1. Here is the summary of attraction forces (F = GMm/r2) during Total Eclipse when the Moon M is between Sun S and Earth E.
Sun (F1 = GMm/r2) Moon (F2= GMm/r2) Earth

(F1 = GMm/r2) = S - M = 4.1984 x 1020
(F2 = GMm/r2) = M - E = 2.2 x 10^20

Net force on the Moon= F3 = F1-F2= 4.1984 x 1020 Minus 2.2 x 1020 = 1.998 x 1020 towards Sun

At this point why Earth force the moon to revolve around its centre when the net force on the moon is much greater towards the sun ? Explain please. Pls also check the calculation. If we consider the Sun - Earth Force
(F4= GMm/r2) = S - E= 3.67 x 1022 , then

Net Force on the Moon = F3+F4=1.998 x 1020 Plus 3.67 x 1022 = 3.68 x 1022 towards Sun.
Please also note that force of attraction F = GMm/r2 between sun and moon in any case (perigee, apogee, average) is much greater than between moon and earth F = GMm/r2 (perigee, apogee, average). So technically it should revolve around the sun in a separate orbit not earth. So why moon revolves around earth???

Here is the other Forum answer but I disagree because law of gravitation can not applied to the common center of gravity of two masses.
Both earth and moon are constantly revolving around the sun. They are also revolving around their common center of gravity as they move around the sun, but they constantly move around the sun.

Their speed of revolution and the vast amount of angular momentum keeps them from simply dropping like proverbial rocks into the sun.

Think of astronauts aboard the Space Station. They are weightless, yet they are just a hundred miles or so farther from the center of the earth than you and me. Why? Why don't they fall?

The answer is that they ARE falling. But as fast as they fall, their momentum has carried them forward so that they endlessly fall around the earth, not into it. The same with the earth and moon, relative to the sun, during a total eclipse and at all other times.

So what do you suggest??  2.

3. Originally Posted by jemswillam

Here is the other Forum answer but I disagree because law of gravitation can not applied to the common center of gravity of two masses.
But that is exactly what you did when you calculated the force of gravity on the Moon caused by the Sun. The Moon is made up of innumerable separate particles, You took the sum of the mass of all those particles and the position of their common center of gravity and applied the law of gravity to it.

It is perfectly legal to do the same thing with two bodies such as the Earth and Moon, as long as you are dealing with distances that are large compared to their separation (which is true when comparing the Earth-Sun distance to the Earth-Moon distance).  