Chapter 13, Problem 38A

A friend proposes an idea for launching space probes that consists of boring a hole completely through Earth. Your friend reasons that a probe dropped into such a hole would accelerate all the way through and shoot like a projectile out the other side. Defend or oppose the reasoning of your friend.

To determine

Acceleration of space probe below the earth’s surface

Explanation of Solution

Introduction:

Gravitational force is fundamental force which attracts two objects having mass. Range of gravitational force is infinite.

Formula of gravitational force given by the newton is as follows;

  $F=G\frac{m_1{m}_2}{r^2}$

Where,

  $G$ = Universal gravitational constant

  $m_1$ = Mass of an object-1

  $m_2$ = Mass of an object-2

  $r$ = Distance between two objects

Gravitational field of earth is maximum at the surface of earth. At the center of earth gravitational field is zero. Then it increases linearly with distance up to surface of earth and then it decreases with distance. The graph is shown below.

From the graph of Earth’s gravitational field, it can be said that space probe decelerates up to the center of Earth. So, the acceleration is minimum at the center of Earth because gravitational force is zero at the center. Then it will oscillate up and down about the center of earth.

Conclusion:

Hence, space probe does not accelerate all the way through inside the Earth’s surface but it does oscillate about the center of earth.