Compare spherical reflection methods: infinite x finite (with almost infinite transmitter height)

[vitorhjr]

Theoretically, the quartic polynomial based on the finite method must converge the interferometric delay with the infinite method when the transmitter height is large enough to be almost infinite.

This is the assumption that will be tested in this issue by comparing both methods with different transmitter heights.

[vitorhjr]

Comparison

I made comparisons by using different heights (from 10m to 500m) and elevations (from zenith to spherical horizon) and applied different transmitter heights. Remember that the transmitter height default was 20.2e6m.

I found the following:

• Both methods tend to converge interferometric delay and specular point position as far as the satellite height;
• However, there is a limit for this;
• The best results for both specular position and delay is for a transmitter height at 10^10m. In this case, specular point differences are 10^-3m in x and 10^-5m in y, and differences of 10^-5m in delay delay;
• The specular position differences become even smaller for a transmitter height above 10^11m. For instance, differences in specular position are 10^-6m and 10^-7m for a transmitter height of 10^13m.
  • At the same time, delay differences increase to 2cm. These differences increase as far as the satellite;
  • It's interesting that these discrepancies in delay seem like noise across the elevations. They don't follow the typical behavior like bigger discrepancies as lower elevation;
  • I think the problem lies in the satellite position computation.

Bellow there are figures for many satellite heights:

10^9

10^10

10^11

10^13

10^14