A rocket is launched normal to the surface of earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is $3 \times 10^5$ times heavier than the Earth and is at a distance $2.5 \times 10^4$ times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is $\mathrm{ve}_{\mathrm{e}}=11.2 \mathrm{~km} \mathrm{~s} \mathrm{~s}^{-1}$. The minimum initial $\left(\mathrm{v}_{\mathrm{s}}\right)$ required for the rocket to be able to leave the Sun-earth system is closest to

(Ignore the rotation and revolution of the Earth and the presence of any other planet)

For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

The speed of a satellite in a circular orbit of radius $R_0$ around the earth is $v_0$. Another satellite is in an elliptic orbit around the earth. If the minimum and maximum speeds of the second satellite are $\alpha v_0$ and $\beta v_0$ respectively, then its time period is

A star is modeled as a uniform spherical distribution of matter keeping mass of star constant. How gravitational pressure on surface depends on volume of the star?

If g is the acceleration due to gravity at the earth's surface and $r$ is the radius of the earth, the escape velocity for the body to escape out of earth's gravitational field is