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Spaceflight Physics Help: Calculating Time From Accelation and Distance

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Mon, 2013-02-04 02:11
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rogue-z rogue-z's picture
Spaceflight Physics Help: Calculating Time From Accelation and Distance
Hi all you smart people! I'm trying to figure out the time it would take for a ship to travel some millions of kilometers between habitats. Actually, I only really want the 1.3 million k from the turn around point. I'm assuming a fusion rocket propulsion, so .05g per the big book. I know my distance, 1.3 million k, or 1,300,000,000 m right? With those two known, it should be easy to figure out time right? So, I turn to the intertubers and looked around because my math is kind of rusty. I came upon [url=http://www.physicsforums.com/showthread.php?t=83408]this equation[/url] which seems to make sense: t=√D/A so plugging in my numbers, it's t=√1300000000/.05 = 51,508s, or a little over 14 hours. Which seems way too fast. Am I doing the math wrong? And yes, I know to a large degree the actual flight times, physics and other troubling real world phenomena can be handwaved, but I kind of wanted to use this as a plot point. Thanks!!
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Mon, 2013-02-04 08:09
Smokeskin Smokeskin's picture
The general formula under
The general formula under constant acceleration is t = sqrt(2d/a). You accelerate halfway so if D is the total distance then time to go halfway is T½ = sqrt(2*D/2/a)= sqrt(D/a). It takes the same time going the rest of the way, so total travel is T = 2*sqrt(D/a), or over 28 hours.
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