$A$ star of mass $M$ and radius $R$ is made up of gases. The average gravitational pressure compressing the star due to the gravitational pull of the gases making up the star depends on $R$ as

Which of the following astronomers first proposed that the Sun is static and the Earth revolves around the Sun?

$Assertion$: Space rockets are usually launched in the equatorial line from west to east.
$Reason$: The acceleration due to gravity is minimum at the equator.

$A$ satellite of mass $m$ is at a distance of $a$ from a star of mass $M$. The speed of the satellite is $u$. Suppose the law of universal gravity is $F = -G \frac{Mm}{r^{2.1}}$ instead of $F = -G \frac{Mm}{r^2}$. Find the speed of the satellite when it is at a distance $b$ from the star.

Fill in the blanks:
$(a)$ The value of gravitational intensity at the center of the Earth is ..... .
$(b)$ The potential energy of a satellite is $-8 \times 10^9 \, J$,then its binding energy is ............ .
$(c)$ Kepler's second law regarding the constancy of the areal velocity of a planet is a consequence of the law of conservation of .......... .

$A$ body situated on the surface of the earth becomes weightless at the equator when the rotational kinetic energy of the earth reaches a critical value '$K$'. The value of '$K$' is given by [$g$ = gravitational acceleration on earth's surface,$M$ = mass of the earth,and $R$ = radius of the earth].