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<blockquote data-quote="Staffan" data-source="post: 6736022" data-attributes="member: 907">The result is a ratio: for every unit of time that passes in the accelerated frame of reference (&quot;on the ship&quot;), X units pass in the frame at rest (&quot;on Earth&quot;). So for every day on the ship, 8.6 days pass at home.Except you made a rather big mistake by putting the speed of light at 300,000 - the right value is 300,000,000 m/s (rounded a bit). You also forgot the 1-(v^2/c^2) on your first line. The two combined lead to a dilation factor that's pretty much too low to be noticed in your example (1.0000000432, or about one day extra in 70,000 years).It's probably easier to use c itself as the unit of speed (that is, instead of expressing a speed as 100,000,000 m/s, it's 0.33c), because that gets rid of the huge &quot;divide by 90 quadrillions&quot; step (c^2 = 90 quadrillion m^2/s^2). That way, the time dilation equation simplifies to:1 / (1-v^2)^-2That is: take the speed you're traveling at as a fraction of the speed of light. Square it, and subtract it from 1. Divide 1 by the root of the result.So let's take the example earlier of 1/3 the speed of light and plug it in:1 / (1-(1/3)^2)^-2 =1 / (1-1/9)^-2 =1 / (8/9)^-2 = 1 / 0.943 = 1.06In other words, when traveling at 1/3 the speed of light, you experience a time dilation of about 6%. Travel for 100 subjective years, and 106 years will have passed at home.</blockquote>

[QUOTE="Staffan, post: 6736022, member: 907"] The result is a ratio: for every unit of time that passes in the accelerated frame of reference ("on the ship"), X units pass in the frame at rest ("on Earth"). So for every day on the ship, 8.6 days pass at home. Except you made a rather big mistake by putting the speed of light at 300,000 - the right value is [I]300,000,000[/I] m/s (rounded a bit). You also forgot the [B]1-[/B](v^2/c^2) on your first line. The two combined lead to a dilation factor that's pretty much too low to be noticed in your example (1.0000000432, or about one day extra in 70,000 years). It's probably easier to use [I]c[/I] itself as the unit of speed (that is, instead of expressing a speed as 100,000,000 m/s, it's 0.33[I]c[/I]), because that gets rid of the huge "divide by 90 quadrillions" step ([I]c[/I]^2 = 90 quadrillion m^2/s^2). That way, the time dilation equation simplifies to: 1 / (1-v^2)^-2 That is: take the speed you're traveling at as a fraction of the speed of light. Square it, and subtract it from 1. Divide 1 by the root of the result. So let's take the example earlier of 1/3 the speed of light and plug it in: 1 / (1-(1/3)^2)^-2 = 1 / (1-1/9)^-2 = 1 / (8/9)^-2 = 1 / 0.943 = 1.06 In other words, when traveling at 1/3 the speed of light, you experience a time dilation of about 6%. Travel for 100 subjective years, and 106 years will have passed at home. [/QUOTE]

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