If the distance of Mercury from the Sun is $0.4$ times the distance of the Earth from the Sun,find the solar constant of Mercury in $cal/min \cdot cm^2$. The solar constant of the Earth is $2 \, cal/min \cdot cm^2$.

$A$ satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then

Match the column $-I$ with column $-II$ for a satellite in circular orbit:

Column $-I$	Column $-II$
$(A)$ Kinetic energy	$(p)$ $-\frac{GM_Em}{2r}$
$(B)$ Potential energy	$(q)$ $\sqrt{\frac{GM_E}{r}}$
$(C)$ Total energy	$(r)$ $-\frac{GM_Em}{r}$
$(D)$ Orbital velocity	$(s)$ $\frac{GM_Em}{2r}$

(where $M_E$ is the mass of the earth,$m$ is the mass of the satellite,and $r$ is the radius of the orbit)

Many exoplanets have been discovered by the transit method,where one monitors a dip in the intensity of the parent star as the exoplanet moves in front of it. The exoplanet has a radius $R$ and the parent star has a radius $100 \,R$. If $I_0$ is the intensity observed on Earth due to the parent star,then as the exoplanet transits:

Two bodies of equal masses are at some distance apart. If $20 \%$ of the mass is transferred from the first body to the second body,then the gravitational force between them

The variation of acceleration due to gravity $g$ with distance $d$ from the centre of the earth is best represented by ($R =$ Earth's radius)