Sunday, September 15, 2013

Gravities * Days^2 = Light Minutes

Hey all, just wanted to say this quick before I forget again:

Suppose you are floating at rest relative to the local star, then accelerate at a constant rate towards a planet, and when you're halfway to that planet you flip end over end and decelerate at that same constant rate, eventually coming to rest above the planet.

If you measure your acceleration in gravities (~9.81 m/s/s) and your time in days (~86400s), then Gravities * Days^2 = the distance you travel in units of 61 light-seconds. That's close enough to light-minutes to make a super easy rule of thumb.

Of course, in a "real" situation you'd want to account for the planet's orbital position and orbital motion, gradually change your acceleration to help passengers transition from the old planetary gravity to the coming planetary gravity, account for relativistic dilation on month+ trips, track fuel use and how the rate of use changes as fuel is expended... probably other things.

But hey! Super easy rule of thumb.