Can someone please explain me what did Newton mean by " we can send signals at infinite speed, and I donot find any relation between the instantaneous nature of G.Forces and "sending signals at infinite speed".... So what did Newton exactly mean?

In principle, you could set up a system where someone shaked a massive body in a certain way. Someone else far away could measure the changes in his local gravitational field caused by that shaking mass. If the field travelled instaneously from source to observer, then the pattern of shaking could be used to send signals instantaneously (think of a radio).

What he means by 'sending signals at infinite speed' is that, according to his theory, we could measure the change in gravitational force from something a great distance away instantaneously. Einstein`s theory says he can't.

Imagine a large body (say the sun) was somehow removed (say it mysteriously disappers) from our solar system. According to Newton's gravity theory, as soon as the sun is removed, we (on earth) would notice a change in our orbit. as we no longer have a sun to orbit around. But according to Einsteins theory, the gravitational change would not be felt on earth straight away, but only after the gravitational 'information' could travel to earth.

Of course this does not mean that we only orbit the sun because it tells us to, we orbit it because of its gravity. So essentially this 'information' is the gravitational effect. This gravitational effect is a warping of spacetime and it travels at the speed of light.

Although it is common to make this statement, it isn't exactly true. The reason is that Einstein's equations (the gravity equations) specifically forbid the sun from suddenly disappearing. You would get gibberish if you tried to work out the math. Having something push the sun out of the way very quickly doesn't quite work out either.

Although physically ridiculous in Newton's theory, this kind of thing is at least mathematically allowed there (restricting oneself only the gravitational equations). GR is much more restrictive.

Anyway, that's why I used the example of shaking something. If somebody suddenly kicked the sun somehow, we wouldn't feel the effects for ~8.5 minutes.

And yes, gravity travels at the speed of light. If the gravitational field is strong (stronger than anything in our solar system), then there are actually components of the field which travel at less than the speed of light as well. If the field is really strong, then whole concept of gravitational speed can't even be defined in a useful way.

Note that the [itex]r[/itex] in Newton's Law of Gravitation
[tex]\vec F=-\displaystyle \frac{GMm}{r^2}{\hat r}[/tex]
is the [instantaneous] distance between their centers. Thus, according to Newton, the effect of a sudden change in position of one mass would be instantanously transmitted to every other mass in the universe.

So ..it means Newton probably thought that we could use something big and bulky and then wave it...and then the disturbance will travel at infinite speed to some other place on earth....and this will be an easy way of communication....which is not the case.

Maybe I`m wrong, but I don't think Newton was conceiving some sort of intergalactic communication device. He just thought that gravitational effects were instantaneous.

I think that the 'information' that you referred to is just the gravitational pull of one body on another.

I think that in Newton's time the idea of 'action at a distance' worried people a lot. What Newton did was to work out the mathematics, without worrying about the mechanism. In the case of electromagnetism the field theory developed in the 19th century meant that this was less of a problem - the field at a point in space only depended on the field at nearby points. This suggests the question 'Why can't you do the same thing with gravity', and in particular why didn't Einstein just treat gravitation as a field in special relativity (in the same way as the electromagnetic field), rather than spend years struggling to devise general relativity. The answer is that it doesn't work. Gravity doesn't behave like light, in that it doesn't show abberation, suggesting instantaneous action. In GR any effects are limited to the speed of light, but some people have in fact suggested that the speed of gravitational effects really is much faster than that of light. This is why there continue to be arguments about the 'speed of gravity'