or along the surface of the Earth). In this case, the Schwarzschild solution proper time equation becomes . Then using the polar radius of the Earth as the radial coordinate (or ), we find that

At the equator, the radius of the Earth is . In addition, the rotation of the Earth needs to be taken into account. This imparts on an observer an angular velocity of of 2? divided by the sidereal period of the Earth's rotation, 86162.4 seconds. So . The proper time equation