At the equator, the radius of the Earth is r = 6 378 137 m. In addition, the rotation of the Earth needs to be taken into account. This imparts on an observer an angular velocity of d θ θ / d t of 2 π divided by the sidereal period of the Earth's rotation, 86162.4 seconds. So d θ θ = 7.2923 × × 10 − − 5 d t . The proper time equation then produces d τ τ = ( 1 − − 1.3908 × × 10 − − 9 ) d t 2 − − 2.4069 × × 10 − − 12 d t 2 = ( 1 − − 6.9660 × × 10 − − 10 ) d t .