Gravitational time-dilation near the Earth

Question

I recently read the statement that near the Earth, in the Newtonian weak gravitational field, gravity is 99.9999% mainly due to  gravitational time dilation, and only about 0.0001% due to the curvature of space. Unfortunately there was no derivation of these values. I'd be interested how you calculate these percentages. What would be the gravitational redshift derived from these data?

Comments

The redshift can be obtained from the Schwarzschild metric. The latter is derived in many books on General Relativity. To obtain the redshift, compare the proper time of an observer at rest at given coordinates with the proper time of an observer at rest at a large distance from the source.

As for the percentages mentioned, such specific numbers probably result from specific given data. You may consider the equation of motion of a point mass in a gravitational field, then specialise to the case of a weak gravitational field (i.e., linearise in the deviations of the metric from the Minkowski metric) and further restrict to velocities much smaller than the speed of light. You can then compare the contributions of the various terms.