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What must be one's speed, relative to a frame S, in order...

  1. Feb 11, 2016 #1
    ... in order that one's clocks will lose:

    (a) 1 second per day as observed from S?
    (b) 1 minute per day as observed from S?

    I was referencing this:( http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html#c2 ) hyperphysics page but I still can't seem to understand what I need to do to solve for velocity.
  2. jcsd
  3. Feb 11, 2016 #2


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    Staff: Mentor

    In the one minute-per-day case, time dilation says that while 24*60 minutes elapse on the stationary clock, (24*60)-1 minutes elapse on the moving clock. The time dilation formula and some algebra will see you home from there.
  4. Feb 12, 2016 #3

    Mister T

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    There are 86400 seconds in a day so on a clock that loses 1 second per day 86401 seconds will pass. Thus ##\gamma## equals ##\frac{86401}{86400}##. You can then use that value in the time dilation formula you linked to and solve for ##v##.
  5. Feb 12, 2016 #4


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    Or, since both of your γ are close to 1, you can use the following approximate formula:

    v2 ≈ 2 c2(γ - 1)
  6. Feb 13, 2016 #5


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    That's a clock gaining 1s. A slow clock will tick 86399 times in a day as measured by a clock at rest in S, which gives ##\gamma =\frac {86400}{86399}##.
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