Time Dilation in a Jumbo Jet

TIME DILATION IN BOEING 777-200ER

Consider an airplane Boeing 777-200ER of mass 243045 kg [without passengers], length 63.73m moving at a velocity of 930kmph [258.333m/s] or 0.87M [Mach]. According to the theory of Special Relativity, the airplane will undergo changes in length, mass and time. The length contracts while time and mass increase. The change in length and mass is negligible, but the change in time is considerable over a period of time.

Let the time measured inside the airplane by the pilot be T = 10minutes [600second]

The clock inside the airplane will move slower than the outside observer’s clock. The time measured by an outside observer is given by,

T’ = T / [√1-v²/c²]

T - Proper time measured inside airplane

T' - Time measured by an outside observer

c – Speed of light 3 x 10^8 m/s

v – Velocity of airplane [258.333m/s]

Substituting all values in the above equation, we get the observer's time to be

T’ = 600.000000000223 s

The time difference is T' - T = 223picosecond

Thus for every 10minutes the clock inside the airplane runs 223picosecond slower than the observer’s clock. For 1hour the airplane gains 1.34nanosecond over the observer’s clock and for 15 hours the airplane gains 20nanosecond over the observer’s clock.