A body is moving in a low circular orbit about a planet of mass \(M\) and radius \(R\). The radius of the orbit can be taken to be \(R\) itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is:
1. \(\sqrt{2}\)
2. \(\frac{1}{\sqrt{2}}\)
3. \(2\)
4. \(1\)
| 1. | \(\sqrt 3 :1\) | 2. | \(1 : \sqrt 3 \) |
| 3. | \(\sqrt 2 :1\) | 4. | \(1:2\) |
A spaceship orbits around a planet at a height of \(20~\text{km}\) from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in \(24\) hours around the planet?
[Given; Mass of planet \(=8 \times 10^{22} ~\text{kg}\), Radius of planet \(=2 \times 10^6 ~\text{m}\), Gravitational constant \(G=6.67 \times 10^{-11} ~\text{Nm}^2 / \text{kg}^2\)]
1. \(13\)
2. \(9\)
3. \(17\)
4. \(11\)