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An EME path depends not only on the round trip distance, but reflection from the Moon depends on its distance (at the time) and surface reflectivity.
We can write the cascade of path elements earth  moon  earth to calculate Pr/Pt for isotropic tx and rx antennas:
\[\frac{P_r}{P_t}=dispersion \cdot A_{e_m} \cdot reflectance \cdot disperson \cdot A_{e_i}\]
Expanding that:
\[ \frac{P_r}{P_t}=(\frac{1}{4 \pi D^2})(\frac{\pi d^2}{4})(\eta)(\frac{1}{4 \pi D^2})(\frac{\lambda^2}{4 \pi}) \] where:
D: distance earth to moon;
d: diameter of moon (3474800m);
η: lunar
surface reflection coefficient (0.065).
This can be rewritten as three terms: the dispersion term though with distance exponent 4, a path loss adjustment factor, and the receiver aperture:
\[\frac{P_r}{P_t}=(\frac{1}{4 \pi D^4})(\frac{d^2 \eta}{16})(\frac{\lambda^2}{4 \pi}) \]
The adjustment term (in the middle) can be calculated:
\[10 \log \frac{d^2 \eta}{16}=106.9 \text{ dB}\]
So, to calculate an EME path in FSC, enter the one way path distance, use exponent=4 and extra path loss 106.9dB.
The above example shows the moon at perigee, 407,000km.
© Copyright: Owen Duffy 1995, 2021. All rights reserved. Disclaimer.
There is an error in Example 5 in the FSC help, the above calculation supercedes the help.