Lecture Notes: Space Environment and Orbits (Intro to Astronautics)

Scale and Perspective

• The speaker emphasizes our tiny place in the universe and uses a logarithmic scale to illustrate distances from the solar system outward (Earth is in the middle; filaments, galaxies, clusters, and superclusters extend far beyond).
• Carl Sagan quote: we are tiny, fragile beings living on a thin film of the surface of a rocky planet; a reminder of our scale and fragile context for design choices.
• A rough scale analogy: if the Sun is a dot on a page, Alpha Centauri would be roughly 8 miles away in that schematic scale (used as a way to build intuition for astronomical distances).
• Astronomical Unit (AU): the mean distance between the Sun and the Earth; used as a human-centric but convenient distance unit.
  • 1~ ext{AU} \approx 1.50 \times 10^{8}~ ext{km}
• Distances in the solar system range from Earth to Moon (small in AU) to Voyager probes (out past the planets).
  • Voyager 1 and Voyager 2 distances: about 165~\text{AU} and 138~\text{AU} respectively (as examples of probes leaving the solar system).
• Light-time and universal speed limit:
  • The speed of light is the universal speed limit, affecting communication and timing in missions.
    ## Distances and Light Time
• Earth–Moon light time: roughly a couple of seconds (since the Moon is ~380,000 km away).
• Sun–Earth light time: about 8\text{ minutes}.
• Mars–Earth light time variation: roughly 4\text{ to } 22\text{ minutes} depending on orbital geometry.
• Sun–Alpha Centauri distance: about 4.2\text{ light-years} (the distance is fixed in light-years).
• Light-time intuition is critical for design and operations (latency, command/response planning, and autonomy requirements).

The Earth’s Atmosphere and Orbital Environment

• Boundary where atmospheric forces balance gravity is the atmosphere–space boundary; in practice the Kármán line is often placed near 100 km altitude.
  • In the vicinity of this boundary, orbital dynamics begin to dominate over aerodynamics.
• Density falls with altitude but does not abruptly drop to zero; there is still drag well above 100 km.
• Atmospheric density and drag depend on altitude, object size, shape, and velocity.
• Drag equation (basic orbital drag context):
  • Fd = \tfrac{1}{2} \rho v^2 Cd A
  • where: (\rho) = atmospheric density, (v) = velocity relative to the atmosphere, (C_d) = drag coefficient, (A) = cross-sectional area.
• The von Kármán line is an approximate boundary; many operations and physics rely on the continuum of the atmosphere above/below this line.
• Typical orbital speeds near the surface:
  • Low Earth Orbit (LEO) speeds are high (on the order of several km/s); higher than suborbital speeds but lower than interplanetary vessels.
• Altitude vs orbital radius distinction:
  • Altitude is measured above Earth's surface, not from Earth's center.
  • Orbital radius for calculations: r = R_{ ext{Earth}} + h where (h) is the altitude.
• Orbital considerations set the stage for mission design: line of sight, communication latency, and coverage depend on the chosen orbit.

Orbits: Low Earth Orbit (LEO) and Geosynchronous Orbit (GEO)

• Two primary circular orbits discussed:
  • Low Earth Orbit (LEO): altitude roughly from a few hundred kilometers up to about 2000\ \text{km} above Earth’s surface.
  • Geosynchronous Orbit (GEO): altitude of h_{GEO} = 35{,}786\ \text{km} above the surface.
• Radius relationships:
  • For LEO: r{LEO} = R{ ext{Earth}} + h_{LEO}
  • For GEO: r{GEO} = R{ ext{Earth}} + h_{GEO} \,.
• Geosynchronous condition:
  • An object in a GEO completes one orbit in exactly the same angular rate as Earth’s rotation, so it appears stationary in the sky to an observer on the ground.
  • Visual analogy: a person sitting at the center of a rotating carousel; objects on the carousel appear stationary to that person.
• Periods and velocities (for circular orbits):
  • Orbital period: T = 2\pi \sqrt{\dfrac{r^3}{\mu}}\,, where (\mu) is Earth's gravitational parameter ((\mu \approx G M_{\oplus})).
  • Orbital velocity: v = \sqrt{\dfrac{\mu}{r}}\,.
• Typical speeds and periods:
  • LEO: speeds around 7.5!\text{ to }!7.7\ \text{km/s}; orbital periods around roughly 90\ \text{minutes}.
  • GEO: speeds around a bit over 3\ \text{km/s}; orbital period T \approx 24\ \text{hours}.
• Mission implications of orbit choice:
  • Line of sight and coverage: LEO sees a large portion of the Earth but not all; GEO provides persistent coverage over a wide area but with limited Earth view at any moment.
  • Latency: LEO has lower communication latency, GEO has higher latency due to distance.
  • Debris and re-entry risk considerations differ by orbit (drag, lifetime, and debris mitigation concerns).
• Scale of the space around Earth:
  • The space around Earth (cis-satellite space) is many times larger than the Earth–GEO volume; the environment volume grows with distance from Earth.

