The Earth is revolving around the Sun. If the distance of the Earth from the Sun is reduced to $\frac{1}{4}$ of the present distance,then the length of the present day will be reduced by a factor of:

The eccentricity of Earth's orbit is $0.0167$. The ratio of its maximum speed in its orbit to its minimum speed is

Two planets $A$ and $B$ of equal mass have periods of revolution $T_{A}$ and $T_{B}$ such that $T_{A} = 2 T_{B}$. These planets are revolving in circular orbits of radii $r_{A}$ and $r_{B}$ respectively. Which of the following is the correct relationship between their orbital radii?

If the radius of the Earth's orbit is made $\frac{1}{4}$ of its original value,the duration of a year will become:

The time period of a satellite revolving around earth in a given orbit is $7 \, hours$. If the radius of orbit is increased to three times its previous value,then the approximate new time period of the satellite will be ...... $hours$.

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A):$ The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus the areal velocity of the planet is constant.
Reason $(R):$ For a central force field,the angular momentum is a constant.
In the light of the above statements,choose the most appropriate answer from the options given below: