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A star that is 225 light-years away from Earth is at rest relative to Earth. You set out from
Earth on a journey to the star at a constant speed of 0.93?.
i) How long does it take you to travel from Earth to the star, according to an
observer on Earth?
ii) According to you, how long does it take for you to travel from Earth to the star?
iii) According to you, what is the distance from Earth to the star?
The proper distance between earth and star is
speed of traveller 0.93c.
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Solved in 4 steps
- Setup: A futuristic race from Earth to Alpha Centauri is taking place. But the winner of the race isn't who gets there first, it's who measures the smallest proper time along the way. The competitors start on Earth, from position (t, x) = (0, 0). They must travel from Earth (considered stationary) to Alpha Centauri, a distance of L = 4.37 light years away, such that they arrive at Alpha Centauri at Earth time of T = 10 years. Upon arrival, they compare their personal times (the proper time they measure along their whole trip) and the team with the smallest proper time wins. Question: a) Team A's spaceship immediately blasts off at (t, x) = (0, 0) and travels at a constant speed until they reach Alpha Centauri at Earth time of 10 years. Team B, on the other hand, have a much faster ship— they can travel so fast, you may consider their maximum speed to be the speed of light. Team B stays stationary on Earth for as long as they can; then, they blast off and travel at constant maximum…A new particle, the aarnion, has just been discovered! Careful measurements show that the aarnion has an average lifetime (at rest) of 14 ns. In one experiment, an aarnion traveled 24 m (as viewed from the lab frame) before it decayed. A.) Determine the proper velocity of the aarnion. Assume it had an average lifetime in its own frame. W = B.) Determine the velocity of the aarnion. Assume it had an average lifetime in its own frame. V = XCIdentify the postulates of special theory of relativity that apply in the following situations. 1. The ball appears to move north at a speed of around 2 m/s and then south at a speed of 2m/s. 2. A planet’s orbit is measured relative to the star it is orbiting around.
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