$A$ particle moves in a circular orbit of radius $r$ under a central attractive force $F = -\frac{k}{r}$,where $k$ is a constant. The periodic time of this motion is proportional to:

Two stars of equal masses $M$ are orbiting in a circle of radius $R$. Their orbital time period is proportional to

$A$ planet is moving around the sun in an elliptical orbit at different positions $A, B, C, D$. The maximum kinetic energy of the planet is at position:

$STATEMENT-1$: 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'.

The orbital angular momentum of a satellite revolving at a distance $r$ from the centre is $L$. If the distance is increased to $16r$,then the new angular momentum will be

If the Earth is considered a point mass of $6 \times 10^{24} \ kg$ revolving around the Sun at a distance of $1.5 \times 10^8 \ km$ in a period of $T = 3.14 \times 10^7 \ s$,then the angular momentum of the Earth around the Sun will be: