Question

Write code to produce an access report, which lists the times when a given spacecraft is in view from a given ground station, along with the azimuth, elevation and range . The idea is to find the spacecraft ECEF location at each time; subtract the ground station ECEF location to obtain the vector pointing from the ground station to the spacecraft; and find the projections of this vector onto local north, east and up vectors.

(a) Taking the ground station to be at 34.0209 degrees N, 118.2982 degrees W, find the ECEF coordinates of the ground station, assuming it is at zero altitude on a spherical Earth of radius R0.

Answer 1

To calculate the ECEF coordinates of a ground station located at 34.0209° N and 118.2982° W at zero altitude, apply spherical to Cartesian conversions using the Earth's radius. The resulting coordinates provide a basis for further calculations of visibility, azimuth, elevation, and range for observing spacecraft.

Step-by-step explanation:

Calculating ECEF Coordinates for a Ground Station

The Earth-Centered, Earth-Fixed (ECEF) coordinate system is key in determining the position of objects on and above the Earth's surface. To calculate the ECEF coordinates of a ground station, we must convert the given geographical coordinates (latitude, longitude) to this Cartesian coordinate system. The ground station's latitude is 34.0209° N and its longitude is 118.2982° W. On a spherical Earth with radius R0 = 6370 km, we can use the following transformation equations:

1. x = R0 × cos(latitude) × cos(longitude)
2. y = R0 × cos(latitude) × sin(longitude)
3. z = R0 × sin(latitude)

Substituting the ground station's coordinates and assuming zero altitude for the purpose of this calculation, we obtain the ECEF coordinates for the ground station. The north, east, and up vectors can then be determined based on this reference point for further calculations involving spacecraft visibility, azimuth, elevation, and range from the ground station.