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Thanks for this interesting article  but I do find the paragraph below confusing. My first problem is the sentence: "But according to Newton's gravity, the effect of the Sun's vanishing would be felt immediately, as the Earth would fly away in an tangential direction to its original path." Does this vanishing refer to sight? If so, this has nothing to do with gravity.
"According to Newton's theory, gravitational interaction is instantaneous. Suppose the Sun were to vanish from the horizon today. We would not notice its disappearance immediately just by looking at the Sun, because light takes some time to travel. But according to Newton's gravity, the effect of the Sun's vanishing would be felt immediately, as the Earth would fly away in an tangential direction to its original path." Einstein's special theory of relativity, however, states that nothing, not even information, can travel faster than the speed of light. "It's possible to use the vanishing Sun analogy to construct [theoretical] gravitational telegraphs which would transmit information instantaneously — and that, according to Einstein, is impossible. That's the reason why Einstein had to reformulate the theory of gravity." Einstein published his reformulation in 1916, under the name of general relativity.
Jan