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Sagot :
Given:
The mass of the satellite is m = 200 kg
The initial radius of the circular orbit is
[tex]r_i=7.5\times10^6\text{ m}[/tex]The final radius of the circular orbit is
[tex]r_f=7.7\times10^6\text{ m}[/tex]The mass of the earth is
[tex]M=5.97\times10^{24}\text{ kg}[/tex]Also, the gravitational constant is
[tex]G=\text{ 6.67}\times10^{-11}\text{ N m}^2\text{ /kg}^2[/tex]To find the approximate change in gravitational force.
Explanation:
In order to calculate the approximate change in the gravitational force, we have to find the difference between the initial and final gravitational forces.
The initial gravitational force can be calculated as
[tex]\begin{gathered} F_i=\frac{GmM}{(r_i)^2} \\ =\frac{6.67\times10^{-11}\times200\times5.97\times10^{24}}{(7.5\times10^6)^2} \\ =\text{ 1415.82 N} \end{gathered}[/tex]The final gravitational force can be calculated as
[tex]\begin{gathered} F_f=\frac{GmM}{(r_f)^2} \\ =\frac{6.67\times10^{-11}\times200\times5.97\times10^{24}}{(7.7\times10^6)^2} \\ =1343.23\text{ N} \end{gathered}[/tex]The approximate change can be calculated as
[tex]\begin{gathered} \Delta F=F_f-F_i \\ =1343.23-1415.82 \\ =-72.6\text{ N} \\ \approx-73\text{ N} \end{gathered}[/tex]Final Answer: The approximate change in the gravitational force is -73 N
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