What is the minimum energy required to launch a satellite of mass from the surface of a planet of mass and radius in a circular orbit at an altitude of ? [2012]

Question

What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ ? [2012]

Smart Achievers · Accepted Answer

(1)

$As we know,$

$R$

$and orbital velocity, v_{0} = \sqrt{\frac{G M}{R + h}}$

$E_{f} = \frac{1}{2} m v_{0}^{2} - \frac{G M m}{3 R} = \frac{1}{2} m \cdot \frac{G M}{3 R} - \frac{G M m}{3 R}$

$= \frac{G M m}{3 R} (\frac{1}{2} - 1) = - \frac{G M m}{6 R}$ $\Rightarrow E_{i} = - \frac{G M m}{R} + K$

$E_{i} = E_{f}$

$Therefore minimum required energy, K = \frac{5 G M m}{6 R}$

Solution

Q.
What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ [2012]

1 $\frac{5 G m M}{6 R}$

2 $\frac{2 G m M}{3 R}$

3 $\frac{G m M}{2 R}$

4 $\frac{2 G m M}{R}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R [2012]

1 5GmM6R

2 2GmM3R

3 GmM2R

4 2GmMR