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A spaceship is traveling toward earth from the spacecolony on Asteroid 1040 $\mathrm{A}$ . The ship is at the halfway point ofthe trip, passing Mars at a speed of 0.9$c$ relative to Mars'sframe of reference. At the same instant, a passenger on thespaceship receives a radio message from her boyfriend on1040 $\mathrm{A}$ and another from her hairdresser on earth. According tothe passenger on the ship, were these messages sent simultane-ously or at different times. If at different times, which one wassent first? Explain your reasoning.

According to passenger frame, the message (signal) coming from the earth was sent firstcompared to message coming from asteroid.

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

Cornell University

University of Michigan - Ann Arbor

Hope College

McMaster University

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Okay, So in this problem we have here, let's represent small. This is point A Ah, here we have the Marce. We have a spaceship traveling towards dear with a velocity. It's called V off 0.9. See, this is this real aas ity is relative to Mars. And here we have an asteroid that's represent if tears, let's call this point C and called this point B. Okay, we know that the distance between the asteroid and Mars in to Mars to the Earth is equal. And we have a message that was sent from the earth toward the spaceship in front. The asteroids to our city, towards the space. You okay, So problem wants to know if the if the message according to the passenger on the ship were sensing moot earnestly or not, And if did and if at the different times, which ones were sent first. And we just need to explain this. Okay, so let's think about this problem first. Let's put the reference frame in the space shift now, because this this system that I draw, we put the reference frame in Mars because Mars sees the spaceship moves with this velocity here But now let's redraw this in which the reference frame into this spaceship. So in this reference frame, we have Mars. We have they spaceship in the reference frame of the spaceship spaceship is not moving. So in this reference frame, the earth is moving towards the spaceship with a velocity that's put velocity of 0.9 C, and the asteroid moves away from the spaceship, also with velocity off 0.9. See, we know that the passenger received the radio mast singer symbol twx earnestly when her distance from the asteroid is equal. Let's put ISS here again when the distance to the asteroid is equal to her distance from the Earth. So this distance needs to be equal distance off the asteroid. Therefore the passenger did uses that this signal from the year let's represent the signal us this red wave in here. This signal from dear were sent other time when she was farther from the earth. So when the spaceship was in a police here or, for example, this signal was sent So since the signal needs to travel are greater distance, then this signal there were sent from the asteroid, the passenger deduce is that a signal from the Earth? Most have been sent before the signal from the extra right. So the only thing we need to understand is that putting the reference frame in this spaceship the understanding of this problem is a lot more easier. But a finger in rethink too, remember, is that if we put the rest frame on observer on Mars, the two signals the two signals travel the same. The instance. Therefore they were sent C motor earnestly from the asteroid and from the year. But since Steve Problem asks us about the reference frame off the passenger, the passenger sees the second system that we draw. So the defer the signal from the earth. Most have been sent first, then this signal from the asteroid, and that's the final answer.

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