WHEN NEWTON AND EINSTEIN AGREE

Einstein's general theory of relativity and Newton's law of gravitation offer radically different interpretations of the phenomenon of gravity. Yet, in practical terms, the difference between their predictions seem to be very small. In Chapter 5 we saw two examples of observations in the solar system: the precession of the orbit of Mercury and the bending of light rays from a distant star by the Sun. In both cases the differences in the predictions of Newton and Einstein are very small and are measurable only with very patient and sophisticated astronomical observations. Is it just a coincidence that these two approaches give almost the same answer?

A mathematical analysis of Einstein's equations tells us that the agreement between the two approaches is not coincidental. It can be shown that, in all phenomena of weak gravitational effects and where the gravitating bodies are moving slowly compared to light, the two theories must almost agree. In our discussion of the escape speed in Chapter 3, we saw how to measure the relative strength of gravity. We use the criterion of the escape speed in the present context to understand the difference between ‘weak’ and ‘strong’ gravity. The rule is simple: compare the escape speed V with the speed of light c. If the ratio V/c is very small compared to 1, the gravitational effects are weak. If the ratio is comparable to 1, say between 0.1 and 1, the gravitational effects are strong (see Figure 6–1). Referring back to Table 3–2, we see that the gravitational effects are weak in all cases except on the surface of neutron stars.