A satellite is moving  in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius \(R_e\). By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that is become \(\sqrt{\frac{3}{2}}\) times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is \(R\). Value  of \(R\) is ? 
1. \( 2 R_e \)
2. \( 2.5 R_e \)
3. \( 3 R_e \)
4. \( 4 R_e\)

A satellite is in an elliptical orbit around a planet \(P\). It is observed that the velocity of the satellite when it is farthest from the planet is \(6\) times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is:
1. \(1:3\)
2. \(1:2\)
3. \(3:4\)
4. \(1:6\)

Consider two satellites, \(S_1\) and \(S_2,\) with periods of revolution \(1~\text{hr}\) and \(8~\text{hr},\) respectively revolving around a planet in circular orbits. The ratio of the angular velocity of the satellite \(S_1\) to the angular velocity of the satellite \(S_2\) is:
1. \(8:1\)
2. \(1:4\)
3. \(2:1\)
4. \(1:8\)

Two satellites A and B of masses \(200\) kg and \(400\) kg are revolving round the earth at height of \(600\) km and \(1600\) km respectively. If \(T_A\) and \(T_B\) are the time periods of \(A\) and \(B\) respectively then the value of \(T_B-T_A\) is: 

[Given : radius of earth = \(6400\) km, mass of earth = \(6\times 10^{24}\)]
1. \( 1.33 \times 10^3 \mathrm{~s} \)
2. \( 3.33 \times 10^2 \mathrm{~s} \)
3. \( 4.24 \times 10^3 \mathrm{~s} \)
4. \( 4.24 \times 10^2 \mathrm{~s}\)