$A$ satellite is launched into a circular orbit of radius $R$ around Earth,while a second satellite is launched into an orbit of radius $1.02 R$. The percentage difference in the time periods of the two satellites is:

The radius of the Martian orbit around the Sun is about $4$ times the radius of the orbit of Mercury. The Martian year is $687$ Earth days. What is the length of $1$ year on Mercury?

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:

Kepler discovered

$A$ planet revolving in an elliptical orbit has:
$(A)$ a constant velocity of revolution.
$(B)$ the least velocity when it is nearest to the sun.
$(C)$ its areal velocity is directly proportional to its velocity.
$(D)$ areal velocity is inversely proportional to its velocity.
$(E)$ a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below:

Earth's orbit is an ellipse with eccentricity $e = 0.0167$. Thus,the Earth's distance from the Sun and its speed as it moves around the Sun vary from day to day. This means that the length of the solar day is not constant throughout the year. Assume that the Earth's spin axis is normal to its orbital plane and find the length of the shortest and the longest day. $A$ day should be taken from noon to noon. Does this explain the variation in the length of the day during the year?