A satellite of mass m, initially at rest on the earth, is launched into a circular orbit at a height equal to the radius of the earth. The minimum energy required is $\frac{x m g R}{y}$ , where x and y are numbers. Find the value of x + y.

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Solution

We have, (Where ki is the minimum energy required
$K_{i} + U_{i} = F_{f} + U_{f}$
$K_{i} - \frac{G M m}{R} = \frac{1}{2} m V_{0}^{2} - \frac{G M m}{2 R}$
$K_{i} = \frac{1}{2} m (\frac{G M}{2 R}) + \frac{G M m}{2 R}$
$K_{i} = \frac{3 G M m}{4 R}$
$\Rightarrow x = 3 & y = 4$
$\Rightarrow x + y = 7$

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A satellite of mass m, initially at rest on the earth, is launched into a circular orbit at a height equal to the radius of the earth. The minimum energy required is xmgRy, where x and y are numbers. Find the value of x + y. ___

We have, (Where ki is the minimum energy required Ki+Ui=Ff+Uf Ki−GMmR=12mV20−GMm2R Ki=12m(GM2R)+GMm2R Ki=3GMm4R ⇒x=3&y=4 ⇒x+y=7

A satellite of mass m, initially at rest on the earth, is launched into a circular orbit at a height equal to the radius of the earth. The minimum energy required is $\frac{x m g R}{y}$ , where x and y are numbers. Find the value of x + y.

___

We have, (Where ki is the minimum energy required
$K_{i} + U_{i} = F_{f} + U_{f}$
$K_{i} - \frac{G M m}{R} = \frac{1}{2} m V_{0}^{2} - \frac{G M m}{2 R}$
$K_{i} = \frac{1}{2} m (\frac{G M}{2 R}) + \frac{G M m}{2 R}$
$K_{i} = \frac{3 G M m}{4 R}$
$\Rightarrow x = 3 & y = 4$
$\Rightarrow x + y = 7$