$($a$)$ Explain the concept of ablative cooling and its application to solid$-$fuelled

rockets, giving examples of ablative materials suitable for $($i$)$ nozzles and

$($ii$)$ seals.

$($b$)$ The International Space Station has a mass of $420{10}^{3}kg$ and orbits

at a speed of $7\mathrm{.}6km{s}^{-1}$ relative to the Earth. A change in speed of

$V=3m{s}^{-1}$ is required to boost the altitude of the station, and a

solid$-$fuelled rocket motor is to be used. Using the data in the Table $2$

below, and assuming negligible casing mass and constant burning rate

exponent, calculate:

i$.$ The mass of propellant required to achieve this velocity change, as$-$

suming $V=v_{e}ln(\frac{M_0}{M_f}),$ where $M_0$ is the initial mass and $M_f$

is the final mass of the spacecraft.

ii$.$ The burning rate of propellant in $mm{s}^{-1}.$

iii. The chamber pressure during the burn, in $Pa.$

Table $2$: Data for Q$4.$

$($c$)$ What is meant by a plateau burning propellant? Can plateau burning

characteristics be achieved in practice?