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How to Calculate Time Warping Due to Acceleration

Time dilation, sometimes called time warping, occurs as an object travels closer to the speed of light than its observer. From the observer's point of view, the time affecting the traveling object will dilate, meaning it will expand or become slower. Thus the object traveling faster will age slower. Time dilation is often thought to be a function of an object's acceleration, but it is in fact a function of its velocity. Acceleration, which is defined as a change in velocity, can be taken into account to calculate a change in time dilation.

Things You'll Need

Calculator

Instructions

- 1
  Write this equation for the time dilation factor from the perspective of the observer of the traveling object:
  
  Time dilation factor = Time / Square root of (1 - velocity^2 / speed of light^2)
  
  ^ = symbol that means "to the power of"
- 2
  Consider the example wherein you want to examine the effect of acceleration on time dilation. For instance, imagine that an object accelerates from 0.8 times the speed of light to 0.9 times the speed of light. Note: the speed of light is approximately 300,000 kilometers per second (km/s).
- 3
  Calculate the time dilation factor for the object when it is traveling at 0.8 times the speed of light, which is 240,000 km/s. We'll use 1 second (s) as a time point of reference, so in our equation, Time = 1 s.
  
  Time dilation factor = 1 s / Square root of (1 - 240,000^2 / 300,000^2) = 1.7 s
  
  Our result of 1.7 seconds means that 1 s experienced by the traveler would be experienced as 1.7 s by the observer.
- 4
  Calculate the time dilation factor for the object when it is traveling at 0.9 times the speed of light, which is 270,000 km/s. Again, we'll use 1 second (s) as a time point of reference, so in our equation, Time = 1 s.
  
  Time dilation factor = 1 s / Square root of (1 - 270,000^2 / 300,000^2) = 2.3 s
  
  Our result of 2.3 seconds means that 1 s experienced by the traveler would be experienced as 2.3 s by the observer.
- 5
  Calculate the effect of the acceleration. Accelerating from 0.8 to 0.9 times the speed of light relative to your observer would increase your time dilation factor by 0.6 seconds per second. The faster the acceleration occurred, the faster the change in time dilation would occur.

Astronomy