bakazings

I got this,...

Whenever 0Hz photons are talked about, it's usually in reference to black holes or objects theoretically moving at the speed of light, but there is (what I think) a much simpler and more realistic situation where this could happen, and I don't really understand what the outcome would be. Imagine the following situation: You have a 10Hz "radio" on a spaceship. The ship gradually accelerates away from the receiver, causing the frequency to steadily decline. What would happen when the ship accelerates fast enough to redshift the radio signal to exactly 0Hz? The ship should be nowhere near the speed of light. There is no overwhelming force of gravity. The photons should, in theory, be reaching the receiver. Some of you might say "if it redshifts to 0Hz, that means there isn't enough energy for it to reach the ship". But what if the ship comes to a stop (relative to the receiver) and the receiver is still able to pick up the 10Hz signal? Now, let's say the ship continues to speed up. I imagine what would happen is the frequency would start to blueshift, since the ship is still nowhere close to the speed of light and the photons ought to still reach the ship.