List of top Physics Questions on Orbital Mechanics

A particle of mass \(m\), and angular momentum \(\ell\) is moving in a circular orbit of radius \(r_0\) under the influence of an attractive force \(\vec{F}(r) = -\frac{k}{r^2}\hat{r}\). Keeping its angular momentum unchanged, the particle is displaced radially by a small distance \(\delta r \ll r_0\), due to which its radial distance varies periodically. The corresponding time period is:
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 ___
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 ___
The orbital velocity of a body near the surface of a planet 'A' is equal to escape velocity of a body from the planet 'B'. If the masses of planets A and B are same, the ratio of their radii is:
A planet is in a highly eccentric orbit about a star. The distance of its closest approach is 300 times smaller than its farthest distance from the star. If the corresponding speeds are \( v_c \) and \( v_f \), then \( \frac{v_c}{v_f} \) is: