An astronaut orbiting the Earth in a circular orbit $120 \ km$ above the surface of the Earth,gently drops a spoon out of the spaceship. The spoon will

Consider a binary star system of star $A$ and star $B$ with masses $m_{A}$ and $m_{B}$ revolving in a circular orbit of radii $r_{A}$ and $r_{B}$,respectively. If $T_{A}$ and $T_{B}$ are the time periods of star $A$ and star $B$,respectively,then -

$A$ satellite of mass $m$ is launched vertically upwards with an initial speed $u$ from the surface of the earth. After it reaches height $R$ ($R =$ radius of the earth), it ejects a rocket of mass $\frac{m}{10}$ so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is ($G$ is the gravitational constant, $M$ is the mass of the earth).

$A$ geostationary satellite above the equator is orbiting around the earth at a fixed distance $r_1$ from the center of the earth. $A$ second satellite is orbiting in the equatorial plane in the opposite direction to the earth's rotation,at a distance $r_2$ from the center of the earth,such that $r_1 = 1.21 r_2$. The time period of the second satellite as measured from the geostationary satellite is $\frac{24}{p}$ hours. The value of $p$ is $....$

If $L$ is the angular momentum of a satellite revolving around the Earth in a circular orbit of radius $r$ with speed $v$,then .........

$A$ satellite revolves in the geostationary orbit but in a direction east to west. The time interval between its successive passing above a point on the equator is ........ $hrs$.