If node send always a TX message (10us for example) for every movement and go to sleep the battery drain is the same ?
Sorry for all question but when the project is ready we must explain to the professor how it work.
It takes several ms (not us) to send a short packet.
And no, its not the same, depends on MANY things, especially the TX power level, how often you transmit, if you use retries etc. To get an approximate power figure, you have to average your sleep and wake/transmission cycles.
So one option is LISTEN_MODE, uncomment the #defines in the RFM69 library to enable it, then there are some examples for it, how to wake a node.
Or you could implement a system where the node wakes periodically and polls the gateway, to see if it needs to sleep. It's more simple but the tradeoff is latency and more power consumption.