The Earth moves around the Sun in an elliptical orbit as shown in the figure. The ratio $OA/OB = x$. The ratio of the speed of the Earth at $B$ to that at $A$ is nearly

The planet Mars has two moons. If one of them has a period of $7\, \text{hours}, 30\, \text{minutes}$ and an orbital radius of $9.0 \times 10^{3}\, \text{km}$, find the mass of Mars. $\left\{\text{Given}: \frac{4 \pi^{2}}{G} = 6 \times 10^{11}\, \text{N}^{-1} \text{m}^{-2} \text{kg}^{2}\right\}$

Two satellites $A$ and $B$ go round a planet in circular orbits having radii $4R$ and $R$,respectively. If the speed of satellite $A$ is $3v$,then the speed of satellite $B$ is:

The relay satellite transmits the television signals continuously from one part of the world to another because its

If the gravitational force between two objects were proportional to $\frac{1}{R}$ (and not as $\frac{1}{R^2}$) where $R$ is the separation between them,then a particle in a circular orbit under such a force would have its orbital speed $v$ proportional to

The International Space Station is maintained in a nearly circular orbit with a mean altitude of $330 \, km$ and a maximum of $410 \, km$. An astronaut is floating in the space station's cabin. The acceleration of the astronaut as measured from the Earth is: