The mass of replicator, specific impulse of the fuel, and travel speed determine the energy required to launch a single probe.
The number of probes to be sent is determined by the number of destinations and the redundancy factor in number of probes sent to ensure that one probe arrives at each destination. Due to collisions with interstellar dust or other failures, we can imagine that not every self-replicating probe will arrive at its destinations.
The number of destinations is limited by one’s travel speed since increasing large regions of space are moving beyond our reach due to expansion of the universe. The faster one travels, the more distant stars one is able to reach before they get too far away.
The authors of Eternity in Six Hours (pg. 21) ``calculated that:
Travelling at 50% c, one could reach 1.16 x 10^8 galaxies
Travelling at 80%c, one could reach 7.62 x 10^8 galaxies
Travelling at 90%c, one could reach 4.13 x 10^9 galaxies
For reference, an average galaxy might have 10^8 stars.
The authors calculated travelling at 99%c, a redundancy factor of 40 is required, i.e. 40 probes for every destination. For 80%c and 50%x, the redundancy is less than 2. I did not prioritize looking into this calculation and am trusting the result that at lower speeds, the redundancy factor required is not very high.
Number of Probes to be Sent
The mass of replicator, specific impulse of the fuel, and travel speed determine the energy required to launch a single probe.
The number of probes to be sent is determined by the number of destinations and the redundancy factor in number of probes sent to ensure that one probe arrives at each destination. Due to collisions with interstellar dust or other failures, we can imagine that not every self-replicating probe will arrive at its destinations.
The number of destinations is limited by one’s travel speed since increasing large regions of space are moving beyond our reach due to expansion of the universe. The faster one travels, the more distant stars one is able to reach before they get too far away.
The authors of Eternity in Six Hours (pg. 21) ``calculated that:
Travelling at 50% c, one could reach 1.16 x 10^8 galaxies
Travelling at 80%c, one could reach 7.62 x 10^8 galaxies
Travelling at 90%c, one could reach 4.13 x 10^9 galaxies
For reference, an average galaxy might have 10^8 stars.
The authors calculated travelling at 99%c, a redundancy factor of 40 is required, i.e. 40 probes for every destination. For 80%c and 50%x, the redundancy is less than 2. I did not prioritize looking into this calculation and am trusting the result that at lower speeds, the redundancy factor required is not very high.