gravitational constant is different at different locations on the eart

Question

Problem 8. In 1672, Jean Richer was examining the period of a pendulum at different locationson the Earth's surface. One way of stating the results of his experiments is the following: He took a pendulum that was used as a clock in Paris to Cayenne, French Guiana. He foundthat the clock “lost" 2.5 minutes per day compared with using it in Paris. This illustrated that the1 gravitational "constant" is different at different locations on the Earth's surface and helped prove that the Earth is not a perfect sphere. Since Cayenne is closer to the equator, it is further from the center of the Earth and the gravitational constant is smaller there. This means that the period of the pendulum will be longer in Cayenne than in Paris which is consistent with the clock "losing"2.5 minutes per day in Cayenne. If g paris = 9.813 m/s², determine the gravitational "constant" in Cayenne.