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A space probe is sent to the vicinity of the star Capella, which is 42.2 light years from the earth. (A light year is the distance light travels in a year.) The probe travels with a speedof 0.9910$c$ relative to the earth. An astronaut recruit on board is 19 years old when the probe leaves the earth. What is her biological age when the probe reaches Capella, as measuredby (a) the astronaut and (b) someone on earth?

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$=61.58$ years

Physics 101 Mechanics

Chapter 27

Relativity

Gravitation

University of Washington

Hope College

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.

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A space probe is sent to t…

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02:09

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A spaceship travels at con…

02:08

A space traveler takes off…

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A woman leaves the earth i…

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Suppose we want to send an…

what? All right. And this problem, we have a star that's 42.2 light years away, and a spaceship travels towards it. 0.991 See? So in part A, we want to know how long this trip takes. Um, relative to an observer on the earth said simply, 42.2 light years divided by 0.991 see? And that comes out to 42.6 years. So if our astronaut was originally 19 they will now be 61.6 years, told you. However, from the perspective of the astronaut, this amount of time is shorter by a factor. One over gamma, and so for them it only takes 5.7 years. And so their age at the end of the drip at the end of the trip, if they start out in 19 is 24.7 years old.

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