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I have that video and have used it several times. I think that it is
compelling. The way he sets it up (and I'm working from memory here,
so I can't remember the exact details), it isn't necessary to do the
Doppler calculation and find speeds. Once he and specifies that the
time between flashes in the spacecraft is twice what the sender is
using on the outbound trip, it immediately follows that the time
between flashes on the inbound trip is half the sender's frequency.