![]() From an inertial viewer's perspective you are travelling toward the sun at nearly speed of light and it takes you ~8 minutes to crash into the sun. Repeat the experiment except I accelerate you to. But from your perspective it only took ~1 minute to crash into the sun. But from your perspective it only took ~14 minutes to crash into the sun. From an inertial viewer's perspective you are travelling toward the sun at half the speed of light and it takes you ~16 minutes to crash into the sun. ![]() Let's say I put you in a spaceship and accelerate you to 50% the speed of light toward the sun. But you can observe what happens as you approach it: It's impossible for an object with mass to go the speed of light. I'm sure there is a much simpler way to intuit it, though :) Now that we have two points in-line with the object, we find the point with the same total mass that exerts and equivalent force, and lo and behold it is at the center. We find that the density is linearly correlated to the area of the corresponding section, and we then take the closer half of the rod, multiply the density by 1/r^2, and find that it is constant!įor the far half of the rod, we cannot do this, so instead we divide it into two halves of equal pull, then divide those to halves and so on, and find that it this reduces to the equivalent of a point. You do this for all distances x, and you will find an equivalent rod going from the attracted objected to the center of the sphere, of a non-uniform but symmetrical density. The intuition we came up with when we had to solve this issue in undergrad physics was interesting.įor each point of any given distance, you can find a disk of points at the plane of the same distance whose gravitational pull will be equivalent to a single point at their center. ![]() On human scales, the time dimension is much "bigger" than the space dimensions (we're quite big in the time dimension and quite small in the spatial dimensions) the ball moves only a small distance through space but a very large distance through time, amounting to a big distance in spacetime, and so the slight curvature has a bigger effect than you might expect. Intuitive answer: the curve is indeed very gentle, and (e.g.) light will be deflected only very slightly by the curvature but the ball is moving for a couple of seconds, and that's an eternity. I'll answer this question as I understand it, but I only took four lectures of General Relativity before I gave it up in favour of computability and logic, so if there is a more intuitive and/or less wrong answer out there, please correct me. I heard an interesting question at one point: "how come, when you throw a ball up on Earth, the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola?"
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