The figure shows the orbit of a planet $P$ around the sun $S.$ $AB$ and $CD$ are the minor and major axes of the ellipse,respectively.
If $t_1$ is the time taken by the planet to travel along the path $ACB$ and $t_2$ is the time taken to travel along the path $BDA,$ then:

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

If the distance of the earth from the Sun is $1.5 \times 10^8 \, km$. Then the distance of an imaginary planet from the Sun,if its period of revolution is $2.83$ years,is $............. \times 10^8 \, km$.

$A$ 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:

$A$ star of mass $M$ (equal to the solar mass) with a planet (much smaller than the star) revolves around the star in a circular orbit. The velocity of the star with respect to the centre of mass of the star-planet system is shown below. The radius of the planet's orbit is closest to .......... $AU$ ($1 \, AU =$ Earth-Sun distance).

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: