You need a better prompt.

> Write, in C++, code that projects voltage levels in an orbiting sensor platform into coordinates on the earth's surface.This is effectively just geolocation for a satellite image. Given the sensor intensities at each band, the code will need up determine exactly where on the earth the sensor is actually looking. You will need to start from physical first principles: orbital dynamics, special relativity, an understanding of how light diffuses through the atmosphere. Use knowledge synthesis of all these fields and others as necessary.

With this and "continue" 6 times, it output a ton of code with a main() of:

int main() {
// Set the orbital parameters
Orbit orbit;
orbit.semi_major_axis = R + 500e3; // altitude of 500 km
orbit.eccentricity = 0.1;
orbit.inclination = deg2rad(45);
orbit.longitude_of_node = deg2rad(90);
orbit.argument_of_periapsis = deg2rad(60);
orbit.true_anomaly = deg2rad(30);

// Compute the satellite's position, direction, and sensor voltages
auto result = computeSatelliteGeolocation(orbit);
double latitude = result.first;
double longitude = result.second;
double azimuth = result.third;
double elevation = result.fourth;
vector<double> sensor_voltages = result.fifth;

cout << "Latitude: " << latitude << endl;
cout << "Longitude: " << longitude << endl;
cout << "Azimuth: " << azimuth << endl;
cout << "Elevation: " << elevation << endl;
cout << "Sensor voltages: [";
for (double voltage : sensor_voltages) {
cout << voltage << ", ";
}
cout << "]" << endl;

return 0;

}

And also its assumptions:

This code assumes that there is a function `computeDiffuseIrradiance` that takes the satellite's direction vector and the Earth's surface normal vector and returns the diffuse irradiance on the Earth's surface at the satellite's location, and a function `computeSensorVoltages` that takes the diffuse irradiance and returns a vector of sensor voltages in each band. The exact implementation of these functions would depend on the specific sensor platform and atmospheric conditions.

In this code, the orbital parameters of the satellite are specified in the Orbit struct. These parameters include the semi-major axis (a), eccentricity (e), inclination (i), longitude of the ascending node (omega), argument of periapsis (omega'), and true anomaly (f). The semi-major axis specifies the size of the orbit, while the eccentricity determines its shape. The inclination specifies the angle between the satellite's orbital plane and the Earth's equatorial plane. The longitude of the ascending node and argument of periapsis specify the orientation of the satellite's orbit relative to the Earth's equatorial plane. The true anomaly specifies the position of the satellite along its orbit.

The code first computes the position, direction, and velocity vectors of the satellite in the orbital plane using the orbital parameters. These vectors are then rotated to the inertial frame using a rotation matrix, which takes into account the inclination, longitude of the ascending node, and argument of periapsis of the satellite's orbit. The position vector is then added to the position of the Earth in the inertial frame to obtain the satellite's position in the earth-centered inertial frame. The latitude and longitude of the satellite are then computed using spherical coordinates.

Next, the direction vector of the satellite in the earth-centered inertial frame is rotated to the earth-centered fixed frame using the same rotation matrix. The azimuth and elevation angles of the satellite are then computed using spherical coordinates.

Finally, the diffuse irradiance on the Earth's surface at the satellite's location is computed using the satellite's direction vector and the Earth's surface normal vector at the satellite's location. The sensor voltages in each band are then computed using the diffuse irradiance.

Note that this code is just a sample implementation and may not be suitable for a real-world satellite geolocation application. In particular, the code does not account for the effects of special relativity, which may be significant for satellites orbiting at high speeds and altitudes. Additionally, the code does not account for atmospheric effects, which can affect the diffusion of light and the accuracy of the sensor voltages. A more comprehensive implementation would need to consider these and other factors in order to accurately project the voltage levels of the satellite's sensors onto the Earth's surface

Still needed to coax it with a follow up prompt below for it to understand better, but I'm sure more can be done.

> You got that a bit wrong, the sensor voltages are provided as inputs and the goal is to use these voltages to determine a longitude and latitude on the surface of Earth