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$\bullet$ An imperial spaceship, moving at high speed relative tothe planet Arrakis, fires a rocket toward the planet with a speedof 0.920$c$ relative to the spaceship. An observer on Arrakismeasures the rocket to be approaching with a speed of 0.360$c .$What is the speed of the spaceship relative to Arrakis? Is thespaceship moving toward or away from Arrakis?

$$0.8373 c$$

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

Cornell University

Rutgers, The State University of New Jersey

University of Sheffield

McMaster University

Lectures

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

03:18

Sir Isaac Newton described the law of universal gravitation in his work "Philosophiæ Naturalis Principia Mathematica" (1687). The law states that every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

04:36

An imperial spaceship, mov…

03:38

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A spaceship is moving away…

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A spaceship moving toward …

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A spaceship travels at 0.7…

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Two rocket ships approach …

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A pursuit spacecraft from …

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A spaceship travels at $0.…

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02:35

02:37

A spacecraft approaching t…

Okay, so in this problem, we have three objects. We have a spaceship. Let's represent the spaceship. Us this box. We have the Rocket JJ, the rocket that the spaceship launches and the direction of a planet. Okay, so first of all, the spaceship is moving. We do not know yet in what direction. So we do not going to put any era right now, but we know he has a spaceship has a velocity. So that's the note. He's as the reference frame s prime. And the planet Since the planet is not moving, he's going to be the reference frame s. We know that relative to the spaceship. So the the rocket has a velocity. The prime off. Zero point. Nice to see and relative to the planet the rocket as a velocity off zero point 36. See? And the problem wants to know what is this? Speed off the spaceship relative to the planet and in which direction is the spaceship moving is towards or east awards are away from the planet. So we need to calculate you. And we know by definition that the velocity yeah, in a relativistic situation is defined us v Prime equals the miners you divided by one miners You ve divided by C square. This is a square where C is the speed of light. You is the relative relative velocity be Were we already know in the V prime? We already know yet so rearranging desecration we have you equals V minus V prime divided by one minus v the prime divided by C square. So this is the relative velocity between the planet and the spaceship. So let's calculate this. We have you equals zero point 36 c minus 0.9 two to see, um, divided by one minus, deter 0.36 multiplies judo 0.92 c square divided by C square and cross this and we have after calculating this minus zero point eight tree, seven c. So this is the speed off the spaceship relative the planet. Since we have the negative sign, we know that the spaceship moves no way for on the planet. And that's the final answer to this problem. Thanks for watching

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