The time period of a satellite of earth is $5$ hours. If the separation between the earth and the satellite is increased to four times the previous value, the new time period will become ......... $hours$
A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant $(a)$ linear speed, $(b)$ angular speed, $(c)$ angular momentum, $(d)$ kinetic energy, $(e)$ potential energy, $(f)$ total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.
The time period of a geostationary satellite is $24\; \mathrm{h}$, at a helght $6 \mathrm{R}_{\mathrm{E}}( \mathrm{R}_{\mathrm{E}}$ is radius of earth) from surface of earth. The time period of another satellite whose helght is $2.5 \mathrm{R}_{\mathrm{E}}$ from surface will be
A planet orbits in an elliptical path of eccentricity $e$ around a massive star considered fixed at one of the foci. The point in space, where it is closest to the star is denoted by $P$ and the point, where it is farthest is denoted by $A$. Let $v_P$ and $v_A$ be the respective speeds at $P$ and $A$, then
If the earth is at one-fourth of its present distance from the sun, the duration of the year will be