Answered: A space traveler weighs 800 N on earth.…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A space traveler weighs 800 N on earth. A planet having a mass of 5(10^25) kg and a diameter of 30(10^6) m orbits a distant star. Determine the weight W of the traveler on the surface of this planet.

Expert Solution

Step 1

Given Data:

The weight of the space traveler on the earth is, $W_{E} = 800 N$ .
The mass of the planet is, $M_{P} = 5 \times 10^{25} kg$ .
The diameter of the planet is, $D_{P} = 30 \times 10^{6} m$ .

Step 2

The expression for the weight of the space traveler on the surface of the earth can be written as below,

$\begin{array}{rcl} W \end{array} \begin{array}{rcl} _{E} \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} m \end{array} \begin{array}{rcl} G \end{array} \begin{array}{rcl} \frac{4 M_{E}}{{D_{E}}^{2}} \end{array}$

Here, $m$ is the mass of space traveler, $G$ is the gravitational constant, $M_{E}$ is the mass of earth which is equal to $5.972 \times 10^{24} kg$ and $D_{E}$ is the diameter of earth which is equal to $12.742 \times 10^{6} m$ .

Substitute 800 N for $W_{E}$ in the above expression.

$\begin{array}{rcl} 800 \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} N \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} m \end{array} \begin{array}{rcl} G \end{array} \begin{array}{rcl} \frac{4 M_{E}}{{D_{E}}^{2}} \end{array}$

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