The potential function of Earth's gravitational field is a measure of the work that would be required to move a unit mass from an infinite distance away to a specific point in the field. In other words, it is a measure of the potential energy of a mass at a particular point in space due to Earth's gravity.
The potential function of Earth's gravitational field is calculated using the equation V = -GM/r, where G is the gravitational constant, M is the mass of Earth, and r is the distance from the center of Earth to the object. This is known as the inverse square law, which means that the potential function decreases as the distance from Earth's center increases.
The gravitational field strength at a point in Earth's gravitational field is equal to the negative gradient of the potential function at that point. This means that the strength of the gravitational field is directly proportional to the rate of change of the potential function at that point.
The potential function and gravitational field on Earth's surface vary depending on the distance from the center of Earth, the distribution of mass within Earth, and the shape of Earth. This leads to slight variations in the strength of the gravitational field and potential function at different points on Earth's surface.
Earth's potential function and gravitational field affect objects on its surface by exerting a force on them, causing them to accelerate towards the center of Earth. This force is what we experience as weight. The strength of this force depends on the mass of the object and the strength of Earth's gravitational field at that point.