Is there a formula for measuring the time dilation as the speed of light is approached? ?

Question

How much time would pass on Earth for a person traveling at 95% of the speed of light for one day his time versus 98%?

Answer 1

yes it is relatively simple, the faster you go the slower time will (as observed from someone standing still relative to you). This can be easily imagined with examples:

http://www.thestargarden.co.uk/special%2...

for a derivation of the equation see:

http://library.thinkquest.org/C008537/re...

Answer 2

The equation is DT = T0 / SQR(1-V2/C2)

'DT' is difference in time

'T0' is time interval on moving clock

'V^2' is the relative velocity of the traveler

'C^2' is the speed of light

Answer 3

mallard is right, although there is no "DT" because it doesnt give you the difference in time. it gives you the time of the object in motion from the point of view of someone not in motion.

the equation is t=t0/sqrt(1-v^2/c^2), which is essentially what mallard said.

at .95c, 3.20256308 days motionless would be one day in the ship moving. at .98c it would be 5.02518908 days. it seems very small, but remember that 2% of c is actually very large, and that it increases exponentially. for example, at .99999999999999 c it is 7,073,895.38 days. thats not far off from .98c, less than .2 away yet the increase is so large.

Answer 4

SQR [1-(V^2/C^2)]

for 95% this is .31

  for 98% this is .2

Answer 5

Of course! The relativity equation is actually quite simple, it is SQRT(1-(v^2)/(c^2)), which is to say you square the velocity, divide that by the square of the speed of light, subtract that from 1 and take the square root of the result. This gives both the time dilation experienced by a moving object and the extent to which external observers will perceive that object to be squished from front to back. In order to find the increase in mass for a moving object, you take divide one by the same factor. At 95% of the speed of light, the time dilation would be at 0.312 (3.203 days on Earth for every day on a relativistic spacecraft), and at 98% of the speed of light, the time dilation wouuld be at 0.199 (5.025 days on Earth for every day on a relativistic spacecraft).