Space Environment and Survivability: Design Concepts

• Key objective: survivability is the ability to perform any function despite environmental stresses; payload survival is essential to mission success.
• Payload-centric design: the payload must accomplish the mission objective, and the spacecraft must protect the payload.
• Distinction between survivability and robustness:
  • Survivability = functional performance under environmental stressors.
  • Robustness = a property of being tough or resistant; it’s related but not identical to survivability.
• Six major environmental stressors (high-level categories) discussed as core concerns:
  1) Gravity (microgravity environments)
  2) Charged particles / radiation
  3) Vacuum (low-pressure environments) and outgassing phenomena
  4) Micrometeoroids / debris (impact risk)
  5) Atmosphere-related effects (drag in lower altitudes; residual atmosphere)
  6) Launch environment (accelerations, vibrations, shock during lift-off)
• Launch environment considerations:
  • Launch typically lasts about 10–15 minutes and involves severe accelerations and shock (commonly a few g’s, e.g., ~3 g).
  • Although not a “space environment” problem during flight, launch loads influence design margins and structural integrity.
• Design mitigations and approaches:
  • Shielding (radiation protection): placing material between radiation sources and sensitive components; lead isn’t always the best; material selection and shielding strategies depend on mission risk.
  • Thermal control: space uses conduction and radiation primarily (convection is limited due to vacuum); thermal management must operate without a surrounding atmosphere.
  • Material selection: avoid volatile outgassing and materials that release contaminants; petroleum products are often problematic due to outgassing.
  • Robustness and redundancy: use of design strategies to ensure mission objectives are met under adverse conditions; often described as satisficing (first satisfy requirements, then optimize trade-offs).
  • Satisficing: a common design philosophy in aerospace to meet requirements before optimizing one aspect.
• Practical considerations to connect to mission design:
  • Environment drives design choices; the environment is often the dominant driver (not only the payload function).
  • The payload-centred design approach ensures the mission remains viable under environmental stressors while balancing mass, power, and cost.

Environmental Effects and Operational Implications

• Microgravity (weightlessness):
  • In orbit around Earth, all objects experience roughly the same gravitational acceleration toward Earth, leading to apparent weightlessness.
  • Relative motion between closely spaced objects (e.g., ISS components) can be near-stationary due to similar accelerations, illustrating microgravity effects.
• Vacuum (low pressure) and outgassing:
  • True vacuum is never perfectly achieved; residual gases and finite density exist.
  • Vacuum affects liquids and gases (boiling at room temperature can occur under low pressure).
  • Outgassing: volatiles embedded in materials can outgas, contaminating sensitive instruments (e.g., telescopes).
  • Material selection must limit volatile components; petroleum products and other outgassing-prone substances are commonly avoided on sensitive payloads.
• Example/theme: water boiling in vacuum and the triple point concept:
  • In vacuum, liquids may boil at room temperature due to low pressure; this complicates thermal and life-support considerations for long-duration missions.
• Debris and micrometeoroids:
  • Small particles and fragments pose impact risks; shielding and debris mitigation strategies are essential for mission durability.
• Radiation and charged particles:
  • Radiation exposure requires shielding design and careful selection of electronics and materials to mitigate single-event effects and cumulative dose.
• Launch environment stresses:
  • 3 g nearly during ascent; mechanical shock and vibrations influence packaging, mounting, and connectors.
• Thermal considerations in space:
  • Without atmospheric convection, radiation and conduction dominate heat transfer; radiative cooling/heating must be engineered into the system.
• Material selection and contamination control:
  • Outgassing and contamination control are critical for sensitive instruments (e.g., optics, sensors).

Ballistic Coefficient, Drag, and Atmosphere Dynamics (Illustrative Example)

