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Found in: Page 385

### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# A spaceship is on a straight-line path between Earth and the Moon. At what distance from Earth is the net gravitational force on the spaceship zero?

Net gravitational force on the spaceship is zero at a distance of $3.44×{10}^{8}\mathrm{m}$ from the earth.

See the step by step solution

## Step 1: Listing the given quantities

The distance between the Earth and the Moon is ${\mathrm{R}}_{\mathrm{Earth}}=3.82×{10}^{8}\mathrm{m}$.

## Step 2: Understanding the concept of gravitational force

Let the distance from Earth to the spaceship be r.

Formula:

$\begin{array}{rcl}{\mathrm{f}}_{\mathrm{E}}& =& \frac{{\mathrm{GM}}_{\mathrm{e}}\mathrm{m}}{{\left({\mathrm{R}}_{\mathrm{em}}-\mathrm{r}\right)}^{2}}\\ & =& \frac{{\mathrm{GM}}_{\mathrm{e}}\mathrm{m}}{{\mathrm{r}}^{2}}\end{array}$

where m is the mass of the spaceship.

## Step 3: Explanation

Solving for r, we obtain

$\begin{array}{rcl}\mathrm{r}& =& \frac{{\mathrm{R}}_{\mathrm{em}}}{\sqrt{\mathrm{M}/{\mathrm{M}}_{\mathrm{e}}}+1}\\ & =& \frac{3.82×{10}^{8}\mathrm{m}}{\sqrt{\left(7.36×{10}^{22}\mathrm{kg}/\left(5.98×{10}^{24}\right)\mathrm{kg}\right)}+1}\\ & =& 3.44×{10}^{8}\mathrm{m}\end{array}$

The net gravitational force on the spaceship is zero at a distance of $3.44×{10}^{8}\mathrm{m}$ from the earth.