Chapter 5, Problem 28P

Calculate the force of Earth's gravity on a spacecraft 2.00 Earth radii above the Earth's surface if its mass is 1850 kg.

To determine

The force of Earth`s gravity on a spacecraft.

Answer to Problem 28P

Solution:

2019 N

Explanation of Solution

Given info:

Mass of spacecraft = 1850 kg

Distance between the center of the earth and spacecraft.

  $\begin{array}{l}\begin{array}{l}\begin{array}{l}r\text{ =3 times of earth }\\ r\text{= 3 ×6371 km}\end{array}\hfill \\ r\text{=19113 km}\hfill \end{array}\\ r=19113000\text{m}\end{array}$

Formula used:

Gravitation force, $F=\frac{G{m}_1{m}_2}{r^2}$

Here, $m_1$ is mass of earth $\text{5}{\text{.972 ×10}}^{\text{24}}\text{kg}$

Mass of spacecraft is $m_2$

  $G=6.67\times {10}^{-11}{\text{m}}^{\text{3}}{\text{kg}}^{\text{-1}}{\text{s}}^{\text{-2}}$ (gravitational constant)

Calculation:

Substitutethe values:

  $\begin{array}{l}F=\frac{6.67\times {10}^{-11}\times 5.972\times {10}^{24} \times 1850\text{ kg}}{{\left(19113000\right)}^2}\hfill \\ F=2019\text{ N}\hfill \end{array}$

Conclusion:

The force of earth gravity on a spacecraft is 2019N.