Because one side of the moon is always facing the Earth, if a geostationary satellite about the moon is placed into orbit, that satellite will also remain remain fixed in its relationship with the Earth (facing or otherwise). The calculations determining the radius for geostationary orbit about the moon are shown in the figure below and yield a radius of about 88,450 km. The moon's radius, mass, and period of rotation were all collected from [3].
Earth Satellites
The location on Earth that our collected data is to be beamed to is fixed. In addition, that data needs to be sent continuously and reliably. Therefore, it was decided to select a geostationary orbit about the Earth for our Earth Satellites as well. The calculation to determine the radius of geostationary orbit follows the equation above but with different parameters and yields 42,164 km [4]. Each of the satellites is placed around the Earth so that they are equally spaced at 120 degrees apart. Following the geometry of the below figure, the distance between each satellite is determined to be 73030 km, as shown by the accompanying equation.
Combined Constellation
Combining the moon and the Earth systems yields the following figure. Note that while the satellite circles are not to scale in this figure, the moon, Earth, and geosynchronous orbits are all to scale.
The distance from the Moon Satellite to the worst case distance for one of the Earth Satellites (i.e., the white traces displayed above) was determined from the CAD program used to draw the constellation. This was found to be 450,000 km, which will be used in later link budget calculations.
