3 ms·

To the probes, wouldn't the 20-year flight 'feel' like 16?

• mikeash 11y ago
  Not that much. Time dilation due to speed is sqrt(1 - v^2/c^2). At 0.2c, that's 98%, so 20 years would "feel like" 19.6 years.
  • gus_massa 11y ago
    (I Agree.) As a rule of thumb, you can approximate sqrt(1 - v^2/c^2) = 1 - 1/2 (v/c)^2. So if v/c = 2, then the correction is approximately 1 - 1/2 .2^2 = 98% as you said. This formula is easier for back of the envelope calculations and the important point is that it's quadratic. (I always forget the 1/2 :(. ) The GP comment used the wrong correction of 1 - v/c, that is not quadratic so the correction is much bigger.
    • mikeash 11y ago
      Cool trick. It starts to fall apart at higher speeds (at c, the approximation produces 1/2, when it should be 0), but it looks like up to 0.5 or 0.5 it's decent.
      • gus_massa 11y ago
        Yes, this is the first two terms of the Taylor series near 0, so it works only at "low" speed. For speeds that are close to c, you have to use another "Taylor" series to get a good approximation. If v is close to c, then the approximation of the correction is sqrt(2(c-v)/c). So at 99%c you get 4.5%.