When a satellite in a circular orbit around the earth enters the atmospheric region,it encounters small air resistance to its motion. Then

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:

$A$ mass $m$,travelling at speed $V_0$ in a straight line from far away,is deflected when it passes near a black hole of mass $M$ which is at a perpendicular distance $R$ from the original line of flight. $a$,the distance of closest approach between the mass and the black hole,is given by the relation:

The relative uncertainty in the period of a satellite orbiting around the Earth is $10^{-2}$. If the relative uncertainty in the radius of the orbit is negligible,the relative uncertainty in the mass of the Earth is:

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)

$A$ particle of mass $m$ moves in a circular orbit under the central potential field,$U(r) = -\frac{C}{r}$,where $C$ is a positive constant. The correct radius-velocity graph of the particle's motion is: