Limitations of Newton's Gravitation

Newton’s law of universal gravitation accurately predicts much of what we see within our solar system. Nevertheless, many phenomena have shown a discrepancy from what Newton’s laws predict, including the orbit of Mercury and the effect that gravity has on light.

The 'speed' of gravitation

Also, Newton inherently assumed that gravitation is an action-at-a-distance force. That is, without physical contact, any change in the position of one mass is instantly communicated to all other masses. This assumption does not come from any first principle, as Newton’s theory simply does not address the question. With Einstein's theory of special relativity the action-at-a-distance assumption was dismissed (the speed limit in the universe is the speed of light) and in 1915 he published his theory of general relativity.

General Relativity

General Relativity is a theory of space-time geometry and how mass (and acceleration) distort and interact with that space-time (see Figure 1).

Big red sphere with visibly large mass has a smaller grey sphere orbiting around it in a geometrical net. The net squared pattern is distorted by the weight of the red ball.

Figure 1: A smaller mass orbiting in the distorted space-time of a larger mass. In fact, all mass or energy distorts space-time.

It is not a theory of gravitational forces. For weak gravitational fields, the results of general relativity do not differ significantly from Newton’s law of gravitation. But for intense gravitational fields, the results diverge, and general relativity has been shown to predict the correct results. Even in our Sun’s relatively weak gravitational field at the distance of Mercury’s orbit, we can observe the effect. Starting in the mid-1800s, Mercury’s elliptical orbit has been carefully measured. However, although it is elliptical, its motion is complicated. But general relativity correctly predicts the measurements. Since then, many measurements, such as the deflection of light of distant objects by the Sun, have verified that general relativity correctly predicts the observations.