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(B) The orbital speed of a satellite is given by $v = \sqrt{\frac{GM}{r}}$,which implies $v \propto r^{-1/2}$.Taking the natural logarithm on both sid

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Increase by $0.5\%$

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(B) The orbital speed of a satellite is given by $v = \sqrt{\frac{GM}{r}}$,which implies $v \propto r^{-1/2}$.Taking the natural logarithm on both sides,we get $\ln v = \ln(GM)^{1/2} - \frac{1}{2} \ln r$.Differentiating both sides,we get $\frac{dv}{v} = -\frac{1}{2} \frac{dr}{r}$.Given that the radius is decreased by $1\%$,we have $\frac{dr}{r} = -0.01$.Substituting this value,$\frac{dv}{v} = -\frac{1}{2} (-0.01) = +0.005$.Therefore,the speed will increase by $0.5\%$.

$A$ satellite is moving around the earth with speed $v$ in a circular orbit of radius $r$. If the orbit radius is decreased by $1\%$,its speed will

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