-1.5 gm/r
at the center of earth
There is nothing special about the center of the Earth itself; the attraction is in that direction, due to the accumulated effect of the attraction from different parts of the Earth. At the center of the Earth itself, the gravitational attraction towards the left, for example, by some pieces of planet Earth, would be exactly compensated by gravitational attraction towards the right, by other pieces of the planet.
The force of mutual gravitational attraction between the earth and any other object pulls the object toward the center of the earth, and pulls the earth toward the center of the object. Both pulls have equal strength.
it has the potential to become a law.
First of all, a clarification on the wording of the question: Gravitational potential energy is the energy associated with the gravitational interaction between objects with mass. Obviously if you just have a single isolated mass, it would not be under the influence of any gravitational fields and therefore there would be no gravitational potential energy. Gravitational potential energy is property that describes a whole system of masses (it could be two masses or three or four or...). When we talk about the gravitational potential energy of an object on Earth, it is implicit that we mean the gravitational potential energy associated with the system of two masses (one being the object in question, and the other being Earth).For simplicity, let's assume that we have two masses labelled m1 and m2. The gravitational potential energy (which I'll label U) is given by the relation:U = (Gm1m2)/r2where r is the distance between the centre of each mass, and G is the universal gravitational constant. You can derive this equation very simply from Newton's Universal Law of Gravitation (which you may be familiar with) and the definition of potential energy. So, what does the potential energy of this system of masses depend upon? Everything that is a variable in the equation! Namely, the mass of each object and their separation. In our everyday example of an object that is some height habove the surface of the Earth, the mass of the Earth doesn't change, and neither does its radius (distance between centre and surface). Therefore, in that particular instance, the potential energy depends only upon two things 1. the height of the object above the surface, and 2. the mass of the object.
the distance between the object and the center of the Earth
Ideally, if the earth were a perfect sphere, the gravitational potential energy would be zero. In the center of a sphere all other points within the sphere have an equal and opposite counterpoint. They work to cancel each other out. However, the earth is not a perfect sphere so there would likely be a gravitational pull towards the area with the greatest mass.
potential energy arises from the earth through gravitational pull.
On Earth, Gravitational Potential Energy (GPE) would increase with an increasing altitude.
Gravitational potential energy - it depends on the distance from the centre of gravity, so on Earth it depends on the height above the Earth's surface
In the cavity at the center of the Earth, your weight would be zero, because you would be pulled equally by gravity in all directions. - The gravitational field of Earth at its center is zero.
The center of the Earth.
at the center of earth
Assuming the Earth to be a uniform sphere, there is no gravitational force experienced at its center due to its mass as it cancels out. Under this assumption the gravitational force experienced at the center of the earth would be due to everything beyond the Earth (like the moon, sun, planets, et c.)
Gravitational potential energy.
If you ignore the small contributions due to every other piece of mass in the universe, it's zero.
That is called gravitational potential energy.