If the distance between the earth and the sun becomes half its present value, the number of days in a year would have been

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

The time period of a satellite in a circular orbit of radius $R$ is $T$. The period of another satellite in a circular orbit of radius $9 R$ is............ $T$

Two satellites are launched at a distance $R$ from a planet of negligible radius. Both satellites are launched in the tangential direction. The first satellite launches correctly at a speed $v_0$ and enters a circular orbit. The second satellite, however, is launched at a speed $\frac {1}{2}v_0$ .  What is the minimum distance between the second satellite and the planet over the course of its orbit?

Kepler's third law states that square of period of revolution $(T)$ of a planet around the sun, is proportional to third power of average distance $r$ between sun and planet i.e.

$\therefore \;{T^2} = k{r^3}$

here $K$ is constant.

If the masses of sun and planet are $M$ and $m$ respectively then as per Newton's law of gravitation force of attraction between them is $F = \frac{{GMm}}{{{r^2}}}$ , here $G$ gravitational constant . The relation between $G$ and $K$ is described as

The time period of a satellite of earth is $24$ hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become $.......\,hours$