Claude Skills by ashfordeOU

Use when you must build the daily ground station contact schedule of a low-earth satellite: propagate the sub-satellite point over the planning horizon, compute the elevation of the satellite above each station, detect the contiguous passes above the station elevation mask, aggregate the daily contact window schedule with its downlink gap analysis, and merge the contacts of several ground stations into one plan. Produces the per-pass start, end, duration and maximum elevation, the daily conta...

Use when you must determine launch windows and launch geometry for orbital missions: compute the launch azimuth for a target inclination from cos(inc) = cos(lat) * sin(az), the daily launch window when the target orbit plane passes through the launch site (window center and half-width from the plane-crossing geometry), sun-synchronous LTAN to RAAN conversion, the plane change delta-v penalty for out-of-plane launches, window duration from the orbit plane regression rate versus Earth rotation,...

Use when you must build the spacecraft mission delta-v budget: sum the launch insertion, orbit transfer, plane change, station keeping, and deorbit contributions, apply a margin allocation, and convert the budget into propellant mass with the Tsiolkovsky rocket equation from the dry mass and the specific impulse. Produces the nominal and margined delta-v totals, the required propellant and wet masses, and the budget verdict that closes the propulsion sizing. Trigger: mission delta-v budget, d...

Use when you must assess the space radiation and orbital debris environment for a spacecraft mission design: estimate the trapped radiation belt (van Allen) dose rate as a function of altitude and inclination with a simplified AE-8/AP-8 style flux band model, add the solar particle event fluence, compute the single-event upset rate with the RPP model from the upset cross-section and LET spectrum, size aluminum shielding against total ionizing dose with exponential attenuation, and estimate th...

Use when you must determine the interplanetary launch-window timing between two planets: compute the synodic period of the launch opportunity recurrence for near-circular coplanar orbits, the heliocentric departure phase angle required for a Hohmann window, the recurrence epochs, and the phase progression between windows. Produces the synodic period, the departure phase angle, the window epochs, and the phase check that gate interplanetary mission window planning. Trigger: synodic period, lau...

Use when you must analyze the bi-elliptic three-impulse transfer between two coplanar circular orbits and compare it against the Hohmann transfer: compute the three burn delta-v values (the perigee raise to the intermediate apogee radius, the intermediate-apogee burn that raises the perigee to the target radius, and the target circularization), the total bi-elliptic delta-v, the Hohmann delta-v for the same orbit pair as the comparison baseline, the delta-v saving of the cheaper strategy, and...

Use when you must propagate and analyze the Clohessy-Wiltshire linearized relative motion of a deputy spacecraft about a chief in a circular orbit: compute the chief mean motion, build the 6x6 relative-motion state-transition-matrix, propagate the deputy-chief relative state (x radial, y along-track, z cross-track), check the bounded relative orbit condition y_dot = -2 n x, and size the two-impulse targeting delta-v to a desired final relative state. Produces the propagated relative trajector...

Use when you must screen a close approach between two objects and assess the collision risk: compute the time of closest approach from the relative position and velocity with a linear relative-motion model, the miss distance at TCA, the encounter-plane sigma from the combined 1-sigma position uncertainty, the probability of collision with the small hard-body approximation against the combined object radius, and the screen verdict against an actionable threshold. Produces the TCA, miss distanc...

Use when you must compute the time a spacecraft spends inside the earth shadow during each orbit: derive the beta angle of the orbit plane relative to the sun vector from the inclination, the right ascension of the ascending node, and the sun position, then evaluate the shadow fraction from the beta angle and the orbit radius and multiply by the orbital period to produce the eclipse time and the daylight fraction. Produces the beta angle in degrees, the shadow fraction, and the eclipse time i...

Use when you must compute geostationary station keeping quantities for a GEO satellite: the geosynchronous radius and orbital speed from the sidereal day, the annual north-south delta-v from the inclination drift with the two-burn-per-year model, the per-burn delta-v, the burn time from thrust and spacecraft mass, the annual propellant from the specific impulse, the east-west deadband drift-cycle period and maneuver cadence from the longitude acceleration and box half-width, and the uncontrol...

Use when you must analyze a gravity-assist swing-by maneuver of a spacecraft past a planet or moon: compute the periapsis speed from the hyperbolic excess velocity with the vis-viva energy integral, the flyby turn angle, the delta-v gain for the heliocentric velocity change, and the outgoing direction for outside or inside passes, and check close approach feasibility against the body radius and minimum altitude. Produces the single-flyby summary with periapsis speed, turn angle, delta-v gain ...

Use when you must compute a repeating ground track for a circular Earth orbit: determine the semimajor axis and mean motion from the altitude, evaluate the J2 nodal regression rate, derive the nodal period, count the integer revolutions per sidereal day, and find the repeat cycle in whole days after which the ground track retraces itself. Produces the semimajor axis, mean motion, nodal regression rate, nodal period, revolutions per day, and repeat cycle that gate repeat-ground-track orbit sel...

Use when you must size a Hohmann transfer between two coplanar circular orbits of a spacecraft: compute the transfer-orbit semimajor axis and period, the circular-orbit velocity at the departure and arrival radii, the periapsis and apoapsis speeds on the transfer ellipse with the vis-viva equation, and the departure and arrival burn impulses that make up the hohmann-transfer delta-v budget. Produces the transfer time, the two impulse burns, and the total delta-v that gate orbit-raising and or...

Use when you must determine the time propagation of a spacecraft orbit from its classical orbital elements: mean motion from the semimajor axis, the Kepler equation M = E - e sin E solved by Newton iteration for the eccentric anomaly, the branch-safe half-angle conversion to true anomaly, the radius at any anomaly, the time since periapsis for a given true anomaly, and the inertial position and velocity vectors after an elapsed time from an element state (a, e, i, RAAN, argp, nu0). Produces t...

Use when you must compute classical orbital elements from a position and velocity state vector: derive the specific angular momentum, node vector and eccentricity vector, then convert to semimajor axis, eccentricity, inclination, right ascension of the ascending node (RAAN), argument of periapsis and true anomaly, and derive the orbital period with periapsis and apoapsis radii for an elliptical Earth orbit. Handles circular and equatorial degenerate cases with documented conventions and raise...

Use when you must solve Lambert's problem for a spacecraft orbit transfer: given two position vectors and a transfer time, find the connecting orbit with the p-iteration method, compute the velocity vectors at both endpoints, the transfer delta-v against circular parking orbits, and the transfer ellipse elements. Produces the semimajor axis, eccentricity, semilatus rectum, the required endpoint velocities, the delta-v budget, and the time-of-flight check, with short-way and long-way branches,...

Use when you must size a low-thrust transfer between two circular orbits under continuous thrust with the Edelbaum approximation, for ion propulsion and other electric-propulsion trajectories: compute the circular-orbit velocity at both radii, the total delta-v budget including the inclination change (no-plane-change spiral case as the di = 0 limit), the propellant mass and final mass from the rocket equation at constant thrust and specific impulse, the spiral transfer time, and the impulsive...

Use when you must estimate orbital decay and deorbit lifetime of a low Earth orbit spacecraft from atmospheric drag: compute the ballistic coefficient from mass, drag area, and drag coefficient, the altitude decay rate and decay per orbit, the decay per day, and the deorbit lifetime down to a target altitude with the closed-form exponential lifetime, then assess compliance with the 25-year disposal rule and size drag augmentation for end-of-life deorbit. Trigger: orbital decay, atmospheric dr...

Use when you must quantify the J2 secular perturbations of a circular Earth orbit: compute the RAAN drift rate and the argument-of-perigee drift from the mean motion, semimajor axis, and inclination, derive the nodal period change against the Keplerian period, and scale the perturbation magnitude with altitude from LEO to GEO. Produces drift rates in radians per second and degrees per day, the critical inclination, and the oblateness acceleration ratio. Trigger: orbital-perturbations, j2-noda...

Use when you must compute the delta-v of an orbital plane change maneuver and compare the pure inclination change against the combined burn that merges the plane change with an orbit transfer: evaluate the circular-orbit speed at the maneuver radius with sqrt(mu/r), the pure plane change delta-v 2 v sin(di/2), the speed on the elliptic transfer orbit at the maneuver point with the vis-viva equation, and the combined-burn delta-v from the law of cosines when the plane change rides the circular...

Use when you must analyze satellite ground coverage and access geometry: compute the instantaneous access circle central angle for a satellite from the orbital altitude and the minimum elevation angle constraint, estimate the swath width and the coverage fraction of a region or the globe, derive the maximum off-nadir angle and the elevation and look-angle geometry at a ground station, and evaluate the access time per pass and the revisit time. Produces the central angle, swath width, off-nadi...

Use when you must compute the sun-synchronous orbital inclination from altitude for a circular Earth orbit: determine the orbital mean motion from the semimajor axis, evaluate the J2 nodal regression rate, solve the sun-synchronous condition cos(i) = -omega_dot_desired / (1.5 n J2 (Re/a)^2), and produce the inclination in radians and degrees. Produces the altitude, semimajor axis, mean motion, and inclination that gate dawn-dusk and local-time-of-ascending-node orbit selection. Trigger: sun-s...

Use when you must analyze the circular restricted three-body problem (CR3BP) for a spacecraft near two massive primaries: compute the mass ratio from the primary masses, locate the collinear points L1, L2, L3 by solving the rotating-frame force balance with a bracketed Newton iteration, place the triangular points L4 and L5 from the closed-form equilateral construction, convert dimensionless coordinates into physical distances from each primary, and evaluate the Jacobi constant for a planar s...

Use when you must parameterize a Walker-Delta constellation: validate the t/p/f triple (total satellites divisible by the plane count, phasing parameter within range), enumerate the planes and the slots per plane, compute the right ascension of ascending node spacing 360/p, the in-plane mean anomaly spacing 360/s with s = t/p satellites per plane, and the inter-plane phasing offset f*360/t, and produce the unique (RAAN, mean anomaly) slot list. Produces the satellites per plane, the RAAN spac...

Use when you must size the parabolic antenna aperture of a spacecraft communications link: convert a required antenna gain into the reflector diameter through the aperture efficiency, compute the achieved gain of the sized aperture, the half-power beamwidth, the pointing budget with pointing loss, and the receive gain-over-temperature G/T figure of merit. Produces the required gain, the reflector diameter, the achieved gain, the beamwidth, the pointing budget and the G/T that gate an antenna ...

Use when the task is command validation, telemetry packetization, CCSDS framing, onboard data storage sizing, downlink budgeting, spacecraft data bus selection, or C&DH redundancy. Design and check spacecraft command and data handling (C&DH): validate telecommands against opcode, length, and CRC-16 checksum; packetize telemetry into CCSDS-style frames with sequence counts and error detection; size onboard storage from per-orbit data volume; and budget downlink time and rate from stored data v...

Use when you must build or check a spacecraft communications link budget: compute the free space path loss from distance and frequency, derive EIRP from transmit power and antenna gain, estimate received power and carrier to noise density ratio, and verify the link margin against the required energy per bit to noise ratio at the data rate. Produces path loss, EIRP, received power, C/N0, Eb/N0, and the margin verdict that closes the link. Trigger: link budget, path loss, eirp, carrier to noise...

Use when you must compute the doppler frequency shift on a spacecraft link: derive the line-of-sight range rate from the circular-orbit altitude and the ground elevation angle, convert it to the received frequency and offset on an s-band downlink carrier, and estimate the worst-case doppler near the horizon and the doppler-rate at acquisition for receiver acquisition design. Produces the range rate, received frequency, delta-f offset, maximum doppler, slant range and doppler rate that gate co...

Use when you must size meteoroid and orbital debris (MMOD) impact protection: compute the Cour-Palais cratering penetration depth and critical projectile diameter of a single aluminum wall, size a Whipple shield bumper and rear wall so a design projectile at its design impact produces no rear-wall penetration, evaluate the Christiansen ballistic limit across low, intermediate, and hypervelocity regimes with the 3 and 7 km/s normal-velocity transitions and the 65 degree obliquity cap, and grad...

Use when sizing spacecraft electrical power and thermal budgets per ECSS practice: estimate battery capacity from eclipse power draw, depth of discharge, and efficiency; size the solar array from daylight-only generation; and check power margins against spacecraft bus requirements. The skill covers orbit-period eclipse fractions, battery sizing, solar array sizing, and margin checks for power budgets. Trigger: power budget, thermal budget, eps, eclipse, battery sizing, solar array, spacecraft...

Use when you must size a spacecraft propellant tank for the propulsion bus: convert the propellant mass into the liquid volume with the propellant density, add the ullage volume for the required tank ullage fraction, compute the spherical tank volume and radius, size the sphere tank wall thickness from the burst pressure and the material allowable, estimate the tank shell mass, and size the helium pressurant mass for the regulated or blowdown pressurization scheme with the blowdown pressure r...

Use when sizing a spacecraft EPS solar array or photovoltaic panel: array area, power demand, eclipse fraction, cell efficiency, packing factor, degradation, end of life, solar irradiance. Compute spacecraft solar-array sizing: determine the required photovoltaic array area in square meters from the orbit-average power demand, the eclipse fraction, the solar cell efficiency, the packing factor, and the end-of-life degradation over the mission life, then verify the array margin at end of life....

Use when you must size the spacecraft battery energy storage for an Earth-orbiting power subsystem: compute the eclipse energy from the eclipse load and the eclipse duration, convert it into the required nameplate capacity with the depth of discharge limit and the discharge efficiency, convert to ampere hours at the bus voltage, lay out the series and parallel Li-ion cell counts for the regulated bus, check the discharge C-rate against the cell limit, and estimate the pack mass from the pack ...

Use when you must size the thermal control subsystem for a spacecraft: compute the radiator area from the Stefan-Boltzmann balance, solve the equilibrium radiator temperature for a heat load, and check the thermal margin against the dissipation budget. Produces the radiator sizing, the equilibrium temperature, and the margin verdict that gate the thermal design. Trigger: thermal design, radiator sizing, thermal balance, heat load, spacecraft thermal control.

Use when a task concerns aerospace structures and materials: guide the router to the structures pack: calculix-linear linear FEA, calculix-nonlinear Newton-Raphson and load stepping, modal-analysis natural frequencies, residual-strength fracture, crack-growth crack propagation, widespread-fatigue-damage MSD/MED, miner-damage cumulative damage, goodman-diagram mean-stress corrections, load-spectrum-counting rainflow, laminate-stiffness CLT/ABD, composite-bolted-joints bearing and bypass, sandw...

Use when you must analyze a single-lap adhesive bonded joint between two identical adherends: compute the Volkersen shear-lag parameter from the adherend modulus and thickness and the adhesive shear modulus and thickness, the average adhesive shear stress from the load, bond width and overlap length, the peak shear stress at the bondline ends with the shear-lag correction, and the joint margin against the adhesive allowable shear stress. Produces the average and peak stresses, the peak to ave...

Use when the task is composite allowables, basis values, coupon pooling, or laminate knockdown factors for polymer matrix composites. Compute composite material design allowables per the CMH-17 method: determine A-basis and B-basis values from coupon test data using the one-sided normal tolerance k-factor approximation, pool coupon batches across environments to enlarge the effective data set, and apply knockdown factors for environmental conditioning, barely visible impact damage, and open h...

Use when you must analyze a bolted joint in a composite laminate under bearing and bypass loading: compute the bolt bearing stress from the applied load, bolt diameter, and laminate thickness, the net-tension stress across the net section, the shear-out stress at the edge distance, and the joint margin against each allowable. Produces the applied stresses, the governing failure mode, the pass or fail verdict, and the margins for the fastener row with the bypass load share. Trigger: bolted joi...

Use when you must size a bonded scarf repair for a damaged composite laminate: compute the scarf length from the parent thickness and the scarf angle, the average adhesive shear stress carried by the scarf joint at the parent laminate stress, the required scarf angle for an adhesive shear allowable, and the external patch thickness that restores the parent stiffness. Produces the scarf length, adhesive shear stress, required scarf angle, and stiffness-matched patch thickness that gate a compo...

Use when you must assess delamination growth in a composite laminate by fracture mechanics: compute the mode I strain energy release rate of a DCB double cantilever beam specimen and the mode II rate of an ENF end-notched flexure specimen from load, crack length and coupon geometry, blend mixed-mode rates with the Benzeggagh-Kenane criterion, and compare the total rate against the critical rate for the onset and growth verdict. Produces G_I, G_II, the mixed-mode ratio, critical rate G_c, onse...

Use when you must evaluate a composite lamina against strength failure criteria: compute the Tsai-Wu, Tsai-Hill, and max-stress failure indices from the in-plane stresses and the ply allowables, and return the failure verdict. Produces each criterion index, the governing criterion, and the pass or fail verdict for the ply stress state. Trigger: lamina failure, tsai wu, tsai hill, max stress, failure index, composite ply strength, in plane stress.

Use when you must predict the equivalent mechanical properties of a hexagonal honeycomb core from the cell geometry and the foil material: compute the relative density of the hexagonal cell with double-thickness vertical walls, the core density from the foil density, the stabilized out-of-plane compressive modulus E3 from the foil modulus, the out-of-plane shear moduli G13 and G23 from the foil shear modulus, and the in-plane cell-wall-bending moduli E1, E2 and G12 by the Gibson and Ashby hex...

Use when you must assemble the full classical lamination theory stiffness of a composite laminate stack for the bending and coupling response: compute the bending-extension coupling matrix B and the bending matrix D by the z-squared and z-cubed thickness integrals over the ply z coordinates, the full ABD stiffness matrices for symmetric and unsymmetric laminates, the D11 D22 D12 and D66 bending terms the laminate plate buckling analysis takes as given inputs, the exact zero-coupling identity ...

Use when you must compute the first-ply-failure load of a composite laminate: recover the mid-plane strains of a symmetric balanced laminate from its in-plane compliance under applied load resultants, transform the strains to each ply material axis, compute the per-ply Tsai-Wu failure index, and return the critical ply. Produces the mid-plane strains, the per-ply failure indices, the critical ply, the first-ply-failure load scale factor, the FPF load resultant, and the reserve factor. Trigger...

Use when you must compute the hygrothermal response of a composite laminate: equilibrium moisture content from relative humidity with a linear isotherm, stiffness-weighted laminate CTE and CME assembled by classical lamination theory from ply-level properties, hygrothermal laminate strain from temperature and moisture changes, and residual strain from the cure-cooldown drop. Produces the moisture content, laminate CTE and CME in raw SI with a parts-per-million helper, and the hygrothermal and...

Use when you must compute the elastic buckling load of an orthotropic or laminated flat plate: evaluate the energy-method critical load N_x_cr(m, n) per unit width for integer half-wave counts m and n from the classical lamination theory bending stiffnesses D11, D22, D12 and D66, minimize over the mode counts, and return the critical load, the governing buckling mode and the stability margin against the applied in-plane compression load. Produces the critical load, the buckling mode and the m...

Use when you must compute the progressive failure of a composite laminate past first-ply failure by the ply-discount method: degrade the stiffness of the failed ply at each ply event, reassemble the in-plane laminate stiffness, reapply the load resultant and march to the last-ply-failure ultimate load. Produces the sequential-ply-failure event loads with the matrix and fiber modes, the degraded laminate stiffness after each event, the first-ply-failure load from the per-ply Tsai-Wu index at u...

Use when you must compute the stiffness of a composite laminate with classical lamination theory: build the ply stiffness from the material constants, rotate it to the ply angle, and assemble the A matrix for a symmetric laminate. Produces the ply stiffness, the rotated stiffness with coupling terms, and the laminate A matrix used in strength and stability analyses. Trigger: composite laminate, classical lamination theory, ply stiffness, laminate a matrix, symmetric laminate, composites.

Use when you must compute the peel stress at the overlap end of a single-lap bonded joint: find the Goland-Reissner bending moment factor from the load per unit width, the adherend thickness, modulus and Poisson ratio, and the overlap half length, form the edge moment at the overlap end, resolve the peak peel stress from the adhesive Winkler-foundation beam model with the peel decay coefficient, and rate the peel margin against an allowable peel strength. Produces the bending moment factor, t...

Use when the task is sandwich panel sizing or analysis, honeycomb or foam core selection, face sheet stress or core shear failure checks, face wrinkling, or sandwich bending stiffness and deflection. Design and analyze aerospace sandwich panels: compute the equivalent bending stiffness from the face modulus, face thickness, and core thickness, the face sheet stresses from a bending moment, the core shear stress from a shear load, the face wrinkling stress from the face and core moduli, and th...