Answer:
The gravitational force changing velocity is
[tex]\frac{dF}{dt}=-8\frac{N}{s}[/tex]
Explanation:
The expression for the gravitational force is
[tex]F=\frac{k}{r^{2}}\\\\k=10x10^{13} N*km^{2}\\\\r=10x10^{4} km\\\\V=0.4 \frac{km}{s}[/tex]
Differentiate the above equation
[tex]\frac{dF}{dt}=\frac{k}{r^{2}}\\\frac{dF}{dt}=k*r^{-2}\\\frac{dF}{dt}=-2*k*r^{-3} \frac{dr}{dt}\\\frac{dF}{dt}=\frac{-2k}{r^{3}}\frac{dr}{dt}[/tex]
The velocity is the distance in at time so
[tex]V=\frac{dr}{dt}=0.4 \frac{km}{s}[/tex]
[tex]\frac{dF}{dt}=\frac{-2*k}{r^{3}}*0.4\\\frac{dF}{dt}=\frac{-8*10x^{13}N*km^{2} }{(10x10^{4}) ^{3}} \\\frac{dF}{dt}=\frac{-8x10^{12} }{1x10^{12}}[/tex]
[tex]\frac{dF}{dt}=-8\frac{N}{s}[/tex]
