Calculating Time Dilation on an Airplane in Special Relativity

[awygle]

Homework Statement

An airplane travels 1250 km/h around the Earth in a circle of radius essentially equal to that of the Earth, returning to the same place.

Using special relativity, estimate the difference in time to make the trip as seen by Earth and airplane observers

Homework Equations

Time dilation:
$$\Delta t' = \Delta t \gamma$$

The Attempt at a Solution

I tried to do this by saying that the time for an observer on the Earth is just t=d/v, and time for the observer in the plane is t'=t*$$\gamma$$, then doing t-t', but I cannot get a decent answer. I suspect rounding errors may be involved since I end up with really big numbers minus really tiny numbers? But I wanted to check to make sure...

 

[Doc Al]

I suspect rounding errors may be involved since I end up with really big numbers minus really tiny numbers? But I wanted to check to make sure...

Those tiny numbers--the time difference--is what you want. Hint: To find 1 - γ, express γ as a binomial expansion in terms of (v/c)^2. Note that (v/c)^2 << 1.