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Physics is an observational science. It measures and observes the way nature behaves, and ever since Newton, models these measurements and observations with mathematics. Mathematics is a discipline where one starts with axioms uses logic and arrives to theorems and expressions that can be proven using the axioms and other theorems. One ends a proof in ...

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The first postulate is satisfied by Galilean relativity with an infinite speed of light, but this violates the second postulate. Therefore the second postulate does not follow from the first. Of course experiment tells us that the speed of light isn't infinite, and if we combine the first postulate with a finite speed of light we find they are inconsistent ...

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If you seriously think the second principle goes without saying, then Galileo should be credited with discovering special relativity. The second principle basically asserts that the laws of electromagnetism are physical laws valid in all frames, not just laws that hold in the frame of a medium. And since that was an actual view back then, it needed and ...

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There is a mutual attraction from gravity, and we generally only consider the smaller object here on earth because the earth is so massive, the acceleration of the earth is negligible. This is because $a = F/m$, and with equal $F$ between the two objects, the acceleration will scale as $a\propto 1/m$. For the earth, this leaves $a$ ridiculously small, but ...

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Does the bigger mass EVER move towards the smaller mass? Yes. $F = KMm/r^2$ $M*a_{M}=F$ $m*a_{m}=F$ As you see the smaller the mass the higher the acceleration and in consequence the higher the traveled distance in a given time t. If the above is true, can we technically move the Earth by us(human population) jumping indefinitely? No. Each ...

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yes, the earth will accelerate towards you , however the Earth's acceleration will be so small for all practical purposes that you usually do not consider it. Earth's acceleration is small because the mutual forces between you and the earth are the same, but the masses are different, so this results in different accelerations (remember: $F=ma$). Now if you ...

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In all cases, the two objects move towards one another. In fact they experience exactly the same gravitational force. However, because acceleration equals force over mass $$\mathbf{a} = \frac{\mathbf{F}}{m}$$ that equal forces causes the heavier object to accelerate much less than the lighter one. But technically, the Earth does move towards you very ...

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Your confusion might originate in what it means a simultaneous measurement. The fact that "Light from farther end leaves before it does from the closer end" is irrelevant. That would be true even if the object were at rest. One way to make a simultaneous measurement to determine the length is to have clocks along the path of the rod, at rest relative to ...

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The length of the rod will always appear smaller in your frame than in the proper frame, the mathematical relation between both lengths is given by: $$L=\gamma L_{o} \,\, ,$$ Where $$\gamma=\sqrt{1-\Big(\frac{v}{c}\Big)^{2}} \,\, .$$ I'm not sure if I've understood very well your question, but I think it can answer your question.

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Cubero et al. 2007: Thermal equilibrium and statistical thermometers in special relativity (http://arxiv.org/abs/0705.3328) came to the conclusion that 'temperature' can be statistically defined and measured in an observer frame independent way. With fully relativistic 1D molecular dynamics simulations they verified that the temperature definition ...

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Actually it is similar to the solution of a body going through the center of the earth through a drilled hole . Neutrinos could go through such an orbit with zero angular momentum as the probability of interacting and disappearing is very small. Planets cannot. If Goldstein is in a chapter for planetary orbits (hint Keplerian) it is obvious why the one ...

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I'm trying to answer my own question. Please feel free to comment and complement me! The earth goes around the sun and it is fixed with respect to it because: ... I have three reasons to give to the man and all things he can check in first person: Mercury and Venus, the other inner planets have phases if you look at them through a telescope. If they were ...

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Moved uniformly in a circle is not correct.Circular motion is always accelerated due to change of direction.Straight line is here important as Newton's first law talks about two cases-what happens to a body in rest/motion when force acts on it or when it does not.To keep a body moving in a circle a constant external force is needed to change it's direction ...

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That "unless" in Newton's law is key. Maybe a more useful way of understanding Newton's statement is as follows: If we see an object that has changed from being at rest to moving (or the other way around), or from moving in a given straight line to another, different straight line (think here of the tangents to a circle at two different points), ...

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Newton's first law is not about forces changing the way things move. That's the content of the second law. The first law states what happens when no force acts. It defines an object on which no net forces act as an object which travels in a straight line or is at rest.

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Also, there is parallax for the closer stars so that over the course of a year, the nearby stars will move back and forth with respect to more distant stars. The measurements are good to about 100 parsecs which equates to the limit of measurement of 0.01 arcsecond. The only way to explain the back and forth motion of the parallax is that the earth is moving ...

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Quite simply, the Sun moves relative to the stars. If you could see stars during the daytime then this would be somewhat easier to measure, but as it is you need some to look at night. Choose a time (say, 9pm) after dark, and go outside and look at the stars everyday for about one or two months. Observing at the same time will keep the Sun in the same ...

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Another proof: relative to stars, the day is 23h56, while relative to Sun, the day is 24h. https://en.wikipedia.org/wiki/Earth%27s_rotation So Earth rotation couldn't expain both stars and Sun rotation, there must be a differential rotation between these two.

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The historical "proof" was about the motion of planets along the year, but it needs some patience and observation. Earth-centric model yields pretty complicated cycloidal motion for planets, while Sun-centric yields simple ellipses (with moderate excentricity). Also the seasonal tilting of the axis is alot simpler in the second case, since the axis keeps a ...

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To expand slightly on John Rennie's comment, almost everyone who discusses ECEF also discusses ECI, the "Earth-centered inertial" frame, and talks about how ECEF is not "inertial," in contrast to ECI. I don't know anyone who considers it "inertial" in all cases. Especially if you're dealing with weather and atmospheric physics, you have the Sun heating up ...

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You are right that it should not be considered an inertial frame for many types of problems. This is how you end up with fictitious forces to account for (such as the Coriolis effect). However, this only has practical effect for larger scale problems. For the types of problems generally considered in physics class, the inertial frame approximation will ...

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Since the EM tensor is a tensor of rank two, the transformation requires two matrices: $$F^{\alpha\beta} \to F'^{\alpha\beta} = R^\alpha_\mu R^\beta_\nu F^{\mu\nu}$$ Or, in matrix form, $$F \to F' = RTR^T$$

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Sometimes people talk about "relativistic mass" which depends on your reference frame... this is perhaps what you're thinking of when you talk of your mass increasing as you approach the speed of light. However, more typically if a physicist says "mass" they mean the "invariant mass" or "rest mass" which is just your energy content (divided by the speed of ...

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The mass of your spaceship and your mass is not affected in your frame of reference. However from an outter stationnary observer measuring your mass in some kind of way would see it increase, they would see your spaceship contract along its direction of motion and they would even see, if they could look at a clock in your spaceship, that your clock tics ...

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This is really just a simplified version of Timaeus' answer, so please accept his answer not mine. Anyhow, you're quite correct that the ball gains energy, but that energy doens't appear from nowhere. in any (inertial) frame total energy is always conserved. What you are seeing is some of the kinetic energy of me and the room being transferred to the ball. ...

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Try arresting the balls motion while standing on a path of ice. What happens is the ball and that floor come to a relative rest. And any force exerted on the ball to slow it down or speed it up has an equal and opposite force exerted on the thing accelerating it. You can analyze it in any frame and get a correct description (though kinetic energy depends ...

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