Question

the sun has a mass of 1.99 x 10^30kg and a radius of 6.96 x 10^8m. if an observer near tge solar "surface" observes a flare event that lasts 30 mins, how long does the flare last as witnessed by observer on earth?

Answer 1

SOLUTION Assuming the Earth-bound observer at a distance of 1.50 X 1011 m from the Sun is "far" away, we may use the gravitational time dilation equa- tion to answer the question. We first calculate the Schwarzschild radius of the Sun: 2GM 2(6.67 X 10-11 N-m/kg) (1.99 x 1030 kg) (3 X 108 m/s)? d= 2,950 m = 2.95 km Substituting into the gravitational time dilation formula with Al, = 30 minutes: 30 min - [1 – (d./a)]1/2 [1 - (2,950 m)/(6.96 x 108 m)]1/2 30 min 30 min [1 – (4.24 x 10-6 m)]1/2 [0.99999576]1/2 AL = (1800 s)/(0.99999788) = 1800.0038 s The observer on Earth sees the flare to have lasted 38 ten-thousands of a sec- ond longer than the observer at the Sun. Although the effect of gravitational time dilation is seemingly small, such time differences are easily measured and must be compensated for as is done for atomic clocks on GPS satellites orbiting Earth. A = Ald

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