Chapter 13, Problem 11A

At what distance away from Earth is Earth’s gravitational force on an object zero?

Solution

The distance away from Earth where Earth’s gravitational force on an object zero -->

Introduction:

At height h , gravitational acceleration will always decrease near the surface of the Earth.

Explanation:

Gravitational acceleration at height is always less than g on surface and with height g decreases.

  $g\text{'}=\left(1-\frac{2h}{R}\right)g$

Here g’= Gravitational acceleration at height h.

And g = Gravitational acceleration on the surface.

So, at a height of one half of the Earth’s radius Earth’s Gravitational force of an object will zero.

Conclusion:

If one fires an object upward, usually it will slow, stop momentarily, return to Earth due to gravity. But at a distance $\frac{R}{2}$ gravity, it will become zero and the object will never come back.