equations

malloc=mest(1+M)m_{alloc}=m_{est}(1+M)
Mass with margin
S=∑wisiS=\sum w_is_i
Weighted trade score
Margin=Capability−NeedNeed\text{Margin}=\frac{\text{Capability}-\text{Need}}{\text{Need}}
Performance margin
∑wi=1\sum w_i=1
Weights sum to one

Worked examples, step by step

Example 1.1 A dry-mass estimate is 800 kg. Allocate with a 20% margin (sample values).

Show the steps
  1. 800 × 1.20.

Answer: 960 kg.

Example 1.2 NASA says Landsat 9 had to collect at least 400 scenes a day and collects 740. Find the margin.

Show the steps
  1. (740 − 400)/400.

Answer: 85% above the requirement (740/400 = 1.85).

Example 1.3 Option A scores 8 (cost) and 6 (performance); B scores 5 and 9. Weights 0.4 and 0.6. Which wins?

Show the steps
  1. A = 3.2 + 3.6 = 6.8.
  2. B = 2.0 + 5.4 = 7.4.

Answer: B wins, 7.4 to 6.8.

Practice problems

Work each on paper first, then check.

  1. Allocate 1200 kg at 25% margin.

    Show answer

    1500 kg.

  2. If weights flip to 0.6/0.4, who wins?

    Show answer

    A: 7.2 vs B: 6.6.

  3. What makes a requirement verifiable?

    Show answer

    A measurable value and a test or analysis to check it.

  4. Why carry margin?

    Show answer

    Estimates grow as designs mature.

Common misconceptions

  • Myth: Requirements are wishes.

    Actually: They are measurable and verifiable.

  • Myth: Margins are waste.

    Actually: They absorb growth and surprises.

  • Myth: Trade studies are objective.

    Actually: The weights carry judgment.

Flashcards

  • Requirement

    Measurable, verifiable need.

  • Budget

    Allocation of a resource.

  • Margin

    Reserve above estimate.

  • Trade study

    Weighted comparison.

  • Life cycle

    Phases from concept to disposal.

  • Verification

    Proof a requirement is met.

Self-check quiz

1. 800 kg + 20%…

Show answer

960 kg. Multiply.

2. Landsat 9 scenes per day…

Show answer

740. NASA.

3. Trade winner…

Show answer

B. 7.4 > 6.8.

4. Margins over time…

Show answer

shrink. Maturity.

How this helps save the planet

NASA says Landsat 9’s program requirements included collecting at least 400 scenes a day and a 5-year design life; Landsat 9 collects 740 scenes a day, almost double the minimum, and carries enough fuel to operate for at least 10 years.

Exceeding requirements like these extends a land record that, NASA notes, spans more than five decades and supports deforestation alerts, water-quality monitoring and crop reports.

On Saving Planets: Earth Observation · Solutions

Sources: NASA Science: Landsat 9

Free learning resources

Back to top

Unit 2 · Week 2

Orbits and the Space Environment

Choosing an orbit, period and speed, sun-synchronous and geostationary orbits, ground tracks and swaths, eclipse, vacuum, radiation and atomic oxygen.

Learning objectives

By the end of this unit you can:

  • Compute orbital period and speed.
  • Count orbits per day.
  • Estimate eclipse duration in low orbit.
  • List environment hazards by orbit.

Key concepts

  • Period T = 2π√(a³/μ); circular speed v = √(μ/a).
  • Sun-synchronous orbits are near-polar and precess once a year, so the satellite crosses the equator at the same local time each day.
  • Low orbits pass through Earth’s shadow; the eclipse fraction for a circular orbit with the Sun in the orbit plane is about (2/2π)·asin(R_E/a).
  • The space environment includes vacuum, extreme temperatures, radiation belts, atomic oxygen in low orbit and debris.
  • Higher orbits see more of Earth but need bigger optics and antennas for the same resolution and data rate.

Key equations

T=2πa3/μT=2\pi\sqrt{a^3/\mu}
Orbital period
v=μ/av=\sqrt{\mu/a}
Circular speed
fe≈sin⁡−1(RE/a)πf_e\approx\frac{\sin^{-1}(R_E/a)}{\pi}
Eclipse fraction (worst case)
N=86400TN=\frac{86400}{T}
Orbits per day

Worked examples, step by step

Example 2.1 Landsat 9 flies at 705 km. Find its period.

Show the steps
  1. a = 6378.137 + 705 = 7083.1 km.
  2. T = 2π√(7083.1³/398,600.4).

Answer: T = 98.9 min (NASA lists 99 min).

Example 2.2 Find orbits per day and speed.

Show the steps
  1. 86,400/5932.7 s.
  2. v = √(398,600.4/7083.1).

Answer: 14.56 orbits/day; 7.50 km/s.

Example 2.3 Estimate the worst-case eclipse.

Show the steps
  1. asin(6378.1/7083.1) = 1.121 rad.
  2. f = 1.121/π = 0.357.

Answer: About 35.3 min per orbit.

Practice problems

Work each on paper first, then check.

  1. Why near-polar?

    Show answer

    To cover the whole globe.

  2. Inclination of Landsat 9?

    Show answer

    98.2°.

  3. Main low-orbit erosion hazard?

    Show answer

    Atomic oxygen.

  4. Does eclipse shrink at higher altitude?

    Show answer

    Yes, the fraction drops.

Common misconceptions

  • Myth: Space is cold, so spacecraft freeze.

    Actually: Sunlit parts can overheat; balance matters.

  • Myth: Higher is always better.

    Actually: Resolution and links suffer.

  • Myth: Sun-synchronous means always sunlit.

    Actually: Only dawn–dusk versions avoid eclipse.

Flashcards

  • Period

    2π√(a³/μ).

  • Sun-synchronous

    Same local crossing time.

  • Eclipse

    Time in Earth’s shadow.

  • Swath

    Ground width imaged.

  • Atomic oxygen

    Erodes LEO surfaces.

  • Radiation belts

    Trapped charged particles.

Self-check quiz

1. Landsat 9 period…

Show answer

≈99 min. NASA.

2. Orbits per day…

Show answer

≈14.5. 86,400/T.

