An astronomy textbook, when printed out, weighs four pounds on the surface of the Earth. After finishing your course, you are so tired of the book, you arrange for NASA to shoot it into space. When it is twice as far from the center of the Earth than when you were reading it, what would it weigh

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25-01-2022
Physics

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An astronomy textbook, when printed out, weighs four pounds on the surface of the Earth. After finishing your course, you are so tired of the book, you arrange for NASA to shoot it into space. When it is twice as far from the center of the Earth than when you were reading it, what would it weigh

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oladayoademosu oladayoademosu · Answer 1 · 2022-01-31T13:40:14+01:00

Its weight would be one-quarter its weight on Earth when it is twice as far from the center of the Earth.

Newton's law of universal gravitation

According to Newton's law of universal gravitation, when the astronomy textbook is on the earth, its weight, W equals the force of attraction of the earth on it, F.

So, W = F = GMm/R² where

G = universal gravitational constant,
M = mass of earth,
m = mass of astronomy textbook and
R = distance of astronomy textbook from earth's center.

New weight of astronomy textbook

Now, when the astronomy textbook is shot into space at a distance twice its initial distance, that is R' = 2R, its new weight, W' is

W' = GMm/R'²

Substituting the value of R' into the equation, we have

W' = GMm/(2R)²

W' = GMm/4R²

W' = W/4 (since W = GMm/R²)

So, its weight would be one-quarter its weight on Earth when it is twice as far from the center of the Earth.

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