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Light travels at the speed $c$ this speed is finite and with out using any relativity we can calculate the time it takes for something travelling at this speed to reach us: $\text{time} = \frac{\text{Distance}}{\text{speed}}$ or $ t= \frac{d}{c} = \text{8 minutes}$ in this case. For a person travelling very close to the speed of light with velocity $v$ from ...


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Do I need to use the angular velocity vector in the rotating or inertial reference frame for this? Yes. You can do it either way. I start with the expression that relates the time derivative of a vector quantity $\boldsymbol u$ in the inertial and rotating frames: $$\left(\frac {d\boldsymbol u}{dt}\right)_I = \left(\frac {d\boldsymbol u}{dt}\right)_R ...


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To add to David Hammen's answer on the question: When numerically integrating this, together with Euler's equation of rotation, is there a way to ensure that the determinant of $R$ remains equal to one (otherwise $\vec{x}(t)$ will also be scaled)? Method 1 Dumb But Effective Naïve Multiplication Whilst you are getting up to speed with more ...


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I was confused by this too -- pop descriptions of the equivalence principle don't mention the problem where the gravitational field points in different directions in different places. It is true that gravity is equivalent to acceleration, and that as a result, if you are freely falling, you feel like you're in an inertial frame. But this frame is only ...


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The whole problem is really about knowing what the words mean. An event is a time and a place together as single object. For instance the event where a light sends its first, last, or only pulse. Or the event where a beam or particle touches something and bounces. Anything you can describe with a time and place together is an event. And different people ...


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This is a good (and notoriously difficult) question. I'm going to follow the explanation given by Crispino, Higuchi, and Matsas in their review 0710.5373, but you should be aware there are different answers out there and also there is no (uncontroversial) experimental test of this effect. Having said all of that, the basic picture I have (and is given in ...


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When physicists use the word velocity it has a precise definition that is meaningful and unambiguous. If I measure the displacement from me to you then the result is a vector i.e. it tells me how far apart we are and in what direction you are. The velocity tells me how this vector is changing in time. The point is that I can do this for any pair of objects: ...


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Are tidal effects from the Sun and/or Moon taken into account in GPS systems? On calculating the orbits of the satellites, yes. The satellites orbit high enough that accurately modeling the orbits of the satellites mandates accounting for third body perturbations from the Moon, the Sun, and the planets. The orbits of the satellites are calculated from ...


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Inertial frame of reference is such that free bodies move with constant velocity. If you detect free body accelerating, the frame is not inertial.


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The thing is, in relativity you cannot have a reference frame "chasing" a photon. You'll get singularities if you try to view the world from a photon's perspective. A photon cannot move like you and you cannot move like a photon. As a photon, travelling along a light-like world line, experiences no proper time it's proper velocity is simply undefined. ...


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You are going in the right direction: Since on a different latitude the pendulum will be rotating with earth, it will change the rotation due to the coriolis force. As the pendulum being at a pole is an extreme case, so is the position at the equator: Here there's no reason for the rotation Foucault's pendulum is famous for. An intuitive guess would ...


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The relevant part of the book is the section titled Motion through Spacetime in chapter 2. I'll copy the paragraph, but it's a bit long so feel free to skip over it: Einstein proclaimed that all objects in the universe are always traveling through spacetime at one fixed speed—that of light. This is a strange idea; we are used to the notion that objects ...


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You can define energy in an accelerating frame, and you do it every day. The surface of the earth is an accelerating frame. Sometimes you say a frame is close enough to inertial and just treat like it is inertial even though it isn't inertial and hope for the best. Other times you just have to sit down and learn how to do physics in a noninertial frame. ...


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Yash, Imagine S is the Sun sending two photons, P1 and P2, and the object O is represented by two asteroids, O1 and O2, equidistant from each other all the time and from S at $t_0$ - they are moving in the same direction at the same velocity (c/2). So for some time one will be moving towards the Sun and one away from it. So you are right that the speed of ...


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I'm afraid this won't work. If for example you have a rocket motor capable of producing 1g of thrust then it will still produce 1g of thrust no matter how long you accelerate for (assuming you don't run out of fuel). From the perspective of the observer on Earth your acceleration will indeed slow down, but at the same time the Earth observer sees your time ...


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That won't work, and here is why. It's subtle. Say that you are on a ship, leaving the solar system with some technology that is able to thrust you in such a way that you experience a constant acceleration of 1g, as measured on the ship. You can measure this by placing a 1kg weight on a scale. From the point of view of the passengers of the ship (where the ...


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The problem with questions like this is that they include many misunderstandings of physics! For example, you say "as one approaches light speed more energy is required to accelerate faster". What you may not be aware of is that in classical mechanics, it's also true that to an observer on the ground, the faster you are going, the more energy you need to ...


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As you know, dealing with "simultaneous" events in relativity is tricky. If I think two things happen at the same time, you may not. However, it is guaranteed that if if I think two things happen at the same time and the same place, you will agree. That's because these two things are just the same spacetime point. In your frame, we have the simultaneous (in ...


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So, just to recap the Twin Paradox, it is a variation of the paradoxes of relative motion of reference frames Alice and Bob, created by the statement "Alice sees Bob's clocks moving slowly, but Bob also sees Alice's clocks moving slowly." The simplest such paradox, in my opinion, is "what if Alice calls Bob up and they talk on the phone? One of them surely ...



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