The earth moves around the Sun in an elliptical orbit as shown in figure.The ratio $OA/OB = x$ . The ratio of the speed of the earth at $B$ to that at $A$ is nearly

- A
$\sqrt x$

- B
$x$

- C
$x \sqrt x$

- D
$x^2$

Aplanet of mass $m$ is in an elliptical orbit about the sun $(m < < M_{sun})$ with an orbital period $T.$ If $A$ be the area of orbit, then its angular momentum would be **:**

India's Mangalyan was sent to the Mars by launching it into a transfer orbit $EOM$ around the sun . It leaves the earth at $E$ and meets Mars at $M$ . If the semi-major axis of Earth's orbit is $a_e = 1.5 \times 10^{11}\, m$, that of Mars orbit $a_m= 2.28 \times 10^{11}\, m$, taken Kepler's laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to ........ $days$.

- [JEE MAIN 2014]

The relative uncertainty in the period of a sateilite orbiting around the earth is $10^{-2}$. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is

- [JEE MAIN 2018]

A satellite is orbiting the earth in a circular orbit of radius $r.$ Its

A planet takes $200$ days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution

- [JEE MAIN 2024]