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

Which of the following quantities does not depend upon the orbital radius of the satellite

If a new planet is discovered rotating around Sun with the orbital radius double that of earth, then what will be its time period (in earth's days)

The angular momentum of a planet of mass $M$ moving around the sun in an elliptical orbit is $\overrightarrow{ L }$. The magnitude of the areal velocity of the planet is:

The time period of an artificial satellite in a circular orbit of radius $R$ is $2\, days$ and its  orbital velocity is $v_0$. If time period of another satellite in a circular orbit is $16 \,days$ then