The planet $\mathrm{A}$ and $\mathrm{B}$ have the same density and star $\mathrm{A}$ is $27 \mathrm{time}$ more massive than star $\mathrm{B}$ mass of the planet $\mathbf{B}$. Calculate the ratio of gravitational field strength on the planet $\mathrm{A}$ to that on planet $\mathrm{B}$.

A star explodes and loses half its mass. Its radius becomes half as large. Determine the new gravitational field strength on the surface of the star in terms of the original one

The diagram shows point $\mathrm{P}$ is halfway between the centres of two equal spherical masses that are separated by a distance of $2\times {10}^9\mathrm{m}$ Calculate the gravitational field strength at a point $\mathrm{P}$ and state the direction of the gravitational field strength at point $\mathrm{Q}$.

A satellite orbits the earth above the equator with a period equal to $24 \mathrm{hrs}.$ Determine the height of the satellite above the earth.

[$\mathrm{G}=\left(6.67 {\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}\right)$]

The Hubble Space Telescope is in the orbit around the earth at a height of $560 \mathrm{km}$ above the earth's surface Calculate the Hubble's speed.

$\left[\mathrm{G}=6.67 {\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}\right]$

In a servicing mission, a space shuttle spotted the Hubble telescope a distance of $10 \mathrm{km}$. Estimate how long it took the shuttle to catch up with the Hubble, assuming that the Shuttle was moving in a circular orbit just $500 \mathrm{m}$ below Hubble's orbit of $560 \mathrm{km}$.

$\left[\mathrm{G}=6.67\times {10}^{-11}{\mathrm{m}}^3{\mathrm{kg}}^{-1}{\mathrm{s}}^{-2}\right]$