3. Worst eclipse at 705 km…

Show answer

≈35 min. Computed.

4. Sun-synchronous gives…

Show answer

same local time. Precession.

How this helps save the planet

NASA lists Landsat 9 in a near-polar, sun-synchronous orbit at 705 km with a 98.2° inclination, a 99-minute period, about 14.5 orbits a day, a 185 km swath and an equatorial crossing near 10:12 a.m. local time.

With Landsat 8, it observes the same place every 8 days. Same-time-of-day lighting is what lets scientists compare images across decades.

On Saving Planets: Orbital Mechanics · Earth Observation

Sources: NASA Science: Landsat 9

Free learning resources

Back to top

Unit 3 · Week 3

Power Generation: Solar Arrays

Solar flux and distance, cell efficiency, sun angle, beginning- and end-of-life power, array sizing and specific power.

Learning objectives

By the end of this unit you can:

  • Compute array output per square meter.
  • Apply the cosine and inverse-square laws.
  • Size an array for a load.
  • Compare cell technologies.

Key concepts

  • Solar flux near Earth is about 1361 W/m² (textbook value) and falls with the inverse square of distance from the Sun.
  • Power drops with the cosine of the angle between the array normal and the Sun.
  • NASA’s small-spacecraft survey reports multi-junction space cells at a nominal 30% efficiency (up to 34%), versus about 20% for single-junction silicon.
  • Degradation from radiation, contamination and aging lowers end-of-life power, so arrays are sized for EOL.
  • Specific power (W/kg) often governs feasibility; NASA notes solar-array missions cluster around 30 W/kg.

Key equations

P=SηAcos⁡θP=S\eta A\cos\theta
Array power
S(r)=1361r2S(r)=\frac{1361}{r^2}
Inverse square (r in AU)
A=PSηfdA=\frac{P}{S\eta f_d}
Array area
SP=PmSP=\frac{P}{m}
Specific power

Worked examples, step by step

Example 3.1 Find output per m² for 30% cells facing the Sun at 1 AU.

Show the steps
  1. 1361 × 0.30.

Answer: 408.3 W/m².

Example 3.2 Find the area for 2 kW with a 0.85 degradation-and-packing factor (sample value).

Show the steps
  1. 2000/(1361 × 0.30 × 0.85).

Answer: 5.76 m².

Example 3.3 Find solar flux at Jupiter (5.2 AU).

Show the steps
  1. 1361/5.2².

Answer: 50.3 W/m², 27 times less.

Practice problems

Work each on paper first, then check.

  1. Output per m² tilted 30°?

    Show answer

    353.6 W/m².

  2. Flux at Mars (1.524 AU)?

    Show answer

    586 W/m².

  3. Output per m² for 20% silicon?

    Show answer

    272.2 W/m².

  4. Array mass for 2 kW at 30 W/kg?

    Show answer

    66.7 kg.

Common misconceptions

  • Myth: Distance hardly matters.

    Actually: Flux falls as 1/r².

  • Myth: BOL power is enough.

    Actually: Size for end of life.

  • Myth: Efficiency is all that matters.

    Actually: Mass and stowed volume matter too.

Flashcards

  • Solar flux

    ≈1361 W/m² at 1 AU.

  • Multi-junction cell

    Stacked bandgaps, ~30%.

  • BOL/EOL

    Beginning/end of life.

  • Cosine loss

    P ∝ cos θ.

  • Inverse square

    S ∝ 1/r².

  • Specific power

    W/kg.

Self-check quiz

1. 30% at 1 AU per m²…

Show answer

408 W. Multiply.

2. Flux at Jupiter…

Show answer

≈50 W/m². 1/r².

3. Nominal multi-junction η (NASA)…

Show answer

30%. SOA report.

4. Tilt reduces power by…

Show answer

cos θ. Cosine.

How this helps save the planet

NASA describes Europa Clipper as a solar-powered spacecraft that, with its solar arrays deployed, spans more than 100 feet (about 30 meters); it launched Oct. 14, 2024, and will travel 1.8 billion miles to reach Jupiter in April 2030.

At Jupiter, sunlight is about 27 times weaker than at Earth, which is why Clipper’s arrays are so large: this unit’s inverse-square law, at mission scale.

On Saving Planets: Solutions · Orbital Mechanics

Sources: NASA Science: Europa Clipper · NASA Small Spacecraft Technology State of the Art: 3.0 Power (May 2026)

Free learning resources

Back to top

Unit 4 · Week 4

Energy Storage and the Power Budget

Load lists, sunlight and eclipse energy balance, battery sizing with depth of discharge, specific energy, power management and distribution.

Learning objectives

By the end of this unit you can:

  • Build a load list and orbit-average power.
  • Size a battery for eclipse.
  • Compute battery mass from specific energy.
  • Explain depth-of-discharge limits.

Key concepts

  • The power budget sums every load by mode; the array must power loads in sunlight and recharge the battery for eclipse.
  • Battery energy = load × eclipse time ÷ allowed depth of discharge (DoD).
  • Shallow DoD extends cycle life; low orbits see about 15 cycles a day, so DoD is often kept low (textbook guidance).
  • NASA’s survey reports commercial Li-ion cells at about 150–270 Wh/kg and 3.6 V average.
  • Power management and distribution regulates bus voltage, switches loads and isolates faults.

Key equations

E=PeteDoDE=\frac{P_et_e}{DoD}
Battery energy
mb=Eespm_b=\frac{E}{e_{sp}}
Battery mass
Pavg=Pdtd+PeteTP_{avg}=\frac{P_dt_d+P_et_e}{T}
Orbit-average load
Ah=WhVAh=\frac{Wh}{V}
Capacity

Worked examples, step by step

Example 4.1 A 500 W load must ride through the 35.3-minute eclipse from Unit 2. Find the energy used.

Show the steps
  1. 500 × 35.28/60.

Answer: 294 Wh.

Example 4.2 Size the battery for 30% DoD (sample value).

Show the steps
  1. 294/0.30.

Answer: 980 Wh.

Example 4.3 Find battery mass at 150 Wh/kg pack level.

Show the steps
  1. 980/150.

Answer: 6.53 kg.

Practice problems

Work each on paper first, then check.

  1. Capacity at 28 V?

    Show answer

    35 Ah.

  2. Mass using 260 Wh/kg cells?

    Show answer

    3.77 kg (cells only).

  3. Cycles per day at 14.56 orbits/day?

    Show answer

    About 14.6.

  4. Why not 100% DoD?

    Show answer

    Cycle life collapses.

Common misconceptions

  • Myth: Watts and watt-hours are the same.

    Actually: Power vs energy.

  • Myth: Deep discharge is fine.

    Actually: It shortens life.

  • Myth: Cell energy = pack energy.

    Actually: Packs add mass for structure and management.

Flashcards

  • Load list

    Power per subsystem and mode.

  • DoD

    Fraction of capacity used.

  • Specific energy

    Wh/kg.

  • PMAD

    Power management and distribution.

  • Eclipse

    No solar power.

  • Orbit-average power

    Time-weighted load.

Self-check quiz

1. Eclipse energy…

Show answer

294 Wh. P × t.

2. Battery at 30% DoD…

Show answer

980 Wh. Divide.

3. Li-ion cell voltage…

Show answer

3.6 V. NASA.

4. Battery mass…

Show answer

6.53 kg. 980/150.

How this helps save the planet

NASA’s small-spacecraft technology survey lists 18650 lithium-ion cells with flight heritage on NASA missions, including LG Chem INR18650-MJ1 cells at 260 Wh/kg for NASA’s PACE mission and LG Chem ICR18650 B3 cells at 191–205 Wh/kg for Europa Clipper.

PACE, launched in February 2024, measures phytoplankton, aerosols and clouds to help monitor ocean health, air quality and climate. Its batteries keep it working through every eclipse.

On Saving Planets: Oceans · Circuits

Sources: NASA Small Spacecraft Technology State of the Art: 3.0 Power (May 2026) · NASA Science: PACE (Plankton, Aerosol, Cloud, ocean Ecosystem)

Free learning resources

Back to top

Unit 5 · Week 5

Thermal Control

Radiation balance, absorptivity and emissivity, equilibrium temperature, radiator sizing, coatings, heaters and multilayer insulation.

Learning objectives

By the end of this unit you can:

  • Compute an equilibrium temperature.
  • Size a radiator.
  • Choose coatings by α/ε.
  • Explain heaters and insulation.

Key concepts

  • In vacuum, heat leaves mainly by radiation: Q = εσAT⁴.
  • Absorbed sunlight is αSA_proj; the ratio α/ε of a surface sets its equilibrium temperature.
  • A black sphere at 1 AU with α = ε settles near (S/4σ)^¼ ≈ 278 K.
  • Radiators reject waste heat; white paints and mirrors have low α/ε, staying cool in sunlight.
  • Multilayer insulation blocks radiation; heaters keep batteries and propellant warm in eclipse.

Key equations

Q=εσAT4Q=\varepsilon\sigma AT^4
Radiated heat
T=(αS4εσ)1/4T=\left(\frac{\alpha S}{4\varepsilon\sigma}\right)^{1/4}
Sphere equilibrium
Ar=QεσT4A_r=\frac{Q}{\varepsilon\sigma T^4}
Radiator area
Qabs=αSApQ_{abs}=\alpha SA_p
Absorbed sunlight

Worked examples, step by step

Example 5.1 Find the equilibrium temperature of a sphere at 1 AU with α = ε.

Show the steps
  1. T = (1361/(4 × 5.6704 × 10⁻⁸))^¼.

Answer: T = 278.3 K (5 °C).

Example 5.2 Size a radiator to reject 500 W at 290 K with ε = 0.85 (ignoring absorbed sunlight).

Show the steps
  1. A = 500/(0.85 × 5.6704 × 10⁻⁸ × 290⁴).

Answer: A = 1.47 m².

Example 5.3 How does equilibrium temperature scale with α/ε?

Show the steps
  1. T ∝ (α/ε)^¼.

Answer: Doubling α/ε raises T by 2^¼ = 1.189.

Practice problems

Work each on paper first, then check.

  1. T for α/ε = 2?

    Show answer

    331 K.

  2. Radiator at 260 K for 500 W?

    Show answer

    2.27 m².

  3. What does MLI do?

    Show answer

    Blocks radiative heat flow.

  4. Why heaters in eclipse?

    Show answer

    To keep parts above minimum temperatures.

Common misconceptions

  • Myth: Space conducts heat away.

    Actually: Vacuum: radiation dominates.

  • Myth: Black is always hot.

    Actually: Depends on α/ε.

  • Myth: Thermal is an afterthought.

    Actually: It drives layout and power.

Flashcards

  • Absorptivity α

    Fraction of sunlight absorbed.

  • Emissivity ε

    Radiating ability.

  • MLI

    Multilayer insulation.

  • Radiator

    Heat-rejecting surface.

  • Heater

    Keeps parts warm.

  • σ

    5.6704 × 10⁻⁸ W/(m²·K⁴).

Self-check quiz

1. Sphere at 1 AU…

Show answer

278 K. Computed.

2. Q = …

Show answer

εσAT⁴. Radiation.

3. Radiator area example…

Show answer

1.47 m². Computed.

4. Low α/ε surface…

Show answer

stays cool. Balance.

How this helps save the planet

NASA explains that Landsat 9’s Thermal Infrared Sensor measures land surface temperature and contains a cryocooler radiator, an Earth shield, and a blackbody plus deep-space view for calibration.

Thermal design is the instrument here: TIRS measures heat from Earth, which NASA notes helps track and manage water use, only because its own detectors are kept cold and stable.

On Saving Planets: Thermodynamics · Earth Observation

Sources: NASA Science: Landsat 9

Free learning resources

Back to top

Unit 6 · Week 6

Structures, Mechanisms and Launch Loads

Launch loads, quasi-static design loads, stiffness and natural frequency requirements, materials, deployables, and heritage buses.

Learning objectives

By the end of this unit you can:

  • Compute a quasi-static launch load.
  • Compute a natural frequency.
  • Explain stiffness requirements.
  • Weigh heritage versus new design.

Key concepts

  • Launch subjects spacecraft to steady acceleration, vibration, acoustics and shock; design starts from quasi-static load factors (often several g, textbook values).
  • Launch vehicles require the spacecraft’s fundamental frequency to stay above a minimum so it does not couple with the rocket.
  • For a simple spring-mass model, f = (1/2π)√(k/m): stiffness raises frequency, mass lowers it.
  • Aluminum honeycomb and composites give stiffness for little mass; mechanisms deploy arrays, antennas and booms.
  • Reusing a flight-proven bus (heritage) cuts risk and schedule.

Key equations

F=n m g0F=n\,m\,g_0
Quasi-static load
f=12πk/mf=\frac{1}{2\pi}\sqrt{k/m}
Natural frequency
σ=F/A\sigma=F/A
Stress
k=EALk=\frac{EA}{L}
Axial stiffness

Worked examples, step by step

Example 6.1 Find the design load for a 1000 kg spacecraft at 6 g (sample values).

Show the steps
  1. 6 × 1000 × 9.80665.

Answer: 58.8 kN.

Example 6.2 A 100 kg instrument on a mount of stiffness 10⁶ N/m (sample values). Find f.

Show the steps
  1. (1/2π)√(10⁶/100).

Answer: f = 15.9 Hz.

Example 6.3 How stiff must the mount be to double f?

Show the steps
  1. f ∝ √k.

Answer: 4 × 10⁶ N/m (31.8 Hz).

Practice problems

Work each on paper first, then check.

  1. f if mass doubles?

    Show answer

    11.3 Hz.

  2. Load at 4 g for 500 kg?

    Show answer

    19.6 kN.

  3. Why minimum frequency?

    Show answer

    Avoid coupling with launcher dynamics.

  4. What is a heritage bus?

    Show answer

    A flight-proven spacecraft platform.

Common misconceptions

  • Myth: Strength is the only goal.

    Actually: Stiffness often drives design.

  • Myth: Heavier is safer.

    Actually: Mass lowers frequency and costs launch.

  • Myth: Deployables are simple.

    Actually: They are common single points of failure.

Flashcards

  • Quasi-static load

    Equivalent steady g.

  • Natural frequency

    (1/2π)√(k/m).

  • Honeycomb

    Light stiff panel.

  • Deployable

    Unfolds in orbit.

  • Heritage

    Flight-proven design.

  • Bus

    Spacecraft platform.

Self-check quiz

1. 6 g on 1000 kg…

Show answer

58.8 kN. nmg.

2. f example…

Show answer

15.9 Hz. Formula.

3. Double f needs k ×…

Show answer

4. f ∝ √k.

4. Heritage reduces…

Show answer

risk. Proven.

How this helps save the planet

NASA says Northrop Grumman designed and built the Landsat 9 spacecraft by adapting the LEOStar bus design used for Landsat 8, and integrated both instruments and ran satellite-level testing.

Reusing a proven bus is a design choice that reduces risk and helps keep the Landsat record continuous, which NASA notes is the longest continuous satellite record of Earth’s land surface.

On Saving Planets: Aerospace Structures · Earth Observation

Sources: NASA Science: Landsat 9

Free learning resources

Back to top

Unit 7 · Week 7

Propulsion and the Delta-v Budget

Δv budgets for orbit insertion, station-keeping, attitude and disposal; the rocket equation for propellant mass; gravity assists; and propulsion choices.

Learning objectives

By the end of this unit you can:

  • Build a Δv budget.
  • Compute propellant mass from Δv.
  • Compute Δv from propellant.
  • Explain gravity assists.

Key concepts

  • A Δv budget lists every maneuver: insertion, orbit maintenance, attitude control, collision avoidance and disposal, plus margin.
  • Propellant needed: m_p = m₀(1 − e^(−Δv/v_e)).
  • Monopropellant thrusters are simple; bipropellant gives higher Isp; electric gives very high Isp at low thrust.
  • Gravity assists borrow momentum from a planet to change speed and direction without propellant.
  • Leftover propellant can extend a mission past its design life.

Key equations

mp=m0(1−e−Δv/ve)m_p=m_0\left(1-e^{-\Delta v/v_e}\right)
Propellant mass
Δv=veln⁡m0mf\Delta v=v_e\ln\frac{m_0}{m_f}
Rocket equation
ve=Ispg0v_e=I_{sp}g_0
Exhaust velocity
Δvtot=∑Δvi(1+M)\Delta v_{tot}=\sum\Delta v_i(1+M)
Budget with margin

Worked examples, step by step

Example 7.1 A 1000 kg spacecraft needs 100 m/s with Isp 300 s (sample values). Find propellant.

Show the steps
  1. v_e = 2942 m/s.
  2. m_p = 1000(1 − e^(−100/2942)).

Answer: 33.4 kg.

Example 7.2 What Δv does 50 kg of propellant give?

Show the steps
  1. 2942 ln(1000/950).

Answer: 150.9 m/s.

Example 7.3 Budget: 60 m/s insertion trim, 30 m/s station-keeping, 10 m/s disposal, 20% margin.

Show the steps
  1. 100 × 1.2.

Answer: 120 m/s.

Practice problems

Work each on paper first, then check.

  1. Propellant for 120 m/s?

    Show answer

    39.9 kg.

  2. v_e for Isp 220 s?

    Show answer

    2157 m/s.

  3. What does a gravity assist save?

    Show answer

    Propellant for the same Δv.

  4. Why budget disposal Δv?

    Show answer

    To leave orbit responsibly.

Common misconceptions

  • Myth: Propellant scales linearly with Δv.

    Actually: Exponentially.

  • Myth: Gravity assists are free energy.

    Actually: Momentum is exchanged with the planet.

  • Myth: Disposal is optional.

    Actually: It protects orbits for others.

Flashcards

  • Δv budget

    Sum of maneuvers.

  • Station-keeping

    Holding an orbit.

  • Monopropellant

    Single propellant, simple.

  • Bipropellant

    Fuel + oxidizer.

  • Gravity assist

    Planetary flyby boost.

  • Disposal

    End-of-life deorbit or graveyard.

Self-check quiz

1. m_p for 100 m/s…

Show answer

33.4 kg. Formula.

2. Δv from 50 kg…

Show answer

151 m/s. Rocket eq.

3. Budget with margin…

Show answer

120 m/s. ×1.2.

4. Clipper’s Dec 2026 Earth pass is a…

Show answer

gravity assist. NASA.

How this helps save the planet

NASA says Europa Clipper flew past Mars in 2025 and will swing by Earth again on Dec. 3, 2026, for a gravity assist that gives it a push for the rest of its trip to Jupiter, where it will make 49 close flybys of Europa.

Gravity assists stretch a fixed propellant load, the same goal this unit’s Δv budget serves for Earth orbiters like Landsat 9, which NASA says carries fuel for at least 10 years.

On Saving Planets: Orbital Mechanics · Propulsion

Sources: NASA Science: Europa Clipper · NASA Science: Landsat 9

Free learning resources

Back to top

Unit 8 · Weeks 8–9

Attitude Determination and Control Subsystem

Pointing requirements from payloads, sensors and actuators, disturbance torques, momentum budgets, and pointing error on the ground.

Learning objectives

By the end of this unit you can:

  • Derive a pointing requirement from ground resolution.
  • Compute ground error from angle error.
  • Build a momentum budget.
  • Pick sensors and actuators.

Key concepts

  • Payloads set pointing: an imager’s pixel subtends an angle of (ground pixel)/(altitude).
  • Ground error ≈ altitude × angle error (small angles).
  • Sensors: star trackers, sun sensors, magnetometers, gyros; actuators: reaction wheels, magnetic torquers, thrusters.
  • Disturbances (gravity gradient, drag, solar pressure, magnetic) build momentum H = τt that wheels must store.
  • Momentum is dumped with magnetic torquers or thrusters before wheels saturate.

Key equations

θ=xh\theta=\frac{x}{h}
Pixel angle
e=hθe=h\theta
Ground error
H=τtH=\tau t
Accumulated momentum
1′′=π648000 rad1^{\prime\prime}=\frac{\pi}{648000}\,\text{rad}
Arcsecond

Worked examples, step by step

Example 8.1 Landsat 9 has 30 m pixels from 705 km. Find the angle per pixel.

Show the steps
  1. 30/705,000 rad.

Answer: 4.26 × 10⁻⁵ rad = 8.78 arcsec.

Example 8.2 A 0.01° pointing error from 705 km shifts the image how far?

Show the steps
  1. 705,000 × 0.0001745.

Answer: 123 m, about four pixels.

Example 8.3 A 10⁻⁵ N·m disturbance acts for a quarter of a 98.9-minute orbit (sample value). Find the momentum.

Show the steps
  1. 10⁻⁵ × 1483 s.

Answer: 0.0148 N·m·s.

Practice problems

Work each on paper first, then check.

  1. Angle for a 15 m pixel?

    Show answer

    4.39 arcsec.

  2. Ground error for 0.001°?

    Show answer

    12.3 m.

  3. Which sensor gives absolute attitude?

    Show answer

    A star tracker.

  4. How are wheels unloaded in LEO?

    Show answer

    Magnetic torquers or thrusters.

Common misconceptions

  • Myth: Pointing knowledge equals control.

    Actually: They are separate budgets.

  • Myth: Wheels can absorb momentum forever.

    Actually: They saturate.

  • Myth: Small angles do not matter.

    Actually: Altitude multiplies them.

Flashcards

  • Pointing accuracy

    Control error.

  • Pointing knowledge

    Measurement error.

  • Star tracker

    Attitude from stars.

  • Magnetic torquer

    Coil reacting with Earth’s field.

  • Gravity gradient

    Tidal torque.

  • Momentum dumping

    Unloading wheels.

Self-check quiz

1. Landsat pixel angle…

Show answer

8.78″. 30/705 km.

2. 0.01° at 705 km…

Show answer

123 m. hθ.

3. H = …

Show answer

τt. Momentum.

4. Absolute attitude sensor…

Show answer

star tracker. Stars.

How this helps save the planet

NASA lists Landsat 9’s spatial resolution as 30 m for visible and shortwave infrared bands, 15 m panchromatic and 100 m thermal, from 705 km.

Holding a 30 m pixel steady from that height takes arcsecond-level control, the reason Landsat images line up across years for change detection.

On Saving Planets: Flight Dynamics & Controls · Earth Observation

Sources: NASA Science: Landsat 9

Free learning resources

Back to top

Unit 9 · Weeks 10–11

Communications and Data Handling

Data volume, downlink rates, the link budget in decibels, free-space path loss, antenna gain, and onboard computing and storage.

Learning objectives

By the end of this unit you can:

  • Compute free-space path loss.
  • Compute dish antenna gain.
  • Build a simple link budget.
  • Estimate daily data volume.

Key concepts

  • Free-space path loss L = 20 log₁₀(4πd/λ) dB grows with distance and frequency.
  • Dish gain G = η(πD/λ)²; bigger dishes and higher frequencies give narrower, stronger beams.
  • Link budget: received power = transmit power + gains − losses (all in dB); the margin over what the receiver needs must be positive.
  • Data volume = images × bits per image; rate × contact time must exceed it.
  • Command and data handling computers store data, run software and manage faults.

Key equations

L=20log⁡104πdλL=20\log_{10}\frac{4\pi d}{\lambda}
Free-space path loss
G=η(πDλ)2G=\eta\left(\frac{\pi D}{\lambda}\right)^2
Dish gain
Pr=Pt+Gt+Gr−LP_r=P_t+G_t+G_r-L
Link budget (dB)
λ=c/f\lambda=c/f
Wavelength

Worked examples, step by step

Example 9.1 Find the X-band (8.2 GHz) path loss at 2000 km (c = 3 × 10⁸ m/s).

Show the steps
  1. λ = 0.03659 m.
  2. 20 log₁₀(4π × 2 × 10⁶/0.03659).

Answer: L = 176.7 dB.

Example 9.2 Find the gain of a 3 m dish at 8.2 GHz with η = 0.55 (sample value).

Show the steps
  1. 0.55 × (π × 3/0.03659)².

Answer: G = 45.6 dBi.

Example 9.3 What happens to path loss if distance doubles?

Show the steps
  1. +20 log₁₀ 2.

Answer: +6.0 dB (182.8 dB at 4000 km).

Practice problems

Work each on paper first, then check.

  1. Wavelength at 8.2 GHz?

    Show answer

    3.66 cm.

  2. Gain change for a 6 m dish?

    Show answer

    +6.0 dB.

  3. Landsat 9 scenes per day?

    Show answer

    About 740.

  4. Bits per pixel for Landsat 9 OLI?

    Show answer

    14.

Common misconceptions

  • Myth: Decibels add like watts.

    Actually: dB add for products.

  • Myth: Higher frequency is always worse.

    Actually: Loss rises but dish gain rises too.

  • Myth: Data volume is small.

    Actually: It often drives ground-station design.

Flashcards

  • Path loss

    Spreading loss in dB.

  • Antenna gain

    Beam concentration.

  • Link margin

    Received minus required.

  • X-band

    ≈8 GHz.

  • C&DH

    Command and data handling.

  • Data volume

    Bits per day.

Self-check quiz

1. Path loss 2000 km X-band…

Show answer

176.7 dB. Formula.

2. 3 m dish gain…

Show answer

45.6 dBi. Formula.

3. Double distance…

Show answer

+6 dB loss. 20 log 2.

4. Link budget uses…

Show answer

dB sums. Log units.

How this helps save the planet

NASA says Europa Clipper carries nine science instruments plus a gravity experiment that uses its telecommunications system, and shows its 10-foot (3-meter) high-gain antenna installed in August 2023.

Closer to home, NASA reports Landsat 9 records 14-bit data and collects more than 700 scenes a day. Moving that much data to the ground every day is a communications design problem first.

On Saving Planets: Earth Observation · Circuits

Sources: NASA Science: Europa Clipper · NASA Science: Landsat 9

Free learning resources

Back to top

Unit 10 · Weeks 12–13

Reliability, Testing and End of Life

Failure rates and reliability, redundancy, environmental testing, calibration and verification, operations and responsible disposal.

Learning objectives

By the end of this unit you can:

  • Compute reliability from a failure rate.
  • Compute the benefit of redundancy.
  • Describe environmental tests.
  • Plan end-of-life disposal.

Key concepts

  • With a constant failure rate λ, reliability R(t) = e^(−λt) and mean time between failures is 1/λ.
  • Two units in parallel: R = 1 − (1 − R₁)²; redundancy trades mass and cost for reliability.
  • “Test like you fly”: vibration, acoustic, shock, thermal-vacuum and electromagnetic tests before launch.
  • Calibration keeps science data accurate over time; cross-calibration with other satellites ties records together.
  • At end of life, spacecraft should be deorbited or moved to a disposal orbit to limit debris.

Key equations

R(t)=e−λtR(t)=e^{-\lambda t}
Reliability
Rp=1−(1−R)2R_p=1-(1-R)^2
Two in parallel
MTBF=1/λMTBF=1/\lambda
Mean time between failures
Rs=∏RiR_s=\prod R_i
Series system

Worked examples, step by step

Example 10.1 A unit has λ = 10⁻⁵ per hour (sample value). Find its 5-year reliability.

Show the steps
  1. t = 43,800 h.
  2. e^(−0.438).

Answer: R = 0.645.

Example 10.2 Add a redundant unit in parallel.

Show the steps
  1. 1 − 0.355².

Answer: R = 0.874.

Example 10.3 Find the MTBF.

Show the steps
  1. 1/10⁻⁵ h.

Answer: 100,000 h = 11.4 years.

Practice problems

Work each on paper first, then check.

  1. 10-year reliability of one unit?

    Show answer

    0.416.

  2. Series system of 0.95 and 0.90?

    Show answer

    0.855.

  3. Name a pre-launch environmental test.

    Show answer

    Thermal vacuum or vibration.

  4. Why cross-calibrate?

    Show answer

    To keep records consistent across satellites.

Common misconceptions

  • Myth: Redundancy is free.

    Actually: It costs mass, power and money.

  • Myth: Testing proves zero risk.

    Actually: It reduces risk.

  • Myth: Disposal is someone else’s job.

    Actually: It is designed in from the start.

Flashcards

  • Reliability

    Probability of working.

  • Failure rate λ

    Failures per hour.

  • Redundancy

    Backup units.

  • Thermal vacuum test

    Space conditions on the ground.

  • Calibration

    Keeping measurements accurate.

  • Disposal

    End-of-life deorbit.

Self-check quiz

1. 5-year R…

Show answer

0.645. e^(−0.438).

2. Parallel pair…

Show answer

0.874. 1 − 0.355².

3. MTBF…

Show answer

100,000 h. 1/λ.

4. Landsat underfly purpose…

Show answer

cross-calibration. NASA.

How this helps save the planet

NASA reports that just after launch, Landsat 9 flew directly below Landsat 8 in a once-in-a-mission “underfly,” collecting 2,396 images from November 12–16, 2021, so calibration experts could compare both satellites’ measurements and ensure data continuity.

NASA notes that onboard calibration and redundancy help Landsat 9 collect accurate, reliable data for its mission life: reliability engineering in service of a planetary record.

On Saving Planets: Earth Observation · Solutions

Sources: NASA Science: Landsat 9

Free learning resources

Back to top

The lab (Spacecraft design lab)

The lab is the hands-on part of the course. Here it is free and for practice only, with no credit.

Every lab runs in a free simulation or a spreadsheet, so there are no physical hazards. Do not build, charge or modify battery packs for this course. Take screen breaks, sit with good posture, and keep cables out of walkways.

Safety reference: OSHA: Walking-working surfaces (slip, trip and fall hazards)

Lab A: Mass and power budgets with margin

Week 1

Goal: Build a spreadsheet mass and power budget for a small Earth-observing satellite and apply margins.

malloc=mest(1+M)m_{alloc}=m_{est}(1+M)
Allocation with margin

Procedure

  1. List subsystems: payload, structure, power, thermal, ADCS, propulsion, comms, C&DH.
  2. Enter sample mass estimates totaling 800 kg and power estimates totaling 500 W.
  3. Apply 20% margin to each total.
  4. Run the two-option weighted trade from Unit 1 and change the weights.

Data table

BudgetEstimateWith 20% margin
Dry mass800 kg960 kg
Power500 W600 W

Sample values.

Sample calculation

  1. 800 × 1.2 = 960 kg.
  2. 500 × 1.2 = 600 W.

Safety

  • Computer only.

Home or virtual alternative

  • Any spreadsheet works.

NASA Systems Engineering Handbook

Planet link: NASA: Landsat 9 collects 740 scenes a day against a 400-scene requirement. NASA Science: Landsat 9

Lab B: Orbit period and eclipse calculator

Week 2

Goal: Compute period and worst-case eclipse for several low-orbit altitudes.

T=2πa3/μT=2\pi\sqrt{a^3/\mu}
Orbital period

Procedure

  1. Enter altitudes of 400, 705 and 1000 km.
  2. Compute a, T and orbits per day.
  3. Compute the eclipse fraction and minutes.
  4. Compare 705 km with NASA’s Landsat 9 values.

Data table

Altitude (km)T (min)Eclipse (min)
40092.636.1
70598.935.3
1000105.134.9

Computed worst-case values (Sun in the orbit plane).

Sample calculation

  1. T(400) = 2π√(6778.1³/398,600.4) = 92.6 min.
  2. Eclipse(705) = 0.357 × 98.9 = 35.3 min.

Safety

  • Computer only.

Home or virtual alternative

  • Any spreadsheet works.

NASA Science: Landsat 9

Planet link: NASA lists Landsat 9 at 705 km with a 99-minute period. NASA Science: Landsat 9

Lab C: Solar cells in series and parallel

Week 3

Goal: Wire cells as batteries in PhET Circuit Construction Kit to see series and parallel strings, then size arrays across the solar system.

A=PSηfdA=\frac{P}{S\eta f_d}
Array area

Procedure

  1. In PhET Circuit Construction Kit, connect sources in series and in parallel and note voltage and current.
  2. In a spreadsheet, compute array area for 500 W with η = 0.30 and f_d = 0.85.
  3. Repeat at 1, 1.524 and 5.2 AU.
  4. Explain why outer-planet missions need huge arrays.

Data table

Distance (AU)Area for 500 W (m²)
11.44
1.5243.35
5.239.0

Computed sample values.

Sample calculation

  1. 500/(1361 × 0.3 × 0.85) = 1.44 m².
  2. 1.44 × 5.2² = 39.0 m².

Safety

  • Computer only.

Home or virtual alternative

  • Any browser and spreadsheet work.

PhET: Circuit Construction Kit: DC · NASA Small Spacecraft Technology State of the Art: 3.0 Power (May 2026)

Planet link: NASA: Europa Clipper’s deployed arrays span more than 30 meters. NASA Science: Europa Clipper

Lab D: Eclipse battery sizing

Week 4

Goal: Size batteries for different loads through a 35.3-minute eclipse.

E=PeteDoDE=\frac{P_et_e}{DoD}
Battery energy

Procedure

  1. Use the 705 km eclipse from Lab B.
  2. Enter loads of 300, 500 and 800 W.
  3. Compute battery energy at 30% DoD and mass at 150 Wh/kg.
  4. Repeat with 20% DoD and discuss cycle life.

Data table

Load (W)Battery (Wh)Mass (kg)
3005883.92
5009806.53
800156810.45

Computed sample values.

Sample calculation

  1. 300 × 0.588 h/0.3 = 588 Wh.
  2. 1568/150 = 10.45 kg.

Safety

  • Computer only.

Home or virtual alternative

  • Any spreadsheet works.

NASA Small Spacecraft Technology State of the Art: 3.0 Power (May 2026)

Planet link: NASA lists 260 Wh/kg 18650 cells with heritage on its PACE mission. NASA Small Spacecraft Technology State of the Art: 3.0 Power (May 2026)

Lab E: Radiation balance and radiator sizing

Week 5

Goal: Explore thermal radiation in PhET Blackbody Spectrum, then compute equilibrium temperatures and radiator areas.

T=(αS4εσ)1/4T=\left(\frac{\alpha S}{4\varepsilon\sigma}\right)^{1/4}
Sphere equilibrium

Procedure

  1. In PhET Blackbody Spectrum, compare spectra at 250, 290 and 6000 K.
  2. Compute sphere temperatures for α/ε = 0.5, 1 and 2.
  3. Compute radiator area for 500 W at 250, 290 and 320 K with ε = 0.85.
  4. Pick a radiator temperature and explain the trade.

Data table

CaseResult
α/ε = 0.5234.0 K
α/ε = 1278.3 K
α/ε = 2331.0 K
Radiator at 250 K2.66 m²
Radiator at 320 K0.99 m²

Computed values.

Sample calculation

  1. T = 278.3 × 0.5^¼ = 234.0 K.
  2. A = 500/(0.85σ × 320⁴) = 0.99 m².

Safety

  • Computer only.

Home or virtual alternative

  • Any browser and spreadsheet work.

PhET: Blackbody Spectrum · NASA Small Spacecraft Technology State of the Art: Thermal Control

Planet link: NASA: Landsat 9’s TIRS uses a cryocooler radiator and onboard blackbody. NASA Science: Landsat 9

Lab F: Downlink link budget

Week 11

Goal: Build a decibel link budget and see how distance and antenna size change the margin.

L=20log⁡104πdλL=20\log_{10}\frac{4\pi d}{\lambda}
Free-space path loss

Procedure

  1. Use f = 8.2 GHz and c = 3 × 10⁸ m/s.
  2. Compute path loss at 1000, 2000 and 4000 km.
  3. Add transmit power, both antenna gains and other losses.
  4. Find the dish size that restores margin at 4000 km.

Data table

Distance (km)Path loss (dB)
1000170.7
2000176.7
4000182.8

Computed values.

Sample calculation

  1. λ = 0.03659 m.
  2. 20 log₁₀(4π × 10⁶/0.03659) = 170.7 dB.

Safety

  • Computer only.

Home or virtual alternative

  • Any spreadsheet works.

MIT OpenCourseWare 16.851 Satellite Engineering (Fall 2003)

Planet link: NASA: Europa Clipper carries a 3-meter high-gain antenna. NASA Science: Europa Clipper

Back to top

Exam prep practice sets

Time yourself: about 10 minutes per problem. Then compare with the full solutions.

Midterm practice set (Units 1–5)

  1. Allocate a 500 kg estimate with 30% margin.

    Show full solution
    1. 500 × 1.3.

    Answer: 650 kg.

  2. Find the period of a 550 km circular orbit.

    Show full solution
    1. a = 6928.1 km.
    2. T = 2π√(a³/μ).

    Answer: 95.6 min.

  3. Array area for 1 kW at 1 AU, η = 0.30, f_d = 0.85?

    Show full solution
    1. 1000/(1361 × 0.3 × 0.85).

    Answer: 2.88 m².

  4. Battery for 400 W over 35 min at 25% DoD?

    Show full solution
    1. 400 × 35/60/0.25.

    Answer: 933 Wh.

  5. Radiator for 300 W at 300 K, ε = 0.9?

    Show full solution
    1. 300/(0.9σ × 300⁴).

    Answer: 0.73 m².

Final practice set (Units 1–10)

  1. Natural frequency for k = 4 × 10⁵ N/m, m = 40 kg?

    Show full solution
    1. (1/2π)√(10⁴).

    Answer: 15.9 Hz.

  2. Propellant for 200 m/s on 800 kg at Isp 230 s?

    Show full solution
    1. 800(1 − e^(−200/2255.5)).

    Answer: 67.9 kg.

  3. Ground error for 0.005° from 600 km?

    Show full solution
    1. 600,000 × 8.727 × 10⁻⁵.

    Answer: 52.4 m.

  4. Path loss at 1500 km, 8.2 GHz?

    Show full solution
    1. 20 log₁₀(4π × 1.5 × 10⁶/0.03659).

    Answer: 174.2 dB.

  5. Reliability for λ = 2 × 10⁻⁶ /h over 7 years?

    Show full solution
    1. e^(−0.1226).

    Answer: 0.885.

  6. Parallel pair of 0.885 units?

    Show full solution
    1. 1 − 0.115².

    Answer: 0.987.

Back to top

Formula sheet

malloc=mest(1+M), S=∑wisim_{alloc}=m_{est}(1+M),\ S=\sum w_is_i
T=2πa3/μ, v=μ/a, fe≈sin⁡−1(RE/a)/πT=2\pi\sqrt{a^3/\mu},\ v=\sqrt{\mu/a},\ f_e\approx\sin^{-1}(R_E/a)/\pi
P=SηAcos⁡θ, S=1361/r2P=S\eta A\cos\theta,\ S=1361/r^2
E=Pete/DoD, mb=E/espE=P_et_e/DoD,\ m_b=E/e_{sp}
Q=εσAT4, T=(αS/4εσ)1/4Q=\varepsilon\sigma AT^4,\ T=(\alpha S/4\varepsilon\sigma)^{1/4}
F=nmg0, f=12πk/mF=nmg_0,\ f=\frac{1}{2\pi}\sqrt{k/m}
mp=m0(1−e−Δv/ve)m_p=m_0(1-e^{-\Delta v/v_e})
θ=x/h, e=hθ, H=τt\theta=x/h,\ e=h\theta,\ H=\tau t
L=20log⁡10(4πd/λ), G=η(πD/λ)2L=20\log_{10}(4\pi d/\lambda),\ G=\eta(\pi D/\lambda)^2
R=e−λt, Rp=1−(1−R)2R=e^{-\lambda t},\ R_p=1-(1-R)^2

Constants

ConstantValue
Earth μ398,600.4418 km³/s²
Earth radius (equatorial)6378.137 km
Solar flux at 1 AU (textbook value)1361 W/m²
Stefan–Boltzmann constantσ = 5.670374419 × 10⁻⁸ W/(m²·K⁴)
Speed of light299,792,458 m/s (3 × 10⁸ used in examples)
Standard gravityg₀ = 9.80665 m/s²

Source: NIST: CODATA value, Stefan–Boltzmann constant

Back to top

Free texts and simulations

Use these free lectures, NASA references and simulations alongside the course.

Back to top

Glossary

ADCS
Attitude determination and control subsystem.
Antenna gain
Beam concentration relative to isotropic.
Bus
Spacecraft platform carrying the payload.
C&DH
Command and data handling.
Depth of discharge
Fraction of battery capacity used.
Eclipse
Time in a planet’s shadow.
Emissivity
Ability to radiate heat.
End of life
Performance after degradation.
Gravity assist
Planetary flyby that changes velocity.
Heritage
Flight-proven design.
Link budget
Sum of gains and losses in a radio link.
Margin
Reserve above need.
Multilayer insulation
Thermal blanket that blocks radiation.
Path loss
Signal spreading loss.
Payload
Instruments the mission exists for.
Redundancy
Backup hardware.
Requirement
Measurable, verifiable need.
Solar flux
Sunlight power per area.
Specific power
Power per mass.
Sun-synchronous orbit
Orbit crossing at the same local time daily.

Back to top

Self-assessment rubric

No grade or credit is given. Use this to judge honestly where you are in each unit.

LevelWhat it looks like
4 · MasteryStarts from requirements, keeps consistent budgets with margins, checks units and orders of magnitude, and explains subsystem trades in plain words.
3 · ProficientSolves the practice problems with occasional slips in units or margins.
2 · DevelopingFollows worked examples but confuses power and energy or dB and linear values.
1 · BeginningPlugs numbers into formulas without a requirement or budget; needs to revisit the unit.

Suggested weighting if you want a score

PartWeight
Practice problems20%
Labs25%
Midterm practice set25%
Final practice set30%

Aim for level 3 or better in every unit before moving to the next course.

Back to top

Help / Donate