# Gravitational attraction force

June 23, 2015

 The relationship between the masses of the Earth, moon and sun and their distances to each other play critical roles in affecting tides. Click the image for a larger view.

Gravity is one major force that creates tides. In 1687, Sir Isaac Newton explained that ocean tides result from the gravitational attraction of the sun and moon on the oceans of the earth (Sumich, J.L., 1996).

Newton’s law of universal gravitation states that the gravitational attraction between two bodies is directly proportional to the product of their masses, and inversely proportional to the square of the distance between the bodies (Sumich, J.L., 1996; Thurman, H.V., 1994). Therefore, the greater the mass of the objects and the closer they are to each other, the greater the gravitational attraction between them (Ross, D.A. 1995).

Tidal generating forces are based on the gravitational attractive force. While gravitational attractive forces vary inversely to the square of the distance between the objects, tidal generating forces vary inversely as the cube of the distance of the tide generating object. Therefore with tidal generating forces, distance is a more highly weighted variable than it is in the gravitational attractive force. (Thurman, H.V. 1994). The effect of distance on tidal generating forces is seen in the relationship between the sun, the moon, and the Earth’s waters.

Although the gravitational attraction between the Earth and the Sun is more than 177 times that between the Earth and the Moon, the moon dominates the tides. Our sun is 27 million times more massive than our moon. If tidal forces were based solely on comparative masses alone, the sun should have a tide-generating force that is 27 million times greater than that of the moon. However, the sun is 390 times further from the Earth than is the moon. Thus, its tide-generating force is reduced by 3903, or about 59 million times compared to that of the moon. Because of these conditions, the sun’s tide-generating force is 27/59, or about half that of the moon (Thurman, H.V., 1994).

Source: oceanservice.noaa.gov