A cord of length 64mis used to connect a 100kgastronaut. Estimate the value of the tension (inNewton) in the cord. Assume that the spaceship is orbiting near earth surface. Also assume that the spaceship and the astronaut fall on a straight line from the earth’s centre. The radius of the earth is 6400km.Correct answer is '0.03'. Can you explain this answer?

Question

A cord of length 64mis used to connect a 100kgastronaut. Estimate the value of the tension (inNewton) in the cord. Assume that the spaceship is orbiting near earth surface. Also assume that the spaceship and the astronaut fall on a straight line from the earth&rsquo;s centre. The radius of the earth is 6400km.Correct answer is '0.03'. Can you explain this answer?

Answer

As according to given problem the mass of satellite M is much greater than that of astronaut m so the centre of mass of the system will be close to satellite and as the satellite is orbiting close to the surface of earth, the equation of motion of the system (S + A) will be :

And the equation motion of the astronaut will be

So substituting the given data,

The correct answer is: 0.03

And the equation motion of the astronaut will be

So substituting the given data,

The correct answer is: 0.03

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