• Ballistic coefficient concept (relevant for atmospheric drag analysis):
  • The ballistic coefficient describes how easily an object slows due to drag and is commonly defined as:
  • \beta = \dfrac{m}{C_d A}
  • Note: some slides (as quoted in the transcript) define it as \beta' = \dfrac{Cd A}{m}; the standard convention in many analyses is the inverse, $m/(Cd A)$, which increases with mass and decreases with cross-sectional area and drag coefficient.
• Drag coefficient and area example:
  • Drag force: Fd = \dfrac{1}{2} \rho v^2 Cd A
  • For the International Space Station (ISS) in a reference case, $C_d \approx 1$ is assumed.
  • ISS cross-sectional area: approximately A \approx 4 \times 10^{3} \text{ to } 5 \times 10^{3} \text{ m}^2
  • This large area coupled with density ρ and velocity v yields non-negligible drag even in relatively high orbits.
• Atmospheric density and solar activity:
  • Increases in solar activity heat and expand Earth's upper atmosphere, raising density at a fixed altitude.
  • Higher density leads to greater drag, shortening spacecraft lifetime and increasing decay rates.
  • This coupling ($\rho$ dependent on solar activity) is a key driver of mission lifetime predictions for LEO satellites.
• Practical takeaway:
  • Drag and atmospheric density are central to lifetime planning, re-entry risk, and station-keeping for LEO missions; higher solar activity reduces lifetime through increased drag.

Quick Reference: Notable Numbers and Concepts from the Lecture

• Altitudes and orbital radii:
  • Von Kármán line (approximate boundary between atmosphere and space): ~100\ \text{km}
  • LEO altitude range: ~200\ \text{km} to ~2000\ \text{km} above Earth’s surface
  • Geosynchronous altitude: h_{GEO} = 35{,}786\ \text{km}
• Distances and times:
  • Earth–Moon light time: ~1–2 seconds
  • Sun–Earth light time: ~8 minutes
  • Mars–Earth light time: ~4–22 minutes
  • Alpha Centauri distance: ~4.2\text{ light-years}
• Orbital characteristics:
  • LEO orbital velocity: ~7.5\text{ to }7.7\ \text{km/s}
  • GEO orbital velocity: ~3\text{ km/s} (a few km/s range in slide context)
  • LEO orbital period: ~90\text{ minutes}
  • GEO orbital period: ~24\text{ hours}
• Cross-sectional area of ISS (illustrative): A \approx 4{,}000\ to\ 5{,}000\ \text{m}^2
• Important concepts:
  • Payload-centric design and satisfice concept: first satisfy the mission requirements; then optimize trade-offs.
  • Survivability vs robustness: survivability is about mission function under environmental stress; robustness is about toughness.
  • Six environmental stressors (primary design drivers): gravity (microgravity), vacuum, charged particles/radiation, debris/micrometeoroids, atmosphere/drag, launch environment.
  • Energy and heat transfer in space: conduction, convection (limited in vacuum), radiation (dominant in space).
  • Outgassing and contaminant control: critical for sensitive instruments; avoid petroleum-based materials if possible.
• Conceptual takeaways for exam-ready understanding:
  • The choice of orbit directly influences communication latency, line of sight, coverage, and debris risk.
  • The space environment imposes critical constraints that guide design choices (shielding, thermal control, materials, and mission architecture).
  • Predicting lifetime requires understanding how solar activity modulates atmospheric density and drag at a given altitude.

Summary Connections to Broader Concepts

• Scale and perspective connect to mission planning: the vastness of space drives decisions about autonomy, reliability, and ground support.
• Orbital mechanics foundations (period and velocity) underpin mission design, rendezvous, and station-keeping strategies.
• The space environment is a primary driver of system engineering: survivability, robustness, material selection, and risk management are central to successful missions.
• Practical design philosophy (satisficing) is about balancing mission objectives with environmental constraints, mass, cost, and risk.
• Real-world implications include planning for long communication delays, contamination control for telescopes and sensors, and robust shielding for radiation environments.

Light-Response/Reflection Prompts (for Quick Studying)

• If weather on the Sun changes (solar activity increases), what happens to atmospheric density at a fixed altitude, and how does that affect drag and lifetime of a satellite in LEO? Answer: atmosphere expands, density at fixed altitude increases, drag increases, reducing satellite lifetime.
• Compare LEO and GEO in terms of line-of-sight coverage and latency. Answer: LEO covers less instantaneous Earth area but with much lower latency; GEO provides near-continuous visibility for longitudes but higher latency due to distance.
• Explain the difference between orbital velocity and orbital period with respect to radius: v = \sqrt{\mu/r} and T = 2\pi \sqrt{r^3/\mu}. These equations show that as r increases, v decreases and T increases.
• What is the purpose of shielding in space radiation protection, and why is “lead” not always the best choice? Answer: Shielding reduces radiation exposure; lead is not always optimal due to mass, secondary radiation, and material interactions; alternatives and engineering strategies depend on mission specifics.
• Define ballistic coefficient and explain why it matters for drag calculations in LEO. Answer: The ballistic coefficient $\beta = m/(C_d A)$ (standard form) indicates how mass and cross-sectional area with drag coefficient influence drag; smaller $\beta$ means more deceleration by drag for a given density and velocity.