A geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then, the time period of a satellite orbiting a few hundred kilometres above the earth’s surface (${\mathrm{R}}_{\mathrm{earth}}$= 6400 km) will approximately be -

(1) 1/2 h                   

(2) 1 h

(3) 2 h                       

(4) 4 h

A planet revolves around the sun whose mean distance is 1.588 times the mean distance between earth and the sun. The revolution time of the planet will be:

(1) 1.25 years                               

(2) 1.59 years

(3) 0.89 years                               

(4) 2 years

The earth E moves in an elliptical orbit with the sun S at one of the foci as shown in figure. Its speed of motion will be maximum at the point

(1) C

(2) A

(3) B

(4) D

The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is how many times greater than that of B from the sun ?

(1) 2                                         

(2) 3                                      

(3) 4                                        

(4) 5

If the radius of earth's orbit is made 1/4 th, the duration of an year will become -

(1) 8 times                                     

(2) 4 times

(3) 1/8 times                                   

(4) 1/4 times

If the mass of a satellite is doubled and the time period remain constant, the ratio of orbit in the two cases will be

(1)   1 : 2                                   

(2)   1 : 1

(3)   1 : 3                                   

(4)   None of these

The maximum and minimum distances of a comet from the sun are $8\times {10}^{12}$ m and $1.6\times {10}^{12}$ m. If its velocity when nearest to the sun is 60 m/s, what will be its velocity in m/s when it is farthest -

(1) 12                                      

(2) 60

(3) 112                                     

(4) 6

A body revolved around the sun 27 times faster than the earth. What is the ratio of their radii?

(1)   1/3                                    

(2)   1/9

(3)   1/27                                  

(4)   1/4

The period of the moon’s rotation around the earth is nearly 29 days. If the moon’s mass were 2 fold, its present value and all other things remained unchanged, the period of the moon’s rotation would be nearly:

(1)$29\sqrt{2} days$                                       

(2)$29/\sqrt{2} days$

(3)$29\times 2 days$                                       

(4)29 days

If two planets are at mean distances $d_1$ and $d_2$ from the sun and their frequencies are n₁ and n₂ respectively, then:

1. ${n_1}^2{d_1}^2=n_2{d_2}^2$                                 

2. ${n_2}^2{d_2}^3={n_1}^2{d_1}^3$

3. $n_1{d_1}^2=n_2{d_2}^2$                                   

4. ${n_1}^2{d}_1={n_2}^2{d}_2$