Einstein and GPS 2

The orbital radius of a GPS satellite is about $R=26,600 km$ . According to Einstein's theory of general relativity, clocks on the satellite will appear to run faster than clocks on the Earth. That is because the space-time curvature generated by the Earth's mass makes a clock running slower if the clock is closer to the Earth and this effect is stronger on the Earth surface $(R_E=6370km$ from the center) than on the satellite, that is farther away from the center. The relative time difference, in a good approximation, is $\frac{\Delta t}{t}= \frac{\Delta U}{c^2}$ , where $c$ is the speed of light and $U=\frac{GM_E}{R}$ is the gravitational potential ( $G$ is the gravitational constant and $M_E$ is the mass of the Earth). If we synchronize a clock on the satellite with a clock on the Earth at noon today, how much will the time difference be at noon tomorrow? Give your answer in micro-seconds, rounded to the nearest integer.

Note: Close to a black hole, that has a really strong effect on space-time, the clocks run very slow and they appear to stop at the event horizon.

See my other problem about the timing error explained by special relativity (it is smaller, and in the opposite direction).