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Chapter 8: Problem 3

When you stand on Earth, the distance between you and Earth is zero. So why isn't the gravitational force infinite?

Short Answer

Expert verified
The gravitational force isn't infinite because the 'distance' in Newton's law of gravitation refers to the distance between the centers of the two masses, not the distance from the surfaces of the masses. Thus, even when standing on the surface of the Earth, we are essentially 'standing' at approximately one Earth radius away from the center of the earth.

Step by step solution

01

Understand Newton's law of universal gravitation

Newton's law of universal gravitation states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The equation for this is F = G * m1 * m2 / r^2, where F is the force, G is the gravitational constant, m1 and m2 are masses of the objects, and r is the distance between the centers of the two masses.
02

Recognize the true distance in the law of universal gravitation

Even when standing on the surface of Earth, the distance between the person and Earth is not zero. This is because in Newton's law of gravitation, the 'distance' is not from the surface of the Earth, but from the center. So, when the formula talks about 'r', it actually means the radius of the Earth, not the distance from the surface.
03

Understand that gravity is not infinite at zero distance

The force of gravity only becomes infinite if the distance between the centers of masses becomes zero. In reality, this can't happen. Even if two objects are touching, their centers of mass are not coinciding. In case of Earth and a person, we are essentially 'standing' at approximately one Earth radius away from the center of the earth, so the force is not infinite.

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Most popular questions from this chapter

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