The earth takes $24\; h$ to rotate once about its axis. How much time (in $min$) does the sun take to shift by $1^o$ when viewed from the earth?

$A$ binary star system consists of two stars $A$ (mass $M_A = 2.2 M_S$) and $B$ (mass $M_B = 11 M_S$),where $M_S$ is the mass of the Sun. They are separated by a distance $d$ and rotate about their common centre of mass,which is stationary. What is the ratio of the angular momentum of star $A$ to the angular momentum of star $B$ about the centre of mass?

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

As we move towards the centre of the Sun,what happens to its physical properties?

$A$ spacecraft travels in a straight line from the Earth to the Moon. How will its weight change during this journey?

Fill in the blanks:
$(a)$ In the region inside the Earth,the acceleration due to gravity is proportional to the distance from the center of the Earth as ..... .
$(b)$ If the Earth shrinks such that its radius becomes half and its mass remains constant,the weight of an object on the Earth increases by a factor of ......... .
$(c)$ The orbital velocity of a geostationary satellite of the Earth is approximately ............ .