I'm studying up on the physics around black holes and got myself confused with the concepts of gravitational redship and Doppler effect.
Imagine a spacecraft orbiting a non-spinning black hole. It flashes blue light as signals every second (according to the pilot). As an observer far away at a safe distance observing, what (qualitatively) would you see of the lights? I'm thinking because of gravitational redshift, you'd see red lights instead of blue, and because of Doppler effect, you'd see the lights at longer periods than one second. Is this correct?
Will these observations change if the spacecraft's orbit shrinks? Provided it's still outside of the event horizon.