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 $............. \times 10^8 \, km$.

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

$A$ planet $(P_1)$ is moving around a star of mass $2M$ in an orbit of radius $R$. Another planet $(P_2)$ is moving around another star of mass $4M$ in an orbit of radius $2R$. The ratio of the time periods of revolution of $P_2$ and $P_1$ is . . . . . . .

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

$A$ 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: