The distance of a planet from the sun is $5$ times the distance between the earth and the sun. The time period of the planet is: 

A planet moves around the sun. At a point $P,$ it is closest to the sun at a distance $d_1$ and has speed $v_1.$ At another point $Q,$ when it is farthest from the sun at distance $d_2,$ its speed will be:

If $A$ is the areal velocity of a planet of mass $M,$ then its angular momentum is:

Kepler's third law states that the square of the period of revolution ($T$) of a planet around the sun, is proportional to the third power of average distance $r$ between the sun and planet i.e. $T^2 = Kr^3$, here $K$ is constant. If the masses of the sun and planet are $M$ and $m$ respectively, then as per Newton's law of gravitation, the force of attraction between them is $F = \frac{GMm}{r^2},$ here $G$ is the gravitational constant. The relation between $G$ and $K$ is described as:
1. $GK = 4\pi^2$
2. $GMK = 4\pi^2$
3. $K =G$
4. $K = \frac{1}{G}$

The figure shows the elliptical orbit of a planet $m$ about the sun ${S}.$ The shaded area $SCD$ is twice the shaded area $SAB.$ If $t_1$ is the time for the planet to move from $C$ to $D$ and $t_2$ is the time to move from $A$ to $B,$ then:
                     

If $R$ is the radius of the orbit of a planet and $T$ is the time period of the planet, then which of the following graphs correctly shows the motion of a planet revolving around the sun?

1.		2.
3.		4.

If two planets are at mean distances $d_1$ and $d_2$ from the sun and their frequencies are $n_1$ and $n_2$ respectively, then:
1. $n^2_1d^2_1= n_2d^2_2$
2. $n^2_2d^3_2= n^2_1d^3_1$
3. $n_1d^2_1= n_2d^2_2$
4. $n^2_1d_1= n^2_2d_2$

The figure shows a planet in an elliptical orbit around the sun $(S).$ The ratio of the momentum of the planet at point $A$ to that at point $B$ is:

                           
1. $\frac{r_1}{r_2}$
2. $\frac{r_{1}^{2}}{r_{2}^{2}}$
3. $\frac{r_2}{r_1}$
4. $\frac{r_{2}^{2}}{r_{1}^{2}}$

Two satellites $S_1$ and $S_2$ are revolving around a planet in coplanar and concentric circular orbits of radii $R_1$ and $R_2$ in the same direction respectively. Their respective periods of revolution are $1~\text{hr}$ and $8~\text{hr}.$ The radius of the orbit of satellite $S_1$ is equal to $10^4~\text{km}.$ Find the relative speed when they are closest to each other. 
1. $2\pi \times 10^4~\text{kmph}$
2. $\pi \times 10^4~\text{kmph}$
3. $\frac{\pi}{2} \times 10^4~\text{kmph}$
4. $\frac{\pi}{3} \times 10^4~\text{kmph}$

Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F.$ If the space around the masses is filled with a liquid of specific density $3,$ the gravitational force will become:
1. $3F$
2. $F$
3. $F/3$
4. $F/9$