difference between the gravitational force exerted by the Moon on the particle, and the gravitational force that would be exerted on the particle if it were located at the Earth's center of mass. Whereas the gravitational force subjected by a celestial body on Earth varies inversely as the square of its distance to the Earth, the maximal tidal force varies inversely as, approximately, the cube of this distance. If the tidal force caused by each body were instead equal to its full gravitational force (which is not the case due to the free fall of the whole Earth, not only the oceans, towards these bodies) a different pattern of tidal forces would be observed, e.g. with a much stronger influence from the Sun than from the Moon: The solar gravitational force on the Earth is on average 179 times stronger than the lunar, but because the Sun is on average 389 times farther from the Earth, its field gradient is weaker. The tidal force is proportional to where is the mass of the heavenly body, is its distance, ρ is its average density, and is its radius. The ratio is related to the angle subtended by the object in the sky. Since the sun and the moon have practically the same diameter in the sky, the tidal force of the sun is less than that of the moon because its average density is much less, and it is only 46% as large as the lunar, thus during a spring tide, the Moon contributes 69% while the Sun contributes 31%. More precisely, the lunar tidal acceleration (along the Moon–Earth axis, at the Earth's surface) is about 1.1 × 10−7 g, while the solar tidal acceleration (along the Sun–Earth axis, at the Earth's surface) is about 0.52 × 10−7 g, where g is the gravitational acceleration at the Earth's surface. The effects of the other planets vary as their distances from Earth vary. When Venus is closest to Earth, its effect is 0.000113 times the solar effect. At other times, Jupiter or Mars may have the most effect. The ocean's surface is approximated by a surface referred to as the geoid, which takes into consideration the gravitational force exerted by the earth as well as centrifugal force due to rotation. Now consider the effect of massive external bodies such as the Moon and Sun. These bodies have strong gravitational fields that diminish