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This is an experimental fact. A measurement. Physics is about making mathematical models, called theories, that describe the measurements and predict new phenomena with success. The physics model describing (and predicting ) measurements/gravity is called Newton's gravitational model. It is very successful. Keep in mind if you go on to study physics that ...

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Alpha decay, which is why it generally comes from natural gas fields where the alphas are trapped with the methane (in the US there are several in Kansas, Oklahoma, and Texas with reasonable fractions). There is a long history of helium in the US, where the Bureau of Land Management has been responsible for the helium reserve since the days of giant ...

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Potential energy has absolutely nothing to do with stress-energy or pressure. The following reference is a good source about the origin of the pressure term in the stress-energy tensor: "Momentum due to pressure: A simple model" by Kannan Jagannathan in American Journal of Physics 77, 432 (2009);  http://dx.doi.org/10.1119/1.3081105 Potential energy ...

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I'll try to rephrase the question. If a planet only experiences one external force directed toward the Sun, why does it orbit instead of crashing into the Sun? This question falls under the category of "uniform circular motion," so if you want more detail, you can look up that chapter in a physics text. The main idea is the following: The force of gravity ...

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The gravitational field of a spherical body of mass $M$ at a distance $r$ from its center is $$\frac{GM}{r^2}$$. This is a Newtonian Mechanics answer, but it is an extremely good approximation when dealing with objects of small mass like the Earth, the Moon. etc. For higher mass and energy scales we use the Theory of General Relativity, which describes the ...

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However it makes sense that gravity can't travel faster than light because of the force-carrying photons Whilst it makes sense that gravity can't travel faster than light, we don't actually know this for sure. What we do however know is that the force of gravity is not conveyed by photons. Even electromagnetic force is not conveyed by photons - hydrogen ...

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You didn't do anything wrong, just incomplete. As @Sebastian alluded to, the work will be $$W=E_{3R}-E_{2R}=T_{3R}+V_{3R}-T_{2R}-V_{2R}$$ where the subscript denotes orbital position. You already found the $V_{3R}-V_{2R}$ term, now just use the centripetal motion formula $$\frac{mv^2}{r}=\frac{\gamma Mm}{r^2}$$ to find the difference in kinetic energy ...

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Planets do not move in fixed orbits, they move in very finely balanced stable orbits. What you see in the sky today is the result of 4 billion years of thumping, bumping, gravitational games and a lot of stuff falling into the Sun. It's all a very delicate balance of velocity, vector and gravity and it's not all that difficult to upset. While Jupiter won't ...

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For clarity let's work with a Lorentzian signature. Our $g$ is a metric for a 2 dimensional Lorentzian manifold $M$. It is well-known that any two dimensional pseudo-Riemannian manifold is conformally flat, that is $$g = e^{2\omega}\eta$$ Where $\eta$ is the flat 2D Minkovski metric. Your Lightcone gauge example You didn't define your $x^\pm$s but I ...

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As you point out, there is no way to make artificial gravity work everywhere in a spherical shell by use of the centrifugal force. The obvious fix is to use a cylinder instead, and use the "endcaps" (top and bottom of the cylinder) purely for energy generation. Or, drop the endcaps entirely and make do with an open cylinder. If it's also very short it will ...

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