# The Trip to Saturn

If I am in a spaceship and it begins a constant acceleration of 9.81 m/s^2, would I be able to stand up in the spaceship and it would feel the same as gravity? (This is assuming the fact that my feet were placed in the direction of the thrust source.)

I've done some equations, and a ship with this hypothetical acceleration capacity (regardless of fuel source, and assuming it could compensate for its mass increase due to relativity)...

My calculations put it at reaching Saturn in 225 days...

Here is the data I am using:

Distance to Saturn = 1,321,416,800 km

After 24 hours of continued acceleration (+9.81 m/s every second) the velocity would be roughly 848,000 m/s

By day 100 it would be 84,800,000 m/s

And by the day you reached Saturn (day 225) it would be 190,800,000 m/s or roughly 426 million miles per hour -- and 63.64% of the speed of light.

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The velocity after time t, is gt, but the distance you've reached after a time t = (1/2)gt^2 and this should be equal to the distance to saturn.

this gets you t ^2 = 2(1.321 * 10^12)/9.81, so t = 5.19 * 10^5 s = 144 hours = 6.01 days.
If you want to decelerate as well, you'd accelerate for half the distance, wich you reach in 4.25 days, and then decelerate for the same time, reaching saturn after 8.5 days.

I adjusted my equations and found the error (was multiplying by 60 instead of 86,400 -- that certainly does change the results.) To "free fall" to Saturn with the assumption of Earth's gravity (and no friction) would take 6 days :) I find that kind of interesting. So at the end of the "fall" you'd only be going 1.70% light speed. That makes a ton more sense than what crazy results I had. Thank you.

IF you could accelerate at 9.81m/s2, you could cross the width of the universe well within your lifetime. It's interesting, but it's a BIG "if".

HallsofIvy