What are you trying to do ?
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what are you trying to do ? really I do not understand.
If you have a beam coming from an antenna installed on a spacecraft its footprint on the Earth is just a series of isolevel contour plots (including or not the Earth curvature it depends on what you want see) in terms of antenna gain or EIRP. If you have a circular foot print and assuming that the antenna boresight is pointing at nadir on the Earth, you have a circular symmetric beam (eg pencil beam, isoflux, etc...) the isolevels shall depend on the antenna gain (eg abolsute or relative peak, -1dB -2dB and so on..). If the antenna is not active one the bigger is the antenna, the higher is the gain, the narrower is the foot print... but usually in space based antenna at stage one the link budget is established for a Earth portion, then the "minimum" gain is specified for the antenna in that area (not necessary circular), and consequently the antenna is dimensioned (strongly constrained by the spacecraft allowable volume), essentially the resulting footprint is showing the antenna patter projected on the Earth
what are you trying to do ?