A small Earth-observation satellite is proposed for wildfire monitoring in a circular orbit of radius 7.0 × 10⁶ m from Earth's centre. Use GM = 3.99 × 10¹⁴ m³/s² and T = 2π√(r³/GM). A lower orbit gives finer ground detail but more atmospheric drag and a smaller field of view; a higher orbit gives wider coverage but coarser detail. (a) Calculate the orbital period in minutes. [4] (b) Explain the physical trade-off between altitude, resolution, coverage and revisit planning. [4] (c) Evaluate public benefit, privacy, launch emissions, debris and unequal access to data. [6] (d) Make a conditional recommendation. [2]

Question

Accepted Answer

The ideal circular-orbit period is about 5828 s, or 97.1 min. The mission can be justified only if its resolution and revisit evidence meet the wildfire need and governance addresses privacy, debris, emissions and fair data access. (a) Cube the radius: r³ = (7.0 × 10⁶)³ = 3.43 × 10²⁰ m³. Divide by GM to obtain about 8.596 × 10⁵ s². (a) The square root is about 927.2 s, and multiplying by 2π gives T ≈ 5828 s = 97.1 min. This is the period, not the time over one community. (b) Lower altitude can improve spatial resolution for a fixed instrument and shorten the orbital period, but drag shortens orbital life and the instantaneous field of view is smaller. Revisit time also depends on inclination, swath and Earth's rotation. (b) Higher altitude increases area visible per pass and can reduce drag, but a fixed detector resolves larger ground pixels. The best orbit follows the actual warning requirement rather than maximising one metric. (c) Earlier fire detection can protect lives and ecosystems, yet high-resolution imagery can expose private activity. Launch and replacement create emissions, and failed spacecraft add collision and debris risks. (c) Governments, residents, firefighters, Indigenous communities, researchers and commercial operators may not have equal control or access. A public-benefit claim needs transparent data rules, consent-sensitive use and an end-of-life plan. (d) Proceed if validated coverage and latency meet emergency needs, data access is equitable, privacy is governed and disposal reliability is demonstrated. Otherwise improve or share an existing constellation rather than launch by default.

Select an Earth-observation orbit responsibly

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