Time dilation is a difference in the elapsed time measured by two clocks either due to them having a velocity relative to each other or by there being a gravitational potential difference between their locations.
Satellite time dilation formula.
T t 0 1 v 2 c 2 1 2.
The equation for calculating time dilation is as follows.
Let s keep it simple and assume circular orbits of gps satellites with average height r gps 20180 km.
Time dilation in the theory of special relativity the slowing down of a clock as determined by an observer who is in relative motion with respect to that clock.
Solved example on time dilation formula example 1.
T 0 time in observers own frame of reference rest time v the speed of the moving object.
We ll need some other constants too.
In special relativity an observer in inertial i e nonaccelerating motion has a well defined means of determining which events occur simultaneously with a given event.
C 299792458 m s mass of the earth.
After compensating for varying signal delays due to the changing distance between an observer and a moving clock i e.
Moreover her twin sister alpana stays on the earth.
Doppler effect the observer will measure the moving clock as.
T time observed in the other reference frame.
The effect of time dilation can be seen in nature paired atomic clocks if two atomic clocks start with identical time one remaining stationary and the other placed aboard an intercontinental aircraft the clock on the aircraft will show a slower passage of time compared to the stationary clock when it returns.
Gravitational time dilation is a form of time dilation an actual difference of elapsed time between two events as measured by observers situated at varying distances from a gravitating mass the lower the gravitational potential the closer the clock is to the source of gravitation the slower time passes speeding up as the gravitational potential increases the clock getting away from the.
The special relativity induced time dilation due to the relative velocity of the satellite and the decrease in gravitationally induced time dilation described by general relativity due to the increased height above earth.
M 5 97219 10 24 kg gravitational constant.
Begingroup there are actually two effects at play here.
C the speed of light in a vacuum.
Speed of light.
The net effect is that the satellite clock is actually faster by 38 microseconds per day.
Fortunately einstein gave us an equation for measuring the relative effects of time dilation and it turns out that the implications are mind shattering.
What would the observable effects be like then.
δ t time dilation difference between planet and orbiting satellite at specified time duration sec δ time dilation factor u newtonian gravitational potential in dimensionless form i e divided by the square of the speed of light c speed of light 299792458 m s m mass of the earth 5 97219 x 10 24 kg or some other planet given in kg.
Gps satellites without taking into account the high velocity motion of the.
Suppose that kalpana boards a spaceship and flies past the earth at 0 800 times the speed of light.
In addition the instant kalpana s ship passes the earth both the sisters start timers.
The formula here is relatively simple.
