$A$ satellite orbits the Earth in a circular orbit of radius $R$. Another satellite orbits in an orbit of radius $1.02 R$. What is the percentage increase in the time period of the second satellite compared to the first (in $\%$)?

The earth $E$ moves in an elliptical orbit with the sun $S$ at one of the foci as shown in the figure. Its speed of motion will be maximum at the point:

The distances of Neptune and Saturn from the Sun are nearly $10^{13} \ m$ and $10^{12} \ m$ respectively. Assuming that they move in circular orbits,their periodic times will be in the ratio:

$A$ planet revolves around the Sun in an elliptical orbit as shown in the figure. Which of the following statements is correct?

The distance of Venus from the sun is $0.72\, AU$. The orbital period of Venus is ............ days.

Kepler's third law states that the square of the period of revolution $(T)$ of a planet around the sun is proportional to the cube of the average distance $(r)$ between the sun and the planet,i.e.,$T^2 = Kr^3$,where $K$ is a constant. If the masses of the sun and the planet are $M$ and $m$ respectively,then according to Newton's law of gravitation,the force of attraction between them is $F = \frac{GMm}{r^2}$,where $G$ is the gravitational constant. The relation between $G$ and $K$ is: