Water found on a potentially life-friendly alien planet
I got into the Wait Calculation[1] a few weeks back and made a Jupyter notebook out of it.At our current max speed (692,000 km/hr, stated max speed of Parker Space Probe), it would take about 173,000 years to get to that planet.We could instead choose to Wait and grow our tech. By picking a constant annual growth rate and then doing some calculus to find the minimum, we can calculate the shortest possible time it will take for us to arrive there.One common recommendation for annual energy growth rate is 1.4%, and then taking the square root to get velocity growth rate since velocity has a square root relationship with energy.By plugging that in, we can minimize our time by growing for 1020 years, and then traveling for 144 years, for a total time-from-now at 1164 years.Another paper[2] estimated an annual velocity growth rate of 4.72%, quite a bit faster. Plugging that in, it says we should wait 195 years for a travel time of about 21 years, or 216 years overall. This is of course incorrect since it assumes being able to travel FTL. So if you instead look at how long it would take to get to light speed travel at that rate, you're looking about about 159 years, or arriving at the planet at a time-from-now of about 270 years.Of course, if you're seeking to minimize time-from-now from the perspective of a traveler, maybe you'd take off sooner. Kind of a tradeoff - less time to wait for the traveler, more time to wait for the home planet. I haven't figured out that part of the math yet.[1] https://ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1m...
[2] https://arxiv.org/abs/1705.01481