The orbital velocity of an artificial satellite in a circular orbit just above the Earth's surface is $v$. For a satellite orbiting at an altitude of half of the Earth's radius,the orbital velocity is

The orbit of a geo-stationary satellite is circular. The time period of the satellite depends on:
$(i)$ mass of the satellite
(ii) mass of the earth
(iii) radius of the orbit
(iv) height of the satellite from the surface of the earth
Which of the following is correct?

The speed of a satellite in a circular orbit of radius $R_0$ around the earth is $v_0$. Another satellite is in an elliptic orbit around the earth. If the minimum and maximum speeds of the second satellite are $\alpha v_0$ and $\beta v_0$ respectively,then its time period is

$A$ body is dropped from a satellite in a parking orbit. Which of the following describes its behaviour correctly?

$A$ satellite is revolving very close to a planet of density $\rho$. The period of revolution of the satellite is

$A$ planet is revolving around the sun in an elliptical orbit. Its closest distance from the sun is $r_{min}$,and the farthest distance from the sun is $r_{max}$. If the orbital angular velocity of the planet when it is nearest to the sun is $\omega$,then the orbital angular velocity at the point when it is at the farthest distance from the sun is: