The weight of an object is determined by the gravitational force exerted on it by the Earth. When an object is placed at the Equator, its weight is slightly less than at other locations on Earth due to the centrifugal force caused by the Earth`s rotation. However, the weight is not at its minimum at the Equator.

The weight of an object also decreases as it moves above the Earth`s surface. So, option 1, The Equator and Moon, is incorrect because the weight of an object on the Moon is significantly less than on the Equator.

Similarly, option 2, North Pole and Saturn, is incorrect because the weight of an object on Saturn is much greater than at the North Pole.

Option 3, South Pole, and 1 km beneath the Earth, is also incorrect because the weight is not minimum at the South Pole or inside the Earth.

The correct answer is option 4, the center of the Earth and in an orbiting satellite. At the center of the Earth, the weight of an object would be zero because the gravitational forces from all directions would cancel each other out. Similarly, in an orbiting satellite, the object would experience weightlessness because it is in freefall and not being pulled by gravity.