The Sun revolves around the galaxy with a speed of $250 \, km/s$ and its radius is $3 \times 10^{4} \, \text{light years}$. The mass of the Milky Way is:

The distances of two planets $A$ and $B$ from the sun are $r_A$ and $r_B$ respectively, such that $r_B = 100 r_A$. The ratio of the orbital speed of planet $A$ to that of planet $B$ is (both planets are revolving around the sun in circular orbits).

$A$ spaceship orbits around a planet at a height of $20 \, km$ from its surface. Assuming that only the gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in $24 \, hours$ around the planet? [Given: Mass of planet $= 8 \times 10^{22} \, kg$, Radius of planet $= 2 \times 10^6 \, m$, Gravitational constant $G = 6.67 \times 10^{-11} \, N \cdot m^2/kg^2$]

Even though the gravitational force of the Earth acts on the Moon towards its center,why does the Moon not fall onto the Earth?

$STATEMENT-1$: An astronaut in an orbiting space station above the Earth experiences weightlessness.
$STATEMENT-2$: An object moving around the Earth under the influence of Earth's gravitational force is in a state of 'free-fall'.

$A$ man inside an artificial satellite feels weightlessness because the force of attraction due to the Earth is