At one point, Enterprise uses the transporter to beam up a sample of kemocite from the planet surface while in a stationary position on the far side of the planet's moon to avoid detection. According to Memory Alpha, the range of 22nd Century transporters was around 10,000 km. Earth's Moon is roughly 384,400 km away and the closest natural satellite in the solar system is Phobos which orbits Mars a mere 5,000 km away (and Phobos is not a spherical satellite as shown in the show). This seems very unlikely a possibility. Check out the page at Memory Alpha on transporters where they state: "Range: During the 22nd century, standard Earth transporter systems had a range of ten thousand kilometers..."
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