The rotation period of an earth satellite close to the surface of the earth is 83 minutes. The time period of another earth satellite in an orbit at a distance of three earth radii from its surface will be

1. 83 minutes                                   

2. $83\times \sqrt{8}$ minutes

3. 664 minutes                                 

4. 249 minutes

A satellite of mass m is circulating around the earth with constant angular velocity. If the radius of the orbit is $R_0$ and mass of the earth M, the angular momentum about the centre of the earth is:

1.$\mathrm{ m}\sqrt{GM{R}_0}$                                         

2. $M\sqrt{Gm{R}_0}$

3.$\mathrm{ m}\sqrt{\frac{GM}{R_0}}$                                           

4. $M\sqrt{\frac{GM}{R_0}}$

If the distance between the earth and the sun becomes half its present value, the number of days in a year would have been
1. 64.5                                     

2. 129

3. 182.5                                   

4. 730

A geostationary satellite orbits around the earth in a circular orbit of radius \(36000~\text{km}\). Then, the time period of a satellite orbiting a few hundred kilometres above the earth’s surface \((R_{earth}= 6400~\text{km})\) will approximately be:
1. \(\frac{1}{2}~\text{hrs}\)
2. \(1~\text{hrs}\)
3. \(2~\text{hrs}\)
4. \(4~\text{hrs}\)

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