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. \(1\)

Subtopic:  Orbital velocity |
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The mass and radius of orbit for the two satellites are \((m,r)\) and \((3m, 3r)\) respectively. What will be the ratio of their orbital velocity about the Earth?
1. \(\sqrt 3 :1\) 2. \(1 : \sqrt 3 \)
3. \(\sqrt 2 :1\) 4. \(1:2\)
Subtopic:  Orbital velocity |
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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. \(11\)

Subtopic:  Orbital velocity |
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 A satellite of mass \(\dfrac{M}{2}\) is revolving around earth in a circular orbit at a height of \(\dfrac{R}{3}\) from earth surface. The angular momentum of the satellite is \(M \sqrt{\dfrac{G M R}{x}} .\). The value of \(x\) is: (where \(M,\) \(G\) and \(R\) are the mass, gravitational constant, and radius of Earth, respectively).
1. \(7\)
2. \(3\)
3. \(5\)
4. \(1\)

 
Subtopic:  Orbital velocity |
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