Best Gemini prompts for Aerospace Engineers

Given a set of GPS telemetry data points for a low-earth orbit satellite, use numerical methods to determine the orbital elements and then interpolate the satellite's position at a given time using a cubic spline. Assume a WGS-84 ellipsoid model for the Earth and account for atmospheric drag using the Jacchia-Bowman 2008 model. Provide the resulting orbital elements and interpolated position in ECEF coordinates.

Using the finite element method, analyze the structural integrity of a composite wing subjected to various loads, including lift, drag, and torsion. Assume a layup of carbon fiber reinforced polymer with a foam core and use a mesh size of 1mm. Calculate the stress and strain distributions throughout the wing and identify any potential failure points. Provide the resulting stress and strain plots in a format suitable for import into a CAD program.

Use a genetic algorithm to optimize the design of a propulsion system for a launch vehicle, with the goal of maximizing payload capacity while minimizing fuel consumption. Consider variables such as nozzle geometry, combustion chamber pressure, and fuel flow rate. Assume a rocket equation model with a constant thrust-to-weight ratio and account for gravity losses using a simplified model. Provide the resulting optimized design parameters and a plot of the payload capacity vs fuel consumption.

Develop a data fusion algorithm to combine GPS, accelerometer, and gyroscopic data for a navigation system, using an extended Kalman filter to estimate the system state. Assume a scenario where GPS signals are intermittently available and the system must rely on inertial measurements during outages. Provide the resulting state estimates and a plot of the navigation system's performance metrics, including position error and velocity error.