For the Earth, M = 5.9742 × 10 kg, meaning that m = 4.4354 × 10 m. When standing on the north pole, we can assume d r = d θ θ = d ϕ ϕ = 0 (meaning that we are neither moving up or down or along the surface of the Earth). In this case, the Schwarzschild solution proper time equation becomes d τ τ = d t 1 − − 2 m / r . Then using the polar radius of the Earth as the radial coordinate (or r = 6,356,752 metres ), we find that d τ τ = ( 1 − − 1.3908 × × 10 − − 9 ) d t 2 = ( 1 − − 6.9540 × × 10 − − 10 ) d t .