Originally posted by sonhouse
I am reading a sci fi story by Michail McCollum called 'the Sails of Tau Ceti' and I am checking his math. At one point in the story, he has the intrepid hero's going out in a spacecraft and getting to "12 times the distance from pluto to the sun in 6 weeks". However, a couple pages on, he says the spacecraft reaches 4 percent of C in the same time. I think o McCollum. Will they get that far in 510 days after accel for the figures mentioned?39.48
The average distance from Pluto to the Sun is 39.48 AU. An AU is 149,597,870,691 meters. Assuming he's talking about 12 times the average distance of Pluto from the Sun, the distance is 1795174448292 meters. To keep it simple, let's use 1.8 x 10^12 m.
Let's imagine the spacecraft moved the entire distance at 0.04c,or 1.2 x10^7 m/s. At this speed, it would take 150,000 seconds, or about 6 days.
So, at that speed it's easily possible. I guess we have to do the hard math then
We know initial speed (0 m/s) and we know final speed at the halfway point (1.2 x 10^7 m/s). We know this equation works:
x = xi + 1/2(v+vi)t
Since initial speed and displacement are zero,
x = 1/2vt
1.8 x 10^12m = 1/2*(1.2*10^7 m/s)(t)
Now if we solve for t and get anything more than 3 weeks we know it doesn't work. I'm getting bored now though so I'll stop here.
EDIT - Oops, didn't realize it was a 12 week trip with a coasting period at top speed. Oh well...