Another thread of the mystery of the tides unravels.
In the Equilibrium Theory of Tides chapter of The Tides and Kindred Phenomena in the Solar System George Howard Darwin says:
Thus far we have supposed the moon exists alone, but the sun also acts on the ocean according to similar laws, although with less intensity. We must now consider how the relative strengths of the actions of the two bodies are to be determined. It was indicated in Chapter V. that tide-generating force varies inversely as the cube of the distance from the earth of the tide-generating body. The force of gravity varies inversely as the square of the distance, so that, as we change the distance of the attracting body, tidal force varies with much greater rapidity than does the direct gravitational attraction. Thus if the moon stood at half her present distance from the earth, her tide generating force would be 8 times as great, whereas her direct attraction would only be multiplied 4 times. It is obvious that if the moon were twice as heavy as in reality, her tide-generating force would be doubled; and if she were half as heavy it would be halved. Hence we conclude that tide-generating force varies directly as the mass of the tide-generating body, and inversely as the cube of the distance.The application of this law enables us to compare the sun’s tidal force with that of the moon. The sun is 25,500,000 times as heavy as the moon, so that, on the score of mass, the solar tidal force would be 25½ million times greater than that of the moon. But the sun is 389 times as distant as the moon. And since the cube of 389 is about 59 millions, the solar tidal force should be 59 million times weaker than that of the moon, on the score of distance.
We have, then, a force which is 25½ million times stronger on account of the sun’s greater weight and 59 million times weaker on account of his greater distance; it follows that the sun’s tide-generating force is 25½ - 59ths, or a little less than half of that of the moon.
In the previous chapter he says that as the tide comes in the weight of all that water will depress the coastline in relation to its stiffness, soils being depressed to a greater extent than solid rock. This will make the tide appear to rise to a greater extent than it actually does when compared to the height of the geoid.
Neither Heavens-Above nor CalSky are showing any dial STS-129 and ISS visible passes, or even single visible passes, before Atlantis docks at ISS tomorrow.
