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A spaceship makes the long trip from earth to the neareststar system, Alpha Centauri, at a speed of 0.955$c .$ The star isabout 4.37 light years from earth, as measured in earth'sframe of reference $(1$ light year is the distance light travelsin a year). (a) How many years does the trip take, accordingto an observer on earth? (b) How many years does the triptake according to a passenger on the spaceship? (c) Howmany light years distant is Alpha Centauri from earth, asmeasured by a passenger on the speeding spacecraft? (Notethat, in the ship's frame of reference, the passengers are atrest, while the space between earth and Alpha Centauri goesrushing past at 0.955$c .$ (d) Use your answer from part(c) along with the speed of the spacecraft to calculateanother answer for part (b). Do your two answers for thatpart agree? Should they?

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$$=2.7144 \mathrm{y}$$

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

University of Michigan - Ann Arbor

University of Winnipeg

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.

02:05

A spaceship makes the long…

01:54

Alpha Centauri, a star clo…

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The star ProximaCentau…

02:27

You are going on a trip to…

02:00

Astronomy A spaceship trav…

08:53

The distance to a particul…

08:59

The nearest star to Earth …

06:50

$\bullet$ The distance to …

12:24

An astronaut in a starship…

08:13

04:52

04:11

Alpha Centauri, a distance…

02:29

A spacecraft moving at $0.…

01:44

Astronomy The nearest star…

all right. And this problem, we want to know what a trip to Alfa Centauri will look like. Two different observers. Distant self A Centauri is 4.37 light years, and the speed that the trip is going to be taken a 0.955 si. So in part they were asked how long the trip would take from an observer based on Earth. What? And this is just the usual distance divided by velocity. To get time, penis comes out to 4.58 years now in part B were asked about the length of the trip from the perspective of an astronaut on board, Um, their time is going to be moving slower relative to the observers on Earth, which means that ah, the trip appears shorter from their perspective. So, um, the 4.58 gets contracted by a factor. One over gamma. Okay, I don't want to see their cause. It was divided out. Yeah, and the sequels 1.36 years. Now, from their perspective, the distance that they cover also gets contracted. So the distance is 4.37 and it gets contracted by the same factor to do Lauren's contraction. This comes out Tio 1.3 light years. And, um, if we take this distance and divide by the speed that they're going, wait, get that It takes 1.36 years, which is the same on dancer. We got in part B, and they have to be the same for the theory to be consistent.

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