Astronomy & Space Science

Operations Research in Astrophysics & Mission Design

Four canonical OR problems appear inside operational spacecraft systems and scientific instruments: scheduling under physical resource constraints, survey cadence optimisation, combinatorial trajectory optimisation, and multi-objective facility location.

Space science generates OR problems with no direct industrial equivalent. A space telescope accumulates angular momentum as a physical vector resource. An interplanetary mission requires choosing a sequence of planetary flybys — a problem formally proven NP-hard. A radio interferometer’s imaging quality depends on the geometric placement of its antennas across a landscape.

The four applications span the full range of OR problem families: multi-objective scheduling (JWST), survey cadence optimisation (Rubin/LSST), combinatorial trajectory design (gravity-assist), and bi-objective facility location (radio arrays). Each is operational or published at the research frontier.

Physical Context

The James Webb Space Telescope orbits the Sun–Earth L2 point, 1.5 million km from Earth. Its sunshield must always face the Sun, limiting the roll angle and creating time-dependent visibility windows for each target. Solar radiation pressure exerts a continuous torque that accumulates angular momentum in four reaction wheels. Momentum must stay within 24–30 N·m·s per 22-day planning period; exceeding the limit triggers a momentum dump that costs science time. The scheduling problem couples observation selection with physical resource management.

Formulation

Divide a 365-day cycle into 22-day bins. Each observation has a priority, duration, visibility window, and momentum contribution (dependent on roll angle). The scheduler must maximise weighted science return while respecting momentum limits, visibility constraints, and inter-observation slew times. The problem is a multi-objective variant of RCPSP with a vector resource (angular momentum in three axes).

Objective

min w1 · gaps + w2 · lateObs + w3 · ||momentum||

// gaps = unscheduled high-priority observations

// lateObs = observations scheduled outside preferred window

Subject To

visibility(obs_i, bin_t) = 1 for each scheduled (i, t) pair

Σ_i momentum(obs_i, roll_i) ≤ H_max per 22-day bin

roll_min ≤ roll_i ≤ roll_max (sunshield constraint)

Σ_i duration_i ≤ T_bin (time capacity per bin)

// H_max typically 24–30 Nms; roll range ~5° per target

JWST Cycle Scheduler

Scenario

Algorithm

Key References

Operational

Giuliano, M.E. (2007). “Multiobjective Scheduling for the James Webb Space Telescope.” Proceedings of ICAPS 2007, International Conference on Automated Planning and Scheduling.

Operational

Kinzel, W. et al. (2007). “An Automated Scheduling System for the James Webb Space Telescope.” STScI Technical Report, Space Telescope Science Institute.

Operational

STScI (2022). “SCOPE: Scheduling and Constraint-based Observation Planning Engine.” Space Telescope Science Institute, operational planning system for JWST Cycle 1+.

Physical Context

The Vera C. Rubin Observatory will execute the Legacy Survey of Space and Time (LSST): approximately 5 million 30-second exposures over 10 years through 6 optical filters (u, g, r, i, z, y). Four competing science programs share the same telescope: dark energy (uniform deep coverage), solar system (rapid revisits for asteroid discovery), transient science (short gap cadence for supernovae), and Milky Way mapping (Galactic plane coverage). The scheduler must balance these goals under constraints of weather, Moon brightness, airmass, and filter-change overhead.

Feature-Based Scheduler

Rather than a monolithic optimiser, Rubin uses a feature-based greedy scheduler. At each decision epoch (every ~37 seconds), the scheduler evaluates every observable field and computes a weighted score from numerical features: time since last visit, current airmass, sky brightness, survey progress toward depth targets, and filter balance. The field with the highest composite score is selected. Feature weights encode science priorities and can be tuned to shift emphasis between the four science programs.

Scoring Function

Score(field_f, filter_F, time_t) = Σ_k w_k · feature_k(f, F, t)

Features

f1: time_since_visit(f) — penalise long gaps or too-short revisits

f2: airmass(f, t) — prefer low airmass (high elevation)

f3: sky_brightness(f, t) — match filter to Moon phase

f4: progress(f, F) — steer toward under-observed fields

f5: coadded_depth(f, F) — track cumulative depth toward 10-yr target

// Greedy selection: next_obs = argmax_{f,F} Score(f, F, t)

Rubin Night Simulator

Scenario

Algorithm

Key References

Operational

Naghib, E., Awan, H., Perber, Z. et al. (2019). “A Framework for Telescope Scheduling: The LSST Feature-Based Scheduler.” The Astronomical Journal, 157(4), 151.

Published

Bianco, F.B. et al. (2022). “Optimization of the Observing Cadence for the Rubin Observatory LSST: A White Paper.” The Astrophysical Journal Supplement Series, 258(1), 1.

Operational

LSST Project Science Team (2022). “PSTN-055: Survey Cadence Optimization Committee Final Report.” Rubin Observatory Technical Note, operational baseline cadence.

Physical Context

Gravity assists use a planet’s gravitational field to change a spacecraft’s speed and direction without expending propellant. Cassini used a Venus–Venus–Earth–Jupiter (VVEJGA) sequence to reach Saturn. Voyager 2 performed four consecutive flybys for the grand tour of the outer solar system. Selecting the optimal flyby sequence from all feasible planet orderings is proven NP-hard (Izzo 2007).

Formulation

The Multiple Gravity Assist (MGA) trajectory design problem seeks a planet flyby sequence and launch window that minimise total propulsive Δv while satisfying chronological ordering, flyby velocity limits, Lambert arc feasibility, and launch window constraints. Pruning heuristics such as GASP achieve up to 10⁶× search-space reduction.

Multiple Gravity Assist (MGA) — NP-Hard

Minimise Δv_launch + Σ Δv_DSM + Δv_insertion

Subject To

t_flyby(i) < t_flyby(i+1) (chronological ordering)

v_inf(i) ≤ v_inf_max(planet_i) (flyby velocity limits)

Lambert(r_i, r_{i+1}, TOF) feasible (arc feasibility)

t_launch ∈ [t_min, t_max] (launch window)

// GASP achieves 10^6× search space reduction

Gravity-Assist Trajectory Builder

Scenario

Key References

Published

Izzo, D. (2007). “Global Optimization and Space Pruning for Spacecraft Trajectory Design.” Journal of Global Optimization, Springer.

Published

Ceriotti, M. (2010). “Global Optimisation of Multiple Gravity Assist Trajectories.” PhD Thesis, University of Glasgow.

Published

Peralta, F. & Flanagan, S. (1995). “Cassini Interplanetary Trajectory Design.” AAS/AIAA Spaceflight Mechanics Meeting.

Published

ESA Advanced Concepts Team. “Global Trajectory Optimisation Competition (GTOC).” European Space Agency, ongoing benchmark series.

Physical Context

Radio interferometry combines signals from pairs of antennas to sample the (u,v) plane of spatial frequencies. As the Earth rotates, each antenna pair traces an ellipse in the uv-plane. Complete, uniform coverage yields high-fidelity images; gaps produce artefacts. Designing the array layout is a combinatorial placement problem: choose antenna positions within a site boundary to maximise uv-coverage while minimising cable infrastructure.

Formulation

The array design problem is bi-objective: maximise the number of uv-plane cells covered (image fidelity) while minimising the minimum spanning tree cable length (infrastructure cost). Each antenna pair at each hour angle produces a (u,v) sample computed from their baseline vector and the source declination. Constraints include site boundary limits and minimum antenna separation distances.

Bi-Objective Array Placement

Max f1 = |{uv cells covered}|

Min f2 = MST cable length

Subject To

||pos_i|| ≤ R_site (site boundary)

||pos_i - pos_j|| ≥ d_min ∀ i ≠ j (min separation)

// For each baseline (i,j) at hour angle h:

// u = B_x sin(h) + B_y cos(h)

// v = -B_x sin(δ)cos(h) + B_y sin(δ)sin(h) + B_z cos(δ)

Radio Array Designer

Antennas 6

Scenario

Algorithm

Key References

Published

Cohanim, B.E. et al. (2004). “Minimum-Redundancy Linear Arrays for Interferometric Imaging.” The Astrophysical Journal Supplement Series.

Published

Doeleman, S.S. et al. (2023). “Reference Array and Design Considerations for the Next-Generation EHT.” Galaxies, 11(5), 107.

Operational

PMC 12389914 (2024). “Optimisation of Radio Interferometric Array Configurations.” Operational array design methodology.

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From telescope scheduling to interplanetary trajectory design, operations research techniques power the missions that explore our universe.

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Disclaimer

All examples are simplified for educational purposes. Observation parameters, momentum values, survey metrics, and scheduling outcomes are illustrative and do not represent actual JWST or Rubin Observatory operational data. The solvers demonstrate algorithmic principles rather than production-grade mission planning systems.