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Explorer Power Gain Problem
>From Brian
Kelly, I was looking over your explorer paper and the power section, trying
to understand how you got a power gain of 1E9 W per second. Your equation
went something like:
P = F dx/dt = m*a*dx/dt
The mass of the ship was 100E6 kg. The acceleration was 10m/s^2. The
duration of acceleration was 1E7 seconds. You plugged in the numbers like
this:
100E6kg * 10m/s^2 * 5m/s = 5E9W
Where did that 5m/s come from. I thought dx/dt was a distance traveled in
one second. My physics textbook tells me power is F * v where v is
velocity. Since our average speed is 5E7 m/s (average between our terminal
speed of 1E8 m/s and 0 m/s) the equation should look like this:
100E6kg * 10m/s^2 * 5E7m/s = 5E16W.
If I'm right, that is a hefty difference in power gain which we couldn't
hope to meet without loading tremendous amounts of fusion fuel. Please tell
me that I'm the one who is wrong. Also, when I ran the numbers for K.E.
using the relativity equation and the basic physics equation (these are on
your explorer paper and I don't have time to write them here) I came up with
a 100+ fold difference in power. Can you confirm this? Do you even have
time to read this letter? :)