Two planets are in a circular orbit of radius \(R\) and \(4R\) about a star. At a specific time, the two planets and the star are in a straight line. If the period of the closest planet is \(T,\) then the star and planets will again be in a straight line after a minimum time:
1. | \((4)^2T\) | 2. | \((4)^{\frac13}T\) |
3. | \(2T\) | 4. | \(8T\) |
The time period of a geostationary satellite is \(24~\text{h}\) at a height \(6R_E\) \((R_E\) is the radius of the earth) from the surface of the earth. The time period of another satellite whose height is \(2.5R_E\) from the surface will be:
1. | \(6\sqrt{2}~\text{h}\) | 2. | \(12\sqrt{2}~\text{h}\) |
3. | \(\dfrac{24}{2.5}~\text{h}\) | 4. | \(\dfrac{12}{2.5}~\text{h}\) |