$A$ satellite moves in a circle around the earth. The radius of this circle is equal to one half of the radius of the moon's orbit. The satellite completes one revolution in

$A$ 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:

$A$ planet of mass $m$ is in an elliptical orbit about the sun $(m \ll M_{sun})$ with an orbital period $T$. If $A$ is the area of the orbit,then its angular momentum is:

The time period of a satellite of the Earth is $5$ hours. If the separation between the Earth and the satellite is increased to four times the previous value,the new time period will become ......... $hours$.

Give the contribution of Tycho Brahe on planetary motion.

$A$ satellite moves around the Earth in a circular orbit of radius $R$ making one revolution per day. $A$ second satellite moving in a circular orbit moves around the Earth once in $8$ days. The radius of the orbit of the second satellite is