Using the data given below,find the height at which a communication satellite can reside. $(G=6.67 \times 10^{-11} \text{ N-m}^2 \text{ kg}^{-2}, M=5.98 \times 10^{24} \text{ kg}, R=6.4 \times 10^6 \text{ m})$ (in $\text{ km}$)

$A$ satellite is revolving around a planet in a circular orbit close to its surface. Let $\rho$ be the mean density and $R$ be the radius of the planet; then the period of the satellite is $(G = \text{Universal constant of gravitation})$

Assertion $A$: An astronaut inside a massive spaceship orbiting around the Earth will experience a finite but small gravitational force.
Reason $R$: The centripetal force necessary to keep the spaceship in orbit around the Earth is provided by the gravitational force between the Earth and the spaceship.

Which of the following statements is incorrect regarding a polar satellite?

$A$ satellite of mass $\frac{M}{2}$ is revolving around the Earth in a circular orbit at a height of $\frac{R}{3}$ from the Earth's surface. The angular momentum of the satellite is $M \sqrt{\frac{GMR}{x}}$. The value of $x$ is . . . . . . ,where $M$ and $R$ are the mass and radius of the Earth,respectively. ($G$ is the gravitational constant)

$A$ spaceship approaches the moon (mass $= M$,radius $= R$) along a parabolic path which is almost tangential to its surface. At the moment of maximum approach,the brake rocket is fired to convert the spaceship into a satellite of the moon. Find the change in